/[escript]/trunk/escript/py_src/linearPDEs.py
ViewVC logotype

Diff of /trunk/escript/py_src/linearPDEs.py

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

trunk/esys2/escript/py_src/linearPDEs.py revision 122 by jgs, Thu Jun 9 05:38:05 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1809 by ksteube, Thu Sep 25 06:43:44 2008 UTC
# Line 1  Line 1 
 # $Id$  
1    
2  ## @file linearPDEs.py  ########################################################
3    #
4    # Copyright (c) 2003-2008 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7    #
8    # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11    #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
24    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
25    solver capabilities in itself but hands the PDE over to
26    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
27    The general interface is provided through the L{LinearPDE} class. The
28    L{AdvectivePDE} which is derived from the L{LinearPDE} class
29    provides an interface to PDE dominated by its advective terms. The L{Poisson},
30    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
31    classs which are also derived form the L{LinearPDE} class should be used
32    to define of solve these sepecial PDEs.
33    
34    @var __author__: name of author
35    @var __copyright__: copyrights
36    @var __license__: licence agreement
37    @var __url__: url entry point on documentation
38    @var __version__: version
39    @var __date__: date of the version
40  """  """
41    
42    import math
43  import escript  import escript
44  import util  import util
45  import numarray  import numarray
46    
47    __author__="Lutz Gross, l.gross@uq.edu.au"
48    
49    
50  def _CompTuple2(t1,t2):  class IllegalCoefficient(ValueError):
51       """
52       raised if an illegal coefficient of the general ar particular PDE is requested.
53     """     """
54     Compare two tuples     pass
55    
56     \param t1 The first tuple  class IllegalCoefficientValue(ValueError):
    \param t2 The second tuple  
57     """     """
58       raised if an incorrect value for a coefficient is used.
59       """
60       pass
61    
62     dif=t1[0]+t1[1]-(t2[0]+t2[1])  class IllegalCoefficientFunctionSpace(ValueError):
63     if dif<0: return 1     """
64     elif dif>0: return -1     raised if an incorrect function space for a coefficient is used.
65     else: return 0     """
   
 def ELMAN_RAMAGE(P):  
     return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
   
 def SIMPLIFIED_BROOK_HUGHES(P):  
     c=(P-3.).whereNegative()  
     return P/6.*c+1./2.*(1.-c)  
66    
67  def HALF(P):  class UndefinedPDEError(ValueError):
68      return escript.Scalar(0.5,P.getFunctionSpace())     """
69       raised if a PDE is not fully defined yet.
70       """
71       pass
72    
73  class PDECoefficient:  class PDECoefficient(object):
74      """      """
75      A class for PDE coefficients      A class for describing a PDE coefficient
76    
77        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
78        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
79        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
80        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
81        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
82        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
83        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
84        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
85        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
86        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
87        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
88        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
89        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
90        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
91    
92      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
93      INTERIOR=0      INTERIOR=0
94      BOUNDARY=1      BOUNDARY=1
95      CONTACT=2      CONTACT=2
96      CONTINUOUS=3      SOLUTION=3
97      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
98      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
99      # number of unknowns.      BY_SOLUTION=6
100      EQUATION=3      BY_DIM=7
101      SOLUTION=4      OPERATOR=10
102      DIM=5      RIGHTHANDSIDE=11
103      # indicator for what is altered if the coefficient is altered:      BOTH=12
104      OPERATOR=5      INTERIOR_REDUCED=13
105      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
106      BOTH=7      CONTACT_REDUCED=15
107      def __init__(self,where,pattern,altering):  
108        def __init__(self, where, pattern, altering):
109         """         """
110         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
111    
112           @param where: describes where the coefficient lives
113           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
114                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
115           @param pattern: describes the shape of the coefficient and how the shape is build for a given
116                  spatial dimension and numbers of equation and solution in then PDE. For instance,
117                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
118                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
119                  on a 2-dimensional domain. In the case of single equation and a single solution component
120                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
121                  the example would be read as (2,).
122           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
123           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
124           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
125           @param reduced: indicates if reduced
126           @type reduced: C{bool}
127         """         """
128           super(PDECoefficient, self).__init__()
129         self.what=where         self.what=where
130         self.pattern=pattern         self.pattern=pattern
131         self.altering=altering         self.altering=altering
# Line 68  class PDECoefficient: Line 137  class PDECoefficient:
137         """         """
138         self.value=escript.Data()         self.value=escript.Data()
139    
140      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
141         """         """
142         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
143    
144         @param domain:         @param domain: domain on which the PDE uses the coefficient
145         """         @type domain: L{Domain<escript.Domain>}
146         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
147         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
148         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
149         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
150           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
151           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
152           """
153           if self.what==self.INTERIOR:
154                return escript.Function(domain)
155           elif self.what==self.INTERIOR_REDUCED:
156                return escript.ReducedFunction(domain)
157           elif self.what==self.BOUNDARY:
158                return escript.FunctionOnBoundary(domain)
159           elif self.what==self.BOUNDARY_REDUCED:
160                return escript.ReducedFunctionOnBoundary(domain)
161           elif self.what==self.CONTACT:
162                return escript.FunctionOnContactZero(domain)
163           elif self.what==self.CONTACT_REDUCED:
164                return escript.ReducedFunctionOnContactZero(domain)
165           elif self.what==self.SOLUTION:
166                if reducedEquationOrder and reducedSolutionOrder:
167                    return escript.ReducedSolution(domain)
168                else:
169                    return escript.Solution(domain)
170           elif self.what==self.REDUCED:
171                return escript.ReducedSolution(domain)
172    
173      def getValue(self):      def getValue(self):
174         """         """
175         returns the value of the coefficient:         returns the value of the coefficient
176    
177           @return:  value of the coefficient
178           @rtype:  L{Data<escript.Data>}
179         """         """
180         return self.value         return self.value
181        
182      def setValue(self,newValue):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
        """  
        set the value of the coefficient to new value  
183         """         """
184           set the value of the coefficient to a new value
185    
186           @param domain: domain on which the PDE uses the coefficient
187           @type domain: L{Domain<escript.Domain>}
188           @param numEquations: number of equations of the PDE
189           @type numEquations: C{int}
190           @param numSolutions: number of components of the PDE solution
191           @type numSolutions: C{int}
192           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
193           @type reducedEquationOrder: C{bool}
194           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
195           @type reducedSolutionOrder: C{bool}
196           @param newValue: number of components of the PDE solution
197           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
198           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
199           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
200           """
201           if newValue==None:
202               newValue=escript.Data()
203           elif isinstance(newValue,escript.Data):
204               if not newValue.isEmpty():
205                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
206                    try:
207                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
208                    except:
209                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
210           else:
211               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
212           if not newValue.isEmpty():
213               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
214                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
215         self.value=newValue         self.value=newValue
216        
217      def isAlteringOperator(self):      def isAlteringOperator(self):
218          """          """
219      return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
220    
221            @return:  True if the operator of the PDE is changed when the coefficient is changed
222            @rtype:  C{bool}
223      """      """
224          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
225              return not None              return not None
# Line 102  class PDECoefficient: Line 228  class PDECoefficient:
228    
229      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
230          """          """
231      return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
232    
233        @rtype:  C{bool}
234            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
235      """      """
236          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
237              return not None              return not None
238          else:          else:
239              return None              return None
240    
241      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
242         """         """
243         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
244    
245         @param shape:         @param domain: domain on which the PDE uses the coefficient
246         @param dim:         @type domain: L{Domain<escript.Domain>}
247           @param shape: suggested shape of the coefficient
248           @type shape: C{tuple} of C{int} values
249           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
250                     If no appropriate numbers could be identified, C{None} is returned
251           @rtype: C{tuple} of two C{int} values or C{None}
252         """         """
253           dim=domain.getDim()
254         if len(shape)>0:         if len(shape)>0:
255             num=max(shape)+1             num=max(shape)+1
256         else:         else:
257             num=1             num=1
258         search=[]         search=[]
259         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
260            for e in range(num):            for u in range(num):
261               search.append((e,u))               for e in range(num):
262         search.sort(_CompTuple2)                  search.append((e,u))
263         for item in search:            search.sort(self.__CompTuple2)
264               s=self.buildShape(item[0],item[1],dim)            for item in search:
265                 s=self.getShape(domain,item[0],item[1])
266               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
267                   return (1,1)                   return (1,1)
268               else:               else:
269                   if s==shape: return item                   if s==shape: return item
270           elif self.definesNumEquation():
271              for e in range(num,0,-1):
272                 s=self.getShape(domain,e,0)
273                 if len(s)==0 and len(shape)==0:
274                     return (1,None)
275                 else:
276                     if s==shape: return (e,None)
277    
278           elif self.definesNumSolutions():
279              for u in range(num,0,-1):
280                 s=self.getShape(domain,0,u)
281                 if len(s)==0 and len(shape)==0:
282                     return (None,1)
283                 else:
284                     if s==shape: return (None,u)
285         return None         return None
286        def definesNumSolutions(self):
287           """
288           checks if the coefficient allows to estimate the number of solution components
289    
290      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
291          """         @rtype: C{bool}
292      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
293           for i in self.pattern:
294                 if i==self.BY_SOLUTION: return True
295           return False
296    
297      @param e:      def definesNumEquation(self):
298      @param u:         """
299      @param dim:         checks if the coefficient allows to estimate the number of equations
300      """  
301          s=()         @return: True if the coefficient allows an estimate of the number of equations
302          for i in self.pattern:         @rtype: C{bool}
303               if i==self.EQUATION:         """
304                  if e>1: s=s+(e,)         for i in self.pattern:
305               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
306                  if u>1: s=s+(u,)         return False
307    
308        def __CompTuple2(self,t1,t2):
309          """
310          Compare two tuples of possible number of equations and number of solutions
311    
312          @param t1: The first tuple
313          @param t2: The second tuple
314    
315          """
316    
317          dif=t1[0]+t1[1]-(t2[0]+t2[1])
318          if dif<0: return 1
319          elif dif>0: return -1
320          else: return 0
321    
322        def getShape(self,domain,numEquations=1,numSolutions=1):
323           """
324           builds the required shape of the coefficient
325    
326           @param domain: domain on which the PDE uses the coefficient
327           @type domain: L{Domain<escript.Domain>}
328           @param numEquations: number of equations of the PDE
329           @type numEquations: C{int}
330           @param numSolutions: number of components of the PDE solution
331           @type numSolutions: C{int}
332           @return: shape of the coefficient
333           @rtype: C{tuple} of C{int} values
334           """
335           dim=domain.getDim()
336           s=()
337           for i in self.pattern:
338                 if i==self.BY_EQUATION:
339                    if numEquations>1: s=s+(numEquations,)
340                 elif i==self.BY_SOLUTION:
341                    if numSolutions>1: s=s+(numSolutions,)
342               else:               else:
343                  s=s+(dim,)                  s=s+(dim,)
344          return s         return s
345    
346  class LinearPDE:  class LinearPDE(object):
347     """     """
348     Class to handle a linear PDE     This class is used to define a general linear, steady, second order PDE
349         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
350    
351     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
352    
353     with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
354    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
355    
356     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
357       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
358       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
359       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
360       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
361       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
362       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
363    
364     \f[     The following natural boundary conditions are considered:
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
365    
366     and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
367    
368     \f[     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
369    
    """  
    TOL=1.e-13  
    DEFAULT_METHOD=util.DEFAULT_METHOD  
    DIRECT=util.DIRECT  
    CHOLEVSKY=util.CHOLEVSKY  
    PCG=util.PCG  
    CR=util.CR  
    CGS=util.CGS  
    BICGSTAB=util.BICGSTAB  
    SSOR=util.SSOR  
    GMRES=util.GMRES  
    PRES20=util.PRES20  
    ILU0=util.ILU0  
    JACOBI=util.JACOBI  
370    
371     def __init__(self,domain,numEquations=0,numSolutions=0):     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
      """  
      initializes a new linear PDE.  
372    
373       @param args:     M{u=r}  where M{q>0}
374       """  
375       # COEFFICIENTS can be overwritten by subclasses:     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
376       self.COEFFICIENTS={     The constraints override any other condition set by the PDE or the boundary condition.
377         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
378         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The PDE is symmetrical if
379         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
380         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
381         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
382         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     For a system of PDEs and a solution with several components the PDE has the form
383         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
384         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
385         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
386         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
387         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     The natural boundary conditions take the form:
388         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
389       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
390    
391    
392       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
393    
394       Constraints take the form
395    
396       M{u[i]=r[i]}  where  M{q[i]>0}
397    
398       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
399    
400       The system of PDEs is symmetrical if
401    
402            - M{A[i,j,k,l]=A[k,l,i,j]}
403            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
404            - M{B[i,j,k]=C[k,i,j]}
405            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
406            - M{D[i,k]=D[i,k]}
407            - M{D_reduced[i,k]=D_reduced[i,k]}
408            - M{d[i,k]=d[k,i]}
409            - M{d_reduced[i,k]=d_reduced[k,i]}
410    
411       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
412       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
413       defined as
414    
415       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
416    
417       For the case of single solution component and single PDE M{J} is defined
418    
419       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
420    
421       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
422       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
423       the contact condition takes the form
424    
425       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
426    
427       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
428       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
429       L{jump<util.jump>}.
430       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
431       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
432       In case of a single PDE and a single component solution the contact condition takes the form
433    
434       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
435    
436       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
437    
438       @cvar DEFAULT: The default method used to solve the system of linear equations
439       @cvar DIRECT: The direct solver based on LDU factorization
440       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
441       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
442       @cvar CR: The conjugate residual method
443       @cvar CGS: The conjugate gardient square method
444       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
445       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
446       @cvar MINRES: Minimum residual method.
447       @cvar SSOR: The symmetric overrealaxtion method
448       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449       @cvar ILUT: The incomplete LU factorization preconditioner with will in
450       @cvar JACOBI: The Jacobi preconditioner
451       @cvar GMRES: The Gram-Schmidt minimum residual method
452       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
453       @cvar LUMPING: Matrix lumping.
454       @cvar NO_REORDERING: No matrix reordering allowed
455       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
456       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
457       @cvar PASO: PASO solver package
458       @cvar SCSL: SGI SCSL solver library
459       @cvar MKL: Intel's MKL solver library
460       @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462       @cvar ITERATIVE: The default iterative solver
463       @cvar AMG: algebraic multi grid
464       @cvar RILU: recursive ILU
465    
466       """
467       DEFAULT= 0
468       DIRECT= 1
469       CHOLEVSKY= 2
470       PCG= 3
471       CR= 4
472       CGS= 5
473       BICGSTAB= 6
474       SSOR= 7
475       ILU0= 8
476       ILUT= 9
477       JACOBI= 10
478       GMRES= 11
479       PRES20= 12
480       LUMPING= 13
481       NO_REORDERING= 17
482       MINIMUM_FILL_IN= 18
483       NESTED_DISSECTION= 19
484       SCSL= 14
485       MKL= 15
486       UMFPACK= 16
487       ITERATIVE= 20
488       PASO= 21
489       AMG= 22
490       RILU = 23
491       TRILINOS = 24
492       NONLINEAR_GMRES = 25
493       TFQMR = 26
494       MINRES = 27
495    
496       SMALL_TOLERANCE=1.e-13
497       __PACKAGE_KEY="package"
498       __METHOD_KEY="method"
499       __SYMMETRY_KEY="symmetric"
500       __TOLERANCE_KEY="tolerance"
501       __PRECONDITIONER_KEY="preconditioner"
502    
503    
504       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
505         """
506         initializes a new linear PDE
507    
508         @param domain: domain of the PDE
509         @type domain: L{Domain<escript.Domain>}
510         @param numEquations: number of equations. If numEquations==None the number of equations
511                              is exracted from the PDE coefficients.
512         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
513                              is exracted from the PDE coefficients.
514         @param debug: if True debug informations are printed.
515    
516         """
517         super(LinearPDE, self).__init__()
518         #
519         #   the coefficients of the general PDE:
520         #
521         self.__COEFFICIENTS_OF_GENEARL_PDE={
522           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
523           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
524           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
525           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
527           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
537           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
543           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
544    
545         # COEFFICIENTS can be overwritten by subclasses:
546         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
547         self.__altered_coefficients=False
548       # initialize attributes       # initialize attributes
549       self.__debug=None       self.__debug=debug
550       self.__domain=domain       self.__domain=domain
551       self.__numEquations=numEquations       self.__numEquations=numEquations
552       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
553       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
554    
555       # set some default values:       # set some default values:
556       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
557       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
558       self.__tolerance=1.e-8       self.__tolerance=1.e-8
559       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
560       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
561         self.__preconditioner=self.DEFAULT
562         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
563       self.__sym=False       self.__sym=False
      self.__lumping=False  
564    
565     def createCoefficient(self, name):       self.resetCoefficients()
566         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
567       # =============================================================================
568       #    general stuff:
569       # =============================================================================
570       def __str__(self):
571         """
572         returns string representation of the PDE
573    
574         @return: a simple representation of the PDE
575         @rtype: C{str}
576         """
577         return "<LinearPDE %d>"%id(self)
578       # =============================================================================
579       #    debug :
580       # =============================================================================
581       def setDebugOn(self):
582       """       """
583       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
584       """       """
585       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
   
    def __del__(self):  
      pass  
586    
587     def getCoefficient(self,name):     def setDebugOff(self):
588         """
589         switches off debugging
590       """       """
591       return the value of the parameter name       self.__debug=None
592    
593       @param name:     def trace(self,text):
594         """
595         print the text message if debugging is swiched on.
596         @param text: message
597         @type text: C{string}
598       """       """
599       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
600    
601     def getCoefficientOfPDE(self,name):     # =============================================================================
602       # some service functions:
603       # =============================================================================
604       def getDomain(self):
605       """       """
606       return the value of the coefficient name of the general PDE.       returns the domain of the PDE
      This method is called by the assembling routine it can be  
      overwritten to map coefficients of a particualr PDE to the general PDE.  
607    
608       @param name:       @return: the domain of the PDE
609         @rtype: L{Domain<escript.Domain>}
610       """       """
611       return self.getCoefficient(name)       return self.__domain
612    
613     def hasCoefficient(self,name):     def getDim(self):
614        """       """
615        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
616    
617        @param name:       @return: the spatial dimension of the PDE domain
618        """       @rtype: C{int}
619        return self.COEFFICIENTS.has_key(name)       """
620         return self.getDomain().getDim()
621    
622     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
623       """       """
624       return true if the test functions should use reduced order       returns the number of equations
625    
626         @return: the number of equations
627         @rtype: C{int}
628         @raise UndefinedPDEError: if the number of equations is not be specified yet.
629       """       """
630       return self.__row_function_space       if self.__numEquations==None:
631             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
632         else:
633             return self.__numEquations
634    
635     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
636       """       """
637       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
638    
639         @return: the number of unknowns
640         @rtype: C{int}
641         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
642       """       """
643       return self.__column_function_space       if self.__numSolutions==None:
644            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
645         else:
646            return self.__numSolutions
647    
648     def setValue(self,**coefficients):     def reduceEquationOrder(self):
649        """       """
650        sets new values to coefficients       return status for order reduction for equation
651    
652        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
653        """       @rtype: L{bool}
654        self.__setValue(**coefficients)       """
655               return self.__reduce_equation_order
656    
657     def cleanCoefficients(self):     def reduceSolutionOrder(self):
658       """       """
659       resets all coefficients to default values.       return status for order reduction for the solution
660    
661         @return: return True is reduced interpolation order is used for the represenation of the solution
662         @rtype: L{bool}
663       """       """
664       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
665    
666     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
667       """       """
668       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
669    
670         @return: representation space of equation
671         @rtype: L{FunctionSpace<escript.FunctionSpace>}
672       """       """
673       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
674                   return escript.ReducedSolution(self.getDomain())
675         else:
676             return escript.Solution(self.getDomain())
677    
678     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
679       """       """
680       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
681    
682       @param name:       @return: representation space of solution
683         @rtype: L{FunctionSpace<escript.FunctionSpace>}
684       """       """
685       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
686          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
687       else:       else:
688          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
689    
690     def getFunctionSpaceForCoefficient(self,name):  
691       def getOperator(self):
692       """       """
693       return the atoms of the coefficient name       provides access to the operator of the PDE
694    
695       @param name:       @return: the operator of the PDE
696         @rtype: L{Operator<escript.Operator>}
697       """       """
698       if self.hasCoefficient(name):       m=self.getSystem()[0]
699          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
700             return self.copyConstraint(1./m)
701       else:       else:
702          raise ValueError,"Solution coefficient %s requested"%name           return m
703    
704     def alteredCoefficient(self,name):     def getRightHandSide(self):
705       """       """
706       announce that coefficient name has been changed       provides access to the right hand side of the PDE
707         @return: the right hand side of the PDE
708         @rtype: L{Data<escript.Data>}
709         """
710         r=self.getSystem()[1]
711         if self.isUsingLumping():
712             return self.copyConstraint(r)
713         else:
714             return r
715    
716       @param name:     def applyOperator(self,u=None):
717       """       """
718       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
719          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
720          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
721                   the current solution is used.
722         @type u: L{Data<escript.Data>} or None
723         @return: image of u
724         @rtype: L{Data<escript.Data>}
725         """
726         if u==None:
727            return self.getOperator()*self.getSolution()
728       else:       else:
729          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
730    
731     # ===== debug ==============================================================     def getResidual(self,u=None):
732     def setDebugOn(self):       """
733         """       return the residual of u or the current solution if u is not present.
734    
735         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
736                   the current solution is used.
737         @type u: L{Data<escript.Data>} or None
738         @return: residual of u
739         @rtype: L{Data<escript.Data>}
740         """
741         return self.applyOperator(u)-self.getRightHandSide()
742    
743       def checkSymmetry(self,verbose=True):
744          """
745          test the PDE for symmetry.
746    
747          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
748          @type verbose: C{bool}
749          @return:  True if the PDE is symmetric.
750          @rtype: L{Data<escript.Data>}
751          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
752          """
753          verbose=verbose or self.__debug
754          out=True
755          if self.getNumSolutions()!=self.getNumEquations():
756             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
757             out=False
758          else:
759             A=self.getCoefficientOfGeneralPDE("A")
760             if not A.isEmpty():
761                tol=util.Lsup(A)*self.SMALL_TOLERANCE
762                if self.getNumSolutions()>1:
763                   for i in range(self.getNumEquations()):
764                      for j in range(self.getDim()):
765                         for k in range(self.getNumSolutions()):
766                            for l in range(self.getDim()):
767                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
768                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
769                                   out=False
770                else:
771                   for j in range(self.getDim()):
772                      for l in range(self.getDim()):
773                         if util.Lsup(A[j,l]-A[l,j])>tol:
774                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
775                            out=False
776             B=self.getCoefficientOfGeneralPDE("B")
777             C=self.getCoefficientOfGeneralPDE("C")
778             if B.isEmpty() and not C.isEmpty():
779                if verbose: print "non-symmetric PDE because B is not present but C is"
780                out=False
781             elif not B.isEmpty() and C.isEmpty():
782                if verbose: print "non-symmetric PDE because C is not present but B is"
783                out=False
784             elif not B.isEmpty() and not C.isEmpty():
785                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
786                if self.getNumSolutions()>1:
787                   for i in range(self.getNumEquations()):
788                       for j in range(self.getDim()):
789                          for k in range(self.getNumSolutions()):
790                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
791                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
792                                  out=False
793                else:
794                   for j in range(self.getDim()):
795                      if util.Lsup(B[j]-C[j])>tol:
796                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
797                         out=False
798             if self.getNumSolutions()>1:
799               D=self.getCoefficientOfGeneralPDE("D")
800               if not D.isEmpty():
801                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
802                 for i in range(self.getNumEquations()):
803                    for k in range(self.getNumSolutions()):
804                      if util.Lsup(D[i,k]-D[k,i])>tol:
805                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
806                          out=False
807               d=self.getCoefficientOfGeneralPDE("d")
808               if not d.isEmpty():
809                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
810                 for i in range(self.getNumEquations()):
811                    for k in range(self.getNumSolutions()):
812                      if util.Lsup(d[i,k]-d[k,i])>tol:
813                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
814                          out=False
815               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
816               if not d_contact.isEmpty():
817                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
818                 for i in range(self.getNumEquations()):
819                    for k in range(self.getNumSolutions()):
820                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
821                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
822                          out=False
823             # and now the reduced coefficients
824             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
825             if not A_reduced.isEmpty():
826                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
827                if self.getNumSolutions()>1:
828                   for i in range(self.getNumEquations()):
829                      for j in range(self.getDim()):
830                         for k in range(self.getNumSolutions()):
831                            for l in range(self.getDim()):
832                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
833                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
834                                   out=False
835                else:
836                   for j in range(self.getDim()):
837                      for l in range(self.getDim()):
838                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
839                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
840                            out=False
841             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
842             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
843             if B_reduced.isEmpty() and not C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
850                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
851                if self.getNumSolutions()>1:
852                   for i in range(self.getNumEquations()):
853                       for j in range(self.getDim()):
854                          for k in range(self.getNumSolutions()):
855                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
856                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
857                                  out=False
858                else:
859                   for j in range(self.getDim()):
860                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
861                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
862                         out=False
863             if self.getNumSolutions()>1:
864               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
865               if not D_reduced.isEmpty():
866                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
867                 for i in range(self.getNumEquations()):
868                    for k in range(self.getNumSolutions()):
869                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
870                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
871                          out=False
872               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
873               if not d_reduced.isEmpty():
874                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
875                 for i in range(self.getNumEquations()):
876                    for k in range(self.getNumSolutions()):
877                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
878                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
879                          out=False
880               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
881               if not d_contact_reduced.isEmpty():
882                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
883                 for i in range(self.getNumEquations()):
884                    for k in range(self.getNumSolutions()):
885                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
886                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
887                          out=False
888          return out
889    
890       def getSolution(self,**options):
891         """         """
892         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
893    
894     def setDebugOff(self):         @return: the solution
895           @rtype: L{Data<escript.Data>}
896           @param options: solver options
897           @keyword verbose: True to get some information during PDE solution
898           @type verbose: C{bool}
899           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
900                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
901           @keyword iter_max: maximum number of iteration steps allowed.
902           @keyword drop_tolerance: threshold for drupping in L{ILUT}
903           @keyword drop_storage: maximum of allowed memory in L{ILUT}
904           @keyword truncation: maximum number of residuals in L{GMRES}
905           @keyword restart: restart cycle length in L{GMRES}
906         """         """
907           if not self.__solution_isValid:
908              mat,f=self.getSystem()
909              if self.isUsingLumping():
910                 self.__solution=self.copyConstraint(f*mat)
911              else:
912                 options[self.__TOLERANCE_KEY]=self.getTolerance()
913                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
914                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
915                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
916                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
917                 self.trace("PDE is resolved.")
918                 self.trace("solver options: %s"%str(options))
919                 self.__solution=mat.solve(f,options)
920              self.__solution_isValid=True
921           return self.__solution
922    
923       def getFlux(self,u=None):
924         """
925         returns the flux M{J} for a given M{u}
926    
927         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
928    
929         or
930    
931         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
932    
933         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
934         @type u: L{Data<escript.Data>} or None
935         @return: flux
936         @rtype: L{Data<escript.Data>}
937         """
938         if u==None: u=self.getSolution()
939         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X") \
942               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X_reduced")
945       # =============================================================================
946       #   solver settings:
947       # =============================================================================
948       def setSolverMethod(self,solver=None,preconditioner=None):
949         """         """
950         self.__debug=None         sets a new solver
951    
952     def debug(self):         @param solver: sets a new solver method.
953           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
954           @param preconditioner: sets a new solver method.
955           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
956           """
957           if solver==None: solver=self.__solver_method
958           if preconditioner==None: preconditioner=self.__preconditioner
959           if solver==None: solver=self.DEFAULT
960           if preconditioner==None: preconditioner=self.DEFAULT
961           if not (solver,preconditioner)==self.getSolverMethod():
962               self.__solver_method=solver
963               self.__preconditioner=preconditioner
964               self.__checkMatrixType()
965               self.trace("New solver is %s"%self.getSolverMethodName())
966    
967       def getSolverMethodName(self):
968         """         """
969         returns true if the PDE is in the debug mode         returns the name of the solver currently used
970    
971           @return: the name of the solver currently used.
972           @rtype: C{string}
973         """         """
        return self.__debug  
974    
975     #===== Lumping ===========================         m=self.getSolverMethod()
976     def setLumpingOn(self):         p=self.getSolverPackage()
977        """         method=""
978        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
979        """         elif m[0]==self.DIRECT: method= "DIRECT"
980        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
981           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
982           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
983           self.__lumping=True         elif m[0]==self.TFQMR: method= "TFQMR"
984           elif m[0]==self.MINRES: method= "MINRES"
985           elif m[0]==self.CR: method= "CR"
986           elif m[0]==self.CGS: method= "CGS"
987           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
988           elif m[0]==self.SSOR: method= "SSOR"
989           elif m[0]==self.GMRES: method= "GMRES"
990           elif m[0]==self.PRES20: method= "PRES20"
991           elif m[0]==self.LUMPING: method= "LUMPING"
992           elif m[0]==self.AMG: method= "AMG"
993           if m[1]==self.DEFAULT: method+="+DEFAULT"
994           elif m[1]==self.JACOBI: method+= "+JACOBI"
995           elif m[1]==self.ILU0: method+= "+ILU0"
996           elif m[1]==self.ILUT: method+= "+ILUT"
997           elif m[1]==self.SSOR: method+= "+SSOR"
998           elif m[1]==self.AMG: method+= "+AMG"
999           elif m[1]==self.RILU: method+= "+RILU"
1000           if p==self.DEFAULT: package="DEFAULT"
1001           elif p==self.PASO: package= "PASO"
1002           elif p==self.MKL: package= "MKL"
1003           elif p==self.SCSL: package= "SCSL"
1004           elif p==self.UMFPACK: package= "UMFPACK"
1005           elif p==self.TRILINOS: package= "TRILINOS"
1006           else : method="unknown"
1007           return "%s solver of %s package"%(method,package)
1008    
    def setLumpingOff(self):  
       """  
       switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
1009    
1010     def setLumping(self,flag=False):     def getSolverMethod(self):
1011        """         """
1012        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
1013    
1014     def isUsingLumping(self):         @return: the solver method currently be used.
1015        """         @rtype: C{int}
1016                 """
1017        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
1018    
1019     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
1020         """         """
1021         sets a new solver         sets a new solver package
1022    
1023           @param package: sets a new solver method.
1024           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1025         """         """
1026         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1027             self.__solver_method=solver         if not package==self.getSolverPackage():
1028             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1029             self.__checkMatrixType()             self.__checkMatrixType()
1030               self.trace("New solver is %s"%self.getSolverMethodName())
1031    
1032     def getSolverMethod(self):     def getSolverPackage(self):
1033         """         """
1034         returns the solver method         returns the package of the solver
1035    
1036           @return: the solver package currently being used.
1037           @rtype: C{int}
1038         """         """
1039         return self.__solver_method         return self.__solver_package
1040    
1041       def isUsingLumping(self):
1042          """
1043          checks if matrix lumping is used a solver method
1044    
1045          @return: True is lumping is currently used a solver method.
1046          @rtype: C{bool}
1047          """
1048          return self.getSolverMethod()[0]==self.LUMPING
1049    
    #============ tolerance business =========================================================  
1050     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1051         """         """
1052         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1053    
1054           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1055    
1056           defines the stopping criterion.
1057    
1058           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1059                       the system will be resolved.
1060           @type tol: positive C{float}
1061           @raise ValueError: if tolerance is not positive.
1062         """         """
1063         if not tol>0:         if not tol>0:
1064             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1065         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1066         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1067         self.__tolerance=tol         self.__tolerance=tol
1068         return         return
1069    
1070     def getTolerance(self):     def getTolerance(self):
1071         """         """
1072         returns the tolerance set for the solution         returns the tolerance set for the solution
1073    
1074           @return: tolerance currently used.
1075           @rtype: C{float}
1076         """         """
1077         return self.__tolerance         return self.__tolerance
1078    
1079     #===== symmetry  flag ==========================     # =============================================================================
1080       #    symmetry  flag:
1081       # =============================================================================
1082     def isSymmetric(self):     def isSymmetric(self):
1083        """        """
1084        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1085    
1086          @return: True is a symmetric PDE is indicated, otherwise False is returned
1087          @rtype: C{bool}
1088        """        """
1089        return self.__sym        return self.__sym
1090    
1091     def setSymmetryOn(self):     def setSymmetryOn(self):
1092        """        """
1093        sets the symmetry flag to true        sets the symmetry flag.
1094        """        """
1095        if not self.isSymmetric():        if not self.isSymmetric():
1096           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1097           self.__sym=True           self.__sym=True
1098           self.__checkMatrixType()           self.__checkMatrixType()
1099    
1100     def setSymmetryOff(self):     def setSymmetryOff(self):
1101        """        """
1102        sets the symmetry flag to false        removes the symmetry flag.
1103        """        """
1104        if self.isSymmetric():        if self.isSymmetric():
1105           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1106           self.__sym=False           self.__sym=False
1107           self.__checkMatrixType()           self.__checkMatrixType()
1108    
1109     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1110       """        """
1111       sets the symmetry flag to flag        sets the symmetry flag to flag
1112    
1113       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1114       """        @type flag: C{bool}
1115       if flag:        """
1116          self.setSymmetryOn()        if flag:
1117       else:           self.setSymmetryOn()
1118          self.setSymmetryOff()        else:
1119             self.setSymmetryOff()
1120    
1121     #===== order reduction ==========================     # =============================================================================
1122       # function space handling for the equation as well as the solution
1123       # =============================================================================
1124     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1125       """       """
1126       switches to on reduced order       switches on reduced order for solution and equation representation
1127    
1128         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1129       """       """
1130       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1131       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1132    
1133     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1134       """       """
1135       switches to full order       switches off reduced order for solution and equation representation
1136    
1137         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1138       """       """
1139       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1140       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1141    
1142     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1143       """       """
1144       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1145         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1146       @param flag:                    if flag is not present order reduction is switched off
1147         @type flag: C{bool}
1148         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1149       """       """
1150       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1151       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1152    
1153     #===== order reduction solution ==========================  
1154     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1155       """       """
1156       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1157    
1158         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1159       """       """
1160       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1161       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1162           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1163           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1164           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1165             self.__resetSystem()
1166    
1167     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1168       """       """
1169       switches to full order to interpolate solution       switches off reduced order for solution representation
1170    
1171         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1172       """       """
1173       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1174       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1175           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1176           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1177           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1178             self.__resetSystem()
1179    
1180     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1181       """       """
1182       sets order for test functions according to flag       sets order for test functions according to flag
1183    
1184       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1185                      if flag is not present order reduction is switched off
1186         @type flag: C{bool}
1187         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1188       """       """
1189       if flag:       if flag:
1190          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1191       else:       else:
1192          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1193                                                                                                                                                              
    #===== order reduction equation ==========================  
1194     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1195       """       """
1196       switches to reduced order for test functions       switches on reduced order for equation representation
1197    
1198         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1199       """       """
1200       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1201       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1202           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1203           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1204           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1205             self.__resetSystem()
1206    
1207     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1208       """       """
1209       switches to full order for test functions       switches off reduced order for equation representation
1210    
1211         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1212       """       """
1213       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1214       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1215           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1216           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1217           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1218             self.__resetSystem()
1219    
1220     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1221       """       """
1222       sets order for test functions according to flag       sets order for test functions according to flag
1223    
1224       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1225                      if flag is not present order reduction is switched off
1226         @type flag: C{bool}
1227         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1228       """       """
1229       if flag:       if flag:
1230          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1231       else:       else:
1232          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1233                                                                                                                                                              
1234     # ==== initialization =====================================================================     # =============================================================================
1235       # private method:
1236       # =============================================================================
1237       def __checkMatrixType(self):
1238         """
1239         reassess the matrix type and, if a new matrix is needed, resets the system.
1240         """
1241         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1242         if not new_matrix_type==self.__matrix_type:
1243             self.trace("Matrix type is now %d."%new_matrix_type)
1244             self.__matrix_type=new_matrix_type
1245             self.__resetSystem()
1246       #
1247       #   rebuild switches :
1248       #
1249       def __invalidateSolution(self):
1250           """
1251           indicates the PDE has to be resolved if the solution is requested
1252           """
1253           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1254           self.__solution_isValid=False
1255    
1256       def __invalidateOperator(self):
1257           """
1258           indicates the operator has to be rebuilt next time it is used
1259           """
1260           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1261           self.__invalidateSolution()
1262           self.__operator_is_Valid=False
1263    
1264       def __invalidateRightHandSide(self):
1265           """
1266           indicates the right hand side has to be rebuild next time it is used
1267           """
1268           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1269           self.__invalidateSolution()
1270           self.__righthandside_isValid=False
1271    
1272       def __invalidateSystem(self):
1273           """
1274           annonced that everthing has to be rebuild:
1275           """
1276           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1277           self.__invalidateSolution()
1278           self.__invalidateOperator()
1279           self.__invalidateRightHandSide()
1280    
1281       def __resetSystem(self):
1282           """
1283           annonced that everthing has to be rebuild:
1284           """
1285           self.trace("New System is built from scratch.")
1286           self.__operator=escript.Operator()
1287           self.__operator_is_Valid=False
1288           self.__righthandside=escript.Data()
1289           self.__righthandside_isValid=False
1290           self.__solution=escript.Data()
1291           self.__solution_isValid=False
1292       #
1293       #    system initialization:
1294       #
1295     def __getNewOperator(self):     def __getNewOperator(self):
1296         """         """
1297           returns an instance of a new operator
1298         """         """
1299           self.trace("New operator is allocated.")
1300         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1301                             self.getNumEquations(), \                             self.getNumEquations(), \
1302                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1304  class LinearPDE:
1304                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1305                             self.__matrix_type)                             self.__matrix_type)
1306    
1307     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1308         """         """
1309           returns an instance of a new right hand side
1310         """         """
1311         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1312         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1313             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1314         else:         else:
1315             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1316    
1317     def __getNewSolution(self):     def __getNewSolution(self):
1318         """         """
1319           returns an instance of a new solution
1320         """         """
1321         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1322         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1323             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1324         else:         else:
1325             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1326    
1327       def __makeFreshSolution(self):
1328           """
1329           makes sure that the solution is instantiated and returns it initialized by zeros
1330           """
1331           if self.__solution.isEmpty():
1332               self.__solution=self.__getNewSolution()
1333           else:
1334               self.__solution*=0
1335               self.trace("Solution is reset to zero.")
1336           return self.__solution
1337    
1338       def __makeFreshRightHandSide(self):
1339           """
1340           makes sure that the right hand side is instantiated and returns it initialized by zeros
1341           """
1342           if self.__righthandside.isEmpty():
1343               self.__righthandside=self.__getNewRightHandSide()
1344           else:
1345               self.__righthandside.setToZero()
1346               self.trace("Right hand side is reset to zero.")
1347           return self.__righthandside
1348    
1349     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1350         """         """
1351           makes sure that the operator is instantiated and returns it initialized by zeros
1352         """         """
1353         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1354             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1355         else:         else:
1356             self.__operator.setValue(0.)             self.__operator.resetValues()
1357             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1358         return self.__operator         return self.__operator
1359    
1360     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1361     def getDomain(self):         """
1362           applies the constraints defined by q and r to the system
1363           """
1364           if not self.isUsingLumping():
1365              q=self.getCoefficientOfGeneralPDE("q")
1366              r=self.getCoefficientOfGeneralPDE("r")
1367              if not q.isEmpty() and not self.__operator.isEmpty():
1368                 # q is the row and column mask to indicate where constraints are set:
1369                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1370                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1371                 u=self.__getNewSolution()
1372                 if r.isEmpty():
1373                    r_s=self.__getNewSolution()
1374                 else:
1375                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1376                 u.copyWithMask(r_s,col_q)
1377                 if not self.__righthandside.isEmpty():
1378                    self.__righthandside-=self.__operator*u
1379                    self.__righthandside=self.copyConstraint(self.__righthandside)
1380                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1381       # =============================================================================
1382       # function giving access to coefficients of the general PDE:
1383       # =============================================================================
1384       def getCoefficientOfGeneralPDE(self,name):
1385         """
1386         return the value of the coefficient name of the general PDE.
1387    
1388         @note: This method is called by the assembling routine it can be overwritten
1389               to map coefficients of a particular PDE to the general PDE.
1390         @param name: name of the coefficient requested.
1391         @type name: C{string}
1392         @return: the value of the coefficient  name
1393         @rtype: L{Data<escript.Data>}
1394         @raise IllegalCoefficient: if name is not one of coefficients
1395                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1396                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1397       """       """
1398       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1399            return self.getCoefficient(name)
1400         else:
1401            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1402    
1403       def hasCoefficientOfGeneralPDE(self,name):
1404       """       """
1405       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1406    
1407         @param name: name of the coefficient enquired.
1408         @type name: C{string}
1409         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1410         @rtype: C{bool}
1411    
    def getDim(self):  
1412       """       """
1413       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1414    
1415       def createCoefficientOfGeneralPDE(self,name):
1416       """       """
1417       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1418    
1419     def getNumEquations(self):       @param name: name of the coefficient requested.
1420         @type name: C{string}
1421         @return: a coefficient name initialized to 0.
1422         @rtype: L{Data<escript.Data>}
1423         @raise IllegalCoefficient: if name is not one of coefficients
1424                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1425                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1426       """       """
1427       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1428            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1429         else:
1430            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1431    
1432       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1433       """       """
1434       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1435           return self.__numEquations  
1436         @param name: name of the coefficient enquired.
1437         @type name: C{string}
1438         @return: the function space to be used for coefficient name
1439         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1440         @raise IllegalCoefficient: if name is not one of coefficients
1441                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1442                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1443         """
1444         if self.hasCoefficientOfGeneralPDE(name):
1445            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1446       else:       else:
1447           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1448    
1449     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1450       """       """
1451       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1452    
1453         @param name: name of the coefficient enquired.
1454         @type name: C{string}
1455         @return: the shape of the coefficient name
1456         @rtype: C{tuple} of C{int}
1457         @raise IllegalCoefficient: if name is not one of coefficients
1458                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1459                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1460       """       """
1461       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1462          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1463       else:       else:
1464          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1465    
1466       # =============================================================================
1467       # functions giving access to coefficients of a particular PDE implementation:
1468       # =============================================================================
1469       def getCoefficient(self,name):
1470         """
1471         returns the value of the coefficient name
1472    
1473     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1474        """       @type name: C{string}
1475        returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.       @return: the value of the coefficient name
1476        """       @rtype: L{Data<escript.Data>}
1477        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1478        out=True       """
1479        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1480           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1481           out=False       else:
1482        else:          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          A=self.getCoefficientOfPDE("A")  
          if not A.isEmpty():  
             tol=util.Lsup(A)*self.TOL  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                   for j in range(self.getDim()):  
                      for k in range(self.getNumSolutions()):  
                         for l in range(self.getDim()):  
                             if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:  
                                if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)  
                                out=False  
             else:  
                for j in range(self.getDim()):  
                   for l in range(self.getDim()):  
                      if util.Lsup(A[j,l]-A[l,j])>tol:  
                         if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)  
                         out=False  
          B=self.getCoefficientOfPDE("B")  
          C=self.getCoefficientOfPDE("C")  
          if B.isEmpty() and not C.isEmpty():  
             if verbose: print "non-symmetric PDE because B is not present but C is"  
             out=False  
          elif not B.isEmpty() and C.isEmpty():  
             if verbose: print "non-symmetric PDE because C is not present but B is"  
             out=False  
          elif not B.isEmpty() and not C.isEmpty():  
             tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          if util.Lsup(B[i,j,k]-C[k,i,j])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)  
                               out=False  
             else:  
                for j in range(self.getDim()):  
                   if util.Lsup(B[j]-C[j])>tol:  
                      if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)  
                      out=False  
          if self.getNumSolutions()>1:  
            D=self.getCoefficientOfPDE("D")  
            if not D.isEmpty():  
              tol=util.Lsup(D)*self.TOL  
              for i in range(self.getNumEquations()):  
                 for k in range(self.getNumSolutions()):  
                   if util.Lsup(D[i,k]-D[k,i])>tol:  
                       if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)  
                       out=False  
               
       return out  
1483    
1484     def getFlux(self,u):     def hasCoefficient(self,name):
1485         """       """
1486         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1487    
1488         \f[       @param name: name of the coefficient enquired.
1489         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1490         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1491         @rtype: C{bool}
1492         """
1493         return self.COEFFICIENTS.has_key(name)
1494    
1495         @param u: argument of the operator     def createCoefficient(self, name):
1496         """       """
1497         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1498    
1499     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1500         """       @rtype: L{Data<escript.Data>}
1501         applies the operator of the PDE to a given solution u in weak from       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1502         """
1503         if self.hasCoefficient(name):
1504            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1505         else:
1506            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1507    
1508         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1509         """       """
1510         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        return the residual of u in the weak from  
1511    
1512         @param u:       @param name: name of the coefficient enquired.
1513         """       @type name: C{string}
1514         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1515         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1516         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1517         """
1518         if self.hasCoefficient(name):
1519            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1520         else:
1521            raise ValueError,"unknown coefficient %s requested"%name
1522       def getShapeOfCoefficient(self,name):
1523         """
1524         return the shape of the coefficient name
1525    
1526         @param name: name of the coefficient enquired.
1527         @type name: C{string}
1528         @return: the shape of the coefficient name
1529         @rtype: C{tuple} of C{int}
1530         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1531         """
1532         if self.hasCoefficient(name):
1533            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1534         else:
1535            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1536    
1537       def resetCoefficients(self):
1538         """
1539         resets all coefficients to there default values.
1540         """
1541         for i in self.COEFFICIENTS.iterkeys():
1542             self.COEFFICIENTS[i].resetValue()
1543    
1544       def alteredCoefficient(self,name):
1545         """
1546         announce that coefficient name has been changed
1547    
1548         @param name: name of the coefficient enquired.
1549         @type name: C{string}
1550         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1551         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1552         """
1553         if self.hasCoefficient(name):
1554            self.trace("Coefficient %s has been altered."%name)
1555            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1556               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1557               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1558         else:
1559            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1560    
1561       def copyConstraint(self,u):
1562          """
1563          copies the constraint into u and returns u.
1564    
1565          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1566          @type u: L{Data<escript.Data>}
1567          @return: the input u modified by the constraints.
1568          @rtype: L{Data<escript.Data>}
1569          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1570          """
1571          q=self.getCoefficientOfGeneralPDE("q")
1572          r=self.getCoefficientOfGeneralPDE("r")
1573          if not q.isEmpty():
1574             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1575             if r.isEmpty():
1576                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1577             else:
1578                 r=escript.Data(r,u.getFunctionSpace())
1579             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1580          return u
1581    
1582     def __setValue(self,**coefficients):     def setValue(self,**coefficients):
1583        """        """
1584        sets new values to coefficient        sets new values to coefficients
1585    
1586        @param coefficients:        @param coefficients: new values assigned to coefficients
1587          @keyword A: value for coefficient A.
1588          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589          @keyword A_reduced: value for coefficient A_reduced.
1590          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591          @keyword B: value for coefficient B
1592          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword B_reduced: value for coefficient B_reduced
1594          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595          @keyword C: value for coefficient C
1596          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword C_reduced: value for coefficient C_reduced
1598          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599          @keyword D: value for coefficient D
1600          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword D_reduced: value for coefficient D_reduced
1602          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603          @keyword X: value for coefficient X
1604          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword X_reduced: value for coefficient X_reduced
1606          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1607          @keyword Y: value for coefficient Y
1608          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1609          @keyword Y_reduced: value for coefficient Y_reduced
1610          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1611          @keyword d: value for coefficient d
1612          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_reduced: value for coefficient d_reduced
1614          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1615          @keyword y: value for coefficient y
1616          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1617          @keyword d_contact: value for coefficient d_contact
1618          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1619          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1620          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1621          @keyword y_contact: value for coefficient y_contact
1622          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1623          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1624          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1625          @keyword r: values prescribed to the solution at the locations of constraints
1626          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                   depending of reduced order is used for the solution.
1628          @keyword q: mask for location of constraints
1629          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                   depending of reduced order is used for the representation of the equation.
1631          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1632        """        """
1633        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1634        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1635           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1636              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1637        # if the number of unknowns or equations is still unknown we try to estimate them:        # if the number of unknowns or equations is still unknown we try to estimate them:
1638        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1639           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1640              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1641                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1645  class LinearPDE:
1645                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1646              if s!=None:              if s!=None:
1647                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1648                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1649                  if res==None:                  if res==None:
1650                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1651                  else:                  else:
1652                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1653                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1654        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1655        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1656        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1657        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1658          if d==None:          try:
1659               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1660          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1661               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1662                  d2=d             self.alteredCoefficient(i)
1663               else:          except IllegalCoefficientFunctionSpace,m:
1664                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1665          else:              i_red=i+"_reduced"
1666                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1667          if not d2.isEmpty():                  try:
1668             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1669                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1670          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1671          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1672          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1673          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1674                          except IllegalCoefficientFunctionSpace,m:
1675        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1676        self.__setHomogeneousConstraintFlag()              else:
1677        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1678            except IllegalCoefficientValue,m:
1679     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1680        """        self.__altered_coefficients=True
1681        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1682        """        if len(coefficients)>0 and not self.isUsingLumping():
1683        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1684        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1685        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1686        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1687           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1688        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1689             if self.__homogeneous_constraint:                 self.__invalidateSystem()
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
   
    # ==== rebuild switches =====================================================================  
    def __rebuildSolution(self,deep=False):  
        """  
        indicates the PDE has to be reolved if the solution is requested  
        """  
        if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."  
        self.__solution_isValid=False  
        if deep: self.__solution=escript.Data()  
   
   
    def __rebuildOperator(self,deep=False):  
        """  
        indicates the operator has to be rebuilt next time it is used  
        """  
        if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__operator_isValid=False  
        if deep: self.__operator=escript.Operator()  
   
    def __rebuildRightHandSide(self,deep=False):  
        """  
        indicates the right hand side has to be rebuild next time it is used  
        """  
        if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__righthandside_isValid=False  
        if deep: self.__righthandside=escript.Data()  
   
    def __rebuildSystem(self,deep=False):  
        """  
        annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      reassess the matrix type and, if needed, initiates an operator rebuild  
      """  
      new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())  
      if not new_matrix_type==self.__matrix_type:  
          if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type  
          self.__matrix_type=new_matrix_type  
          self.__rebuildOperator(deep=True)  
   
    #============ assembling =======================================================  
    def __copyConstraint(self):  
       """  
       copies the constrint condition into u  
       """  
       if not self.__righthandside.isEmpty():  
          q=self.getCoefficientOfPDE("q")  
          r=self.getCoefficientOfPDE("r")  
          if not q.isEmpty():  
              if r.isEmpty():  
                 r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace())  
              else:  
                 r2=escript.Data(r,self.__righthandside.getFunctionSpace())  
              self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace()))  
   
    def __applyConstraint(self):  
        """  
        applies the constraints defined by q and r to the system  
        """  
        q=self.getCoefficientOfPDE("q")  
        r=self.getCoefficientOfPDE("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__getNewSolution()  
           if r.isEmpty():  
              r_s=self.__getNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if self.isUsingLumping():  
              self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q)  
           else:  
              if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u  
              self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1690    
1691     def getSystem(self):     def getSystem(self):
1692         """         """
1693         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1694    
1695           @return: the discrete version of the PDE
1696           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1697         """         """
1698         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1699            if self.isUsingLumping():            if self.isUsingLumping():
1700                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1701                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1702                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1703                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1704                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1705                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1706                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1707                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1708                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1709                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1710                   mat=self.__getNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1711                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1712                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1713                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1714                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1715                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1716                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1717                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1718                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1719                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1720                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1721                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1723                   self.__applyConstraint()                   if not D.isEmpty():
1724                   self.__operator_isValid=True                       if self.getNumSolutions()>1:
1725                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1726                         else:
1727                            D_times_e=D
1728                     else:
1729                        D_times_e=escript.Data()
1730                     if not d.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_times_e=d
1735                     else:
1736                        d_times_e=escript.Data()
1737          
1738                     if not D_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            D_reduced_times_e=D_reduced
1743                     else:
1744                        D_reduced_times_e=escript.Data()
1745                     if not d_reduced.isEmpty():
1746                         if self.getNumSolutions()>1:
1747                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1748                         else:
1749                            d_reduced_times_e=d_reduced
1750                     else:
1751                        d_reduced_times_e=escript.Data()
1752    
1753                     self.__operator=self.__getNewRightHandSide()
1754                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1755                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1756                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1757                     else:
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_times_e, \
1761                                                     d_times_e,\
1762                                                     escript.Data())
1763                        self.getDomain().addPDEToRHS(self.__operator, \
1764                                                     escript.Data(), \
1765                                                     D_reduced_times_e, \
1766                                                     d_reduced_times_e,\
1767                                                     escript.Data())
1768                     self.__operator=1./self.__operator
1769                     self.trace("New lumped operator has been built.")
1770                     self.__operator_is_Valid=True
1771                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1772                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1773                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1774                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1775                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1776                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1777                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1780                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1781                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1782                     self.trace("New right hand side as been built.")
1783                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1784            else:            else:
1785               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New system is built."  
1786                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1787                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1788                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1789                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1790                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1791                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1792                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1793                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1794                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1795                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1796                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1797                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1798                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1808                   self.__applyConstraint()                   self.__applyConstraint()
1809                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1810                   self.__operator_isValid=True                   self.trace("New system has been built.")
1811                     self.__operator_is_Valid=True
1812                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1813               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1814                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1815                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1816                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1817                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1818                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1819                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1820                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1821                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1822                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1823                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1824                     self.__righthandside=self.copyConstraint(self.__righthandside)
1825                     self.trace("New right hand side has been built.")
1826                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1827               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1828                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1829                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1830                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1831                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1832                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1833                              escript.Data(), \                              escript.Data(), \
1834                              escript.Data(), \                              escript.Data(), \
1835                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1836                              escript.Data(),\                              escript.Data(),\
1837                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1838                                escript.Data())
1839                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1840                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1842                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1843                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1844                                escript.Data(), \
1845                                escript.Data(), \
1846                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1847                                escript.Data(),\
1848                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1849                              escript.Data())                              escript.Data())
1850                   self.__applyConstraint()                   self.__applyConstraint()
1851                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1852                     self.__operator_is_Valid=True
1853         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1854    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1855    
1856     def solve(self,**options):  class Poisson(LinearPDE):
1857        """     """
1858        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
   
       @param options:  
       """  
       mat,f=self.getSystem()  
       if self.isUsingLumping():  
          out=f/mat  
       else:  
          options[util.TOLERANCE_KEY]=self.getTolerance()  
          options[util.METHOD_KEY]=self.getSolverMethod()  
          options[util.SYMMETRY_KEY]=self.isSymmetric()  
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1859    
1860     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        returns the solution of the PDE  
1861    
1862         @param options:     with natural boundary conditons
        """  
        if not self.__solution_isValid:  
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
1863    
1864       M{n[j]*grad(u)[j] = 0 }
1865    
1866       and constraints:
1867    
1868  def ELMAN_RAMAGE(P):     M{u=0} where M{q>0}
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
 def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
   
 def HALF(P):  
     """ """  
     return escript.Scalar(0.5,P.getFunctionSpace())  
1869    
 class AdvectivePDE(LinearPDE):  
1870     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1871    
1872     \f[     def __init__(self,domain,debug=False):
1873     -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i       """
1874     \f]       initializes a new Poisson equation
1875    
1876     with boundary conditons:       @param domain: domain of the PDE
1877         @type domain: L{Domain<escript.Domain>}
1878         @param debug: if True debug informations are printed.
1879    
1880     \f[       """
1881     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       super(Poisson, self).__init__(domain,1,1,debug)
1882     \f]       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1883                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1884                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1885         self.setSymmetryOn()
1886    
1887     and contact conditions     def setValue(self,**coefficients):
1888         """
1889         sets new values to coefficients
1890    
1891     \f[       @param coefficients: new values assigned to coefficients
1892     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}       @keyword f: value for right hand side M{f}
1893     \f]       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1894         @keyword q: mask for location of constraints
1895         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1896                   depending of reduced order is used for the representation of the equation.
1897         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1898         """
1899         super(Poisson, self).setValue(**coefficients)
1900    
1901       def getCoefficientOfGeneralPDE(self,name):
1902         """
1903         return the value of the coefficient name of the general PDE
1904         @param name: name of the coefficient requested.
1905         @type name: C{string}
1906         @return: the value of the coefficient  name
1907         @rtype: L{Data<escript.Data>}
1908         @raise IllegalCoefficient: if name is not one of coefficients
1909                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1910         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1911         """
1912         if name == "A" :
1913             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1914         elif name == "B" :
1915             return escript.Data()
1916         elif name == "C" :
1917             return escript.Data()
1918         elif name == "D" :
1919             return escript.Data()
1920         elif name == "X" :
1921             return escript.Data()
1922         elif name == "Y" :
1923             return self.getCoefficient("f")
1924         elif name == "d" :
1925             return escript.Data()
1926         elif name == "y" :
1927             return escript.Data()
1928         elif name == "d_contact" :
1929             return escript.Data()
1930         elif name == "y_contact" :
1931             return escript.Data()
1932         elif name == "A_reduced" :
1933             return escript.Data()
1934         elif name == "B_reduced" :
1935             return escript.Data()
1936         elif name == "C_reduced" :
1937             return escript.Data()
1938         elif name == "D_reduced" :
1939             return escript.Data()
1940         elif name == "X_reduced" :
1941             return escript.Data()
1942         elif name == "Y_reduced" :
1943             return self.getCoefficient("f_reduced")
1944         elif name == "d_reduced" :
1945             return escript.Data()
1946         elif name == "y_reduced" :
1947             return escript.Data()
1948         elif name == "d_contact_reduced" :
1949             return escript.Data()
1950         elif name == "y_contact_reduced" :
1951             return escript.Data()
1952         elif name == "r" :
1953             return escript.Data()
1954         elif name == "q" :
1955             return self.getCoefficient("q")
1956         else:
1957            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1958    
1959    class Helmholtz(LinearPDE):
1960       """
1961       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1962    
1963       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1964    
1965       with natural boundary conditons
1966    
1967       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1968    
1969     and constraints:     and constraints:
1970    
1971     \f[     M{u=r} where M{q>0}
1972     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1973     """     """
    def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
       LinearPDE.__init__(self,domain,numEquations,numSolutions)  
       self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def __calculateXi(self,peclet_factor,Z,h):  
        Z_max=util.Lsup(Z)  
        if Z_max>0.:  
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
        else:  
           return 0.  
1974    
1975     def setValue(self,**args):     def __init__(self,domain,debug=False):
1976         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1977         self._LinearPDE__setValue(**args)       initializes a new Poisson equation
             
    def getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2  
                 else:  
                    if self.getNumSolutions()>1:  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2  
                    else:  
                       for l in range(self.getDim()): Z2+=(C[l]-B[l])**2  
                 length_of_Z=util.sqrt(Z2)  
             elif C.isEmpty():  
               length_of_Z=util.length(B)  
             else:  
               length_of_Z=util.length(C)  
1978    
1979              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1980              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1981                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
1982                 A_max=util.Lsup(length_of_A)  
1983                 if A_max>0:       """
1984                      inv_A=1./(length_of_A+A_max*self.TOL)       super(Helmholtz, self).__init__(domain,1,1,debug)
1985                 else:       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                      inv_A=1./self.TOL                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                 peclet_number=length_of_Z*h/2*inv_A                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                 xi=self.__xi(peclet_number)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                 print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991        return self.__Xi                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                                  "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1993                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1994         self.setSymmetryOn()
1995    
1996     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
1997       """       """
1998       return the value of the coefficient name of the general PDE       sets new values to coefficients
1999    
2000       @param name:       @param coefficients: new values assigned to coefficients
2001         @keyword omega: value for coefficient M{S{omega}}
2002         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword k: value for coefficeint M{k}
2004         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2005         @keyword f: value for right hand side M{f}
2006         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2007         @keyword alpha: value for right hand side M{S{alpha}}
2008         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2009         @keyword g: value for right hand side M{g}
2010         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2011         @keyword r: prescribed values M{r} for the solution in constraints.
2012         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                   depending of reduced order is used for the representation of the equation.
2014         @keyword q: mask for location of constraints
2015         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2016                   depending of reduced order is used for the representation of the equation.
2017         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2018       """       """
2019       if not self.getNumEquations() == self.getNumSolutions():       super(Helmholtz, self).setValue(**coefficients)
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
2020    
2021       if name == "A" :     def getCoefficientOfGeneralPDE(self,name):
2022           A=self.getCoefficient("A")       """
2023           B=self.getCoefficient("B")       return the value of the coefficient name of the general PDE
2024           C=self.getCoefficient("C")  
2025           if B.isEmpty() and C.isEmpty():       @param name: name of the coefficient requested.
2026              Aout=A       @type name: C{string}
2027           else:       @return: the value of the coefficient  name
2028              if A.isEmpty():       @rtype: L{Data<escript.Data>}
2029                 Aout=self.createNewCoefficient("A")       @raise IllegalCoefficient: if name is not one of coefficients
2030              else:                    "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2031                 Aout=A[:]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2032              Xi=self.getXi()       """
2033              if self.getNumEquations()>1:       if name == "A" :
2034                  for i in range(self.getNumEquations()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2035                     for j in range(self.getDim()):       elif name == "B" :
2036                        for k in range(self.getNumSolutions()):           return escript.Data()
2037                           for l in range(self.getDim()):       elif name == "C" :
2038                              if not C.isEmpty() and not B.isEmpty():           return escript.Data()
2039                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])       elif name == "D" :
2040                              elif C.isEmpty():           return self.getCoefficient("omega")
2041                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       elif name == "X" :
2042                              else:           return escript.Data()
2043                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       elif name == "Y" :
2044              else:           return self.getCoefficient("f")
2045                  for j in range(self.getDim()):       elif name == "d" :
2046                     for l in range(self.getDim()):           return self.getCoefficient("alpha")
2047                        if not C.isEmpty() and not B.isEmpty():       elif name == "y" :
2048                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])           return self.getCoefficient("g")
2049                        elif C.isEmpty():       elif name == "d_contact" :
2050                            Aout[j,l]+=Xi*B[j]*B[l]           return escript.Data()
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
          return Aout  
      elif name == "B" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.getXi()  
             if B.isEmpty():  
                 Bout=self.createNewCoefficient("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
          return Bout  
      elif name == "C" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.getXi()  
             if C.isEmpty():  
                 Cout=self.createNewCoefficient("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
          else:  
             if X.isEmpty():  
                 Xout=self.createNewCoefficient("X")  
             else:  
                 Xout=X[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
             else:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                     else:  
                        Xout[j]+=tmp*C[j]  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
2051       elif name == "y_contact" :       elif name == "y_contact" :
2052           return self.getCoefficient("y_contact")           return escript.Data()
2053       elif name == "r" :       elif name == "A_reduced" :
2054             return escript.Data()
2055         elif name == "B_reduced" :
2056             return escript.Data()
2057         elif name == "C_reduced" :
2058             return escript.Data()
2059         elif name == "D_reduced" :
2060             return escript.Data()
2061         elif name == "X_reduced" :
2062             return escript.Data()
2063         elif name == "Y_reduced" :
2064             return self.getCoefficient("f_reduced")
2065         elif name == "d_reduced" :
2066             return escript.Data()
2067         elif name == "y_reduced" :
2068            return self.getCoefficient("g_reduced")
2069         elif name == "d_contact_reduced" :
2070             return escript.Data()
2071         elif name == "y_contact_reduced" :
2072             return escript.Data()
2073         elif name == "r" :
2074           return self.getCoefficient("r")           return self.getCoefficient("r")
2075       elif name == "q" :       elif name == "q" :
2076           return self.getCoefficient("q")           return self.getCoefficient("q")
2077       else:       else:
2078           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2079    
2080  class Poisson(LinearPDE):  class LameEquation(LinearPDE):
2081     """     """
2082     Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
2083    
2084       M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2085    
2086     class to define a linear PDE of the form     with natural boundary conditons:
2087     \f[  
2088     -u_{,jj} = f     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
2089    
2090     and constraints:     and constraints:
2091    
2092     \f[     M{u[i]=r[i]} where M{q[i]>0}
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
2093    
2094     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     """
        LinearPDE.__init__(self,domain,1,1)  
        self.COEFFICIENTS={  
        "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
        self.setValue(f,q)  
2095    
2096     def setValue(self,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2097         self._LinearPDE__setValue(f=f,q=q)        super(LameEquation, self).__init__(domain,\
2098                                             domain.getDim(),domain.getDim(),debug)
2099          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2100                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2101                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2102                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2103                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2104                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2105                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2106          self.setSymmetryOn()
2107    
2108       def setValues(self,**coefficients):
2109         """
2110         sets new values to coefficients
2111    
2112         @param coefficients: new values assigned to coefficients
2113         @keyword lame_mu: value for coefficient M{S{mu}}
2114         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2115         @keyword lame_lambda: value for coefficient M{S{lambda}}
2116         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2117         @keyword F: value for internal force M{F}
2118         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2119         @keyword sigma: value for initial stress M{S{sigma}}
2120         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2121         @keyword f: value for extrenal force M{f}
2122         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2123         @keyword r: prescribed values M{r} for the solution in constraints.
2124         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @keyword q: mask for location of constraints
2127         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2128                   depending of reduced order is used for the representation of the equation.
2129         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2130         """
2131         super(LameEquation, self).setValues(**coefficients)
2132    
2133     def getCoefficientOfPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2134       """       """
2135       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2136    
2137       @param name:       @param name: name of the coefficient requested.
2138       """       @type name: C{string}
2139       if name == "A" :       @return: the value of the coefficient  name
2140           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @rtype: L{Data<escript.Data>}
2141       elif name == "B" :       @raise IllegalCoefficient: if name is not one of coefficients
2142                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2143         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2144         """
2145         if name == "A" :
2146             out =self.createCoefficientOfGeneralPDE("A")
2147             for i in range(self.getDim()):
2148               for j in range(self.getDim()):
2149                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2150                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2151                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2152             return out
2153         elif name == "B" :
2154           return escript.Data()           return escript.Data()
2155       elif name == "C" :       elif name == "C" :
2156           return escript.Data()           return escript.Data()
2157       elif name == "D" :       elif name == "D" :
2158           return escript.Data()           return escript.Data()
2159       elif name == "X" :       elif name == "X" :
2160             return self.getCoefficient("sigma")
2161         elif name == "Y" :
2162             return self.getCoefficient("F")
2163         elif name == "d" :
2164           return escript.Data()           return escript.Data()
2165       elif name == "Y" :       elif name == "y" :
2166           return self.getCoefficient("f")           return self.getCoefficient("f")
2167       elif name == "d" :       elif name == "d_contact" :
2168           return escript.Data()           return escript.Data()
2169       elif name == "y" :       elif name == "y_contact" :
2170           return escript.Data()           return escript.Data()
2171       elif name == "d_contact" :       elif name == "A_reduced" :
2172           return escript.Data()           return escript.Data()
2173       elif name == "y_contact" :       elif name == "B_reduced" :
2174             return escript.Data()
2175         elif name == "C_reduced" :
2176             return escript.Data()
2177         elif name == "D_reduced" :
2178             return escript.Data()
2179         elif name == "X_reduced" :
2180             return escript.Data()
2181         elif name == "Y_reduced" :
2182           return escript.Data()           return escript.Data()
2183       elif name == "r" :       elif name == "d_reduced" :
2184           return escript.Data()           return escript.Data()
2185       elif name == "q" :       elif name == "y_reduced" :
2186             return escript.Data()
2187         elif name == "d_contact_reduced" :
2188             return escript.Data()
2189         elif name == "y_contact_reduced" :
2190             return escript.Data()
2191         elif name == "r" :
2192             return self.getCoefficient("r")
2193         elif name == "q" :
2194           return self.getCoefficient("q")           return self.getCoefficient("q")
2195       else:       else:
2196           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2197    
2198  # $Log$  def LinearSinglePDE(domain,debug=False):
2199  # Revision 1.8  2005/06/09 05:37:59  jgs     """
2200  # Merge of development branch back to main trunk on 2005-06-09     defines a single linear PDEs
2201  #  
2202  # Revision 1.7  2005/05/06 04:26:10  jgs     @param domain: domain of the PDE
2203  # Merge of development branch back to main trunk on 2005-05-06     @type domain: L{Domain<escript.Domain>}
2204  #     @param debug: if True debug informations are printed.
2205  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane     @rtype: L{LinearPDE}
2206  # Fixed up some docstrings.  Moved module-level functions to top of file so     """
2207  # that epydoc and doxygen can pick them up properly.     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2208  #  
2209  # Revision 1.1.2.22  2005/05/12 11:41:30  gross  def LinearPDESystem(domain,debug=False):
2210  # some basic Models have been added     """
2211  #     defines a system of linear PDEs
2212  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
2213  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of     @param domain: domain of the PDE
2214  # file so that the AdvectivePDE class is picked up by doxygen.  Some     @type domain: L{Domain<escript.Domain>}
2215  # reformatting of docstrings.  Addition of code to make equations come out     @param debug: if True debug informations are printed.
2216  # as proper LaTeX.     @rtype: L{LinearPDE}
2217  #     """
2218  # Revision 1.1.2.20  2005/04/15 07:09:08  gross     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2219  # some problems with functionspace and linearPDEs fixed.  
2220  #  class TransportPDE(object):
2221  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       """
2222  # bug in SystemPattern fixed.       Warning: This is still a very experimental. The class is still changing!
2223  #  
2224  # Revision 1.1.2.18  2005/02/08 06:16:45  gross       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2225  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed      
2226  #       u=r where q>0
2227  # Revision 1.1.2.17  2005/02/08 05:56:19  gross      
2228  # Reference Number handling added       all coefficients are constant over time.
2229  #  
2230  # Revision 1.1.2.16  2005/02/07 04:41:28  gross       typical usage:
2231  # some function exposed to python to make mesh merging running  
2232  #           p=TransportPDE(dom)
2233  # Revision 1.1.2.15  2005/02/03 00:14:44  gross           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2234  # timeseries add and ESySParameter.py renames esysXML.py for consistence           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2235  #           t=0
2236  # Revision 1.1.2.14  2005/02/01 06:44:10  gross           dt=0.1
2237  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working           while (t<1.):
2238  #                u=p.solve(dt)
2239  # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
2240  # updates in the documentation       """
2241  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2242  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__domain=domain
2243  # Added createCoefficient method for linearPDEs.          self.__num_equations=num_equations
2244  #          self.__useSUPG=useSUPG
2245  # Revision 1.1.2.11  2005/01/11 01:55:34  gross          self.__trace=trace
2246  # a problem in linearPDE class fixed          self.__theta=theta
2247  #          self.__matrix_type=0
2248  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          self.__reduced=True
2249  # some bugs in linearPDE fixed          self.__reassemble=True
2250  #          if self.__useSUPG:
2251  # Revision 1.1.2.9  2005/01/06 06:24:58  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2252  # some bugs in slicing fixed             self.__pde.setSymmetryOn()
2253  #             self.__pde.setReducedOrderOn()
2254  # Revision 1.1.2.8  2005/01/05 04:21:40  gross          else:
2255  # FunctionSpace checking/matchig in slicing added             self.__transport_problem=self.__getNewTransportProblem()
2256  #          self.setTolerance()
2257  # Revision 1.1.2.7  2004/12/29 10:03:41  gross          self.__M=escript.Data()
2258  # bug in setValue fixed          self.__A=escript.Data()
2259  #          self.__B=escript.Data()
2260  # Revision 1.1.2.6  2004/12/29 05:29:59  gross          self.__C=escript.Data()
2261  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()          self.__D=escript.Data()
2262  #          self.__X=escript.Data()
2263  # Revision 1.1.2.5  2004/12/29 00:18:41  gross          self.__Y=escript.Data()
2264  # AdvectivePDE added          self.__d=escript.Data()
2265  #          self.__y=escript.Data()
2266  # Revision 1.1.2.4  2004/12/24 06:05:41  gross          self.__d_contact=escript.Data()
2267  # some changes in linearPDEs to add AdevectivePDE          self.__y_contact=escript.Data()
2268  #          self.__r=escript.Data()
2269  # Revision 1.1.2.3  2004/12/16 00:12:34  gross          self.__q=escript.Data()
2270  # __init__ of LinearPDE does not accept any coefficient anymore  
2271  #       def trace(self,text):
2272  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs               if self.__trace: print text
2273  # *** empty log message ***       def getSafeTimeStepSize(self):
2274  #          if self.__useSUPG:
2275  # Revision 1.1.2.1  2004/12/12 22:53:47  gross              if self.__reassemble:
2276  # linearPDE has been renamed LinearPDE                 h=self.__domain.getSize()
2277  #                 dt=None
2278  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__A.isEmpty():
2279  # GMRES added                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2280  #                    if dt == None:
2281  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2282  # options for GMRES and PRES20 added                    else:
2283  #                       dt=1./(1./dt+1./dt2)
2284  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 if not self.__B.isEmpty():
2285  # some small changes                    dt2=util.inf(h*self.__M/util.length(self.__B))
2286  #                    if dt == None:
2287  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross                       dt = dt2
2288  # Finley solves 4M unknowns now                    else:
2289  #                       dt=1./(1./dt+1./dt2)
2290  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross                 if not  self.__C.isEmpty():
2291  # poisson solver added                    dt2=util.inf(h*self.__M/util.length(self.__C))
2292  #                    if dt == None:
2293  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross                       dt = dt2
2294  # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry                    else:
2295  #                       dt=1./(1./dt+1./dt2)
2296  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                 if not self.__D.isEmpty():
2297  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                    dt2=util.inf(self.__M/util.length(self.__D))
2298  #                    if dt == None:
2299  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                       dt = dt2
2300  # initial import of project esys2                    else:
2301  #                       dt=1./(1./dt+1./dt2)
2302  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                 self.__dt = dt/2
2303  # committing Lutz's and Paul's changes to brach jgs              return self.__dt
2304  #          else:
2305  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane              return self.__getTransportProblem().getSafeTimeStepSize()
2306  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       def getDomain(self):
2307  #          return self.__domain
2308  # Revision 1.3  2004/09/23 00:53:23  jgs       def getTheta(self):
2309  # minor fixes          return self.__theta
2310  #       def getNumEquations(self):
2311  # Revision 1.1  2004/08/28 12:58:06  gross          return self.__num_equations
2312  # SimpleSolve is not running yet: problem with == of functionsspace       def setReducedOn(self):
2313  #            if not self.reduced():
2314  #                if self.__useSUPG:
2315                     self.__pde.setReducedOrderOn()
2316                  else:
2317                     self.__transport_problem=self.__getNewTransportProblem()
2318              self.__reduced=True
2319         def setReducedOff(self):
2320              if self.reduced():
2321                  if self.__useSUPG:
2322                     self.__pde.setReducedOrderOff()
2323                  else:
2324                     self.__transport_problem=self.__getNewTransportProblem()
2325              self.__reduced=False
2326         def reduced(self):
2327             return self.__reduced
2328         def getFunctionSpace(self):
2329            if self.reduced():
2330               return escript.ReducedSolution(self.getDomain())
2331            else:
2332               return escript.Solution(self.getDomain())
2333    
2334         def setTolerance(self,tol=1.e-8):
2335            self.__tolerance=tol
2336            if self.__useSUPG:
2337                  self.__pde.setTolerance(self.__tolerance)
2338    
2339         def __getNewTransportProblem(self):
2340           """
2341           returns an instance of a new operator
2342           """
2343           self.trace("New Transport problem is allocated.")
2344           return self.getDomain().newTransportProblem( \
2345                                   self.getTheta(),
2346                                   self.getNumEquations(), \
2347                                   self.getFunctionSpace(), \
2348                                   self.__matrix_type)
2349              
2350         def __getNewSolutionVector(self):
2351             if self.getNumEquations() ==1 :
2352                    out=escript.Data(0.0,(),self.getFunctionSpace())
2353             else:
2354                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2355             return out
2356    
2357         def __getTransportProblem(self):
2358           if self.__reassemble:
2359                 self.__source=self.__getNewSolutionVector()
2360                 self.__transport_problem.reset()
2361                 self.getDomain().addPDEToTransportProblem(
2362                             self.__transport_problem,
2363                             self.__source,
2364                             self.__M,
2365                             self.__A,
2366                             self.__B,
2367                             self.__C,
2368                             self.__D,
2369                             self.__X,
2370                             self.__Y,
2371                             self.__d,
2372                             self.__y,
2373                             self.__d_contact,
2374                             self.__y_contact)
2375                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2376                 self.__reassemble=False
2377           return self.__transport_problem
2378         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2379                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2380                 if not M==None:
2381                      self.__reassemble=True
2382                      self.__M=M
2383                 if not A==None:
2384                      self.__reassemble=True
2385                      self.__A=A
2386                 if not B==None:
2387                      self.__reassemble=True
2388                      self.__B=B
2389                 if not C==None:
2390                      self.__reassemble=True
2391                      self.__C=C
2392                 if not D==None:
2393                      self.__reassemble=True
2394                      self.__D=D
2395                 if not X==None:
2396                      self.__reassemble=True
2397                      self.__X=X
2398                 if not Y==None:
2399                      self.__reassemble=True
2400                      self.__Y=Y
2401                 if not d==None:
2402                      self.__reassemble=True
2403                      self.__d=d
2404                 if not y==None:
2405                      self.__reassemble=True
2406                      self.__y=y
2407                 if not d_contact==None:
2408                      self.__reassemble=True
2409                      self.__d_contact=d_contact
2410                 if not y_contact==None:
2411                      self.__reassemble=True
2412                      self.__y_contact=y_contact
2413                 if not q==None:
2414                      self.__reassemble=True
2415                      self.__q=q
2416                 if not r==None:
2417                      self.__reassemble=True
2418                      self.__r=r
2419    
2420         def setInitialSolution(self,u):
2421                 if self.__useSUPG:
2422                     self.__u=util.interpolate(u,self.getFunctionSpace())
2423                 else:
2424                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2425    
2426         def solve(self,dt,**kwarg):
2427               if self.__useSUPG:
2428                    if self.__reassemble:
2429                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2430                        self.__reassemble=False
2431                    dt2=self.getSafeTimeStepSize()
2432                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2433                    dt2=dt/nn
2434                    nnn=0
2435                    u=self.__u
2436                    self.trace("number of substeps is %d."%nn)
2437                    while nnn<nn :
2438                        self.__setSUPG(u,u,dt2/2)
2439                        u_half=self.__pde.getSolution(verbose=True)
2440                        self.__setSUPG(u,u_half,dt2)
2441                        u=self.__pde.getSolution(verbose=True)
2442                        nnn+=1
2443                    self.__u=u
2444                    return self.__u
2445               else:
2446                   kwarg["tolerance"]=self.__tolerance
2447                   tp=self.__getTransportProblem()
2448                   return tp.solve(self.__source,dt,kwarg)
2449         def __setSUPG(self,u0,u,dt):
2450                g=util.grad(u)
2451                X=0
2452                Y=self.__M*u0
2453                X=0
2454                self.__pde.setValue(r=u0)
2455                if not self.__A.isEmpty():
2456                   X=X+dt*util.matrixmult(self.__A,g)
2457                if not self.__B.isEmpty():
2458                   X=X+dt*self.__B*u
2459                if not  self.__C.isEmpty():
2460                   Y=Y+dt*util.inner(self.__C,g)
2461                if not self.__D.isEmpty():
2462                   Y=Y+dt*self.__D*u
2463                if not self.__X.isEmpty():
2464                   X=X+dt*self.__X
2465                if not self.__Y.isEmpty():
2466                   Y=Y+dt*self.__Y
2467                self.__pde.setValue(X=X,Y=Y)
2468                if not self.__y.isEmpty():
2469                   self.__pde.setValue(y=dt*self.__y)
2470                if not self.__y_contact.isEmpty():
2471                   self.__pde.setValue(y=dt*self.__y_contact)
2472                self.__pde.setValue(r=u0)

Legend:
Removed from v.122  
changed lines
  Added in v.1809

  ViewVC Help
Powered by ViewVC 1.1.26