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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 1118 by gross, Tue Apr 24 08:55:04 2007 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 ## @file linearPDEs.py  
   
2  """  """
3  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
4    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
5    solver capabilities in itself but hands the PDE over to
6    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
7    The general interface is provided through the L{LinearPDE} class. The
8    L{AdvectivePDE} which is derived from the L{LinearPDE} class
9    provides an interface to PDE dominated by its advective terms. The L{Poisson},
10    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11    classs which are also derived form the L{LinearPDE} class should be used
12    to define of solve these sepecial PDEs.
13    
14    @var __author__: name of author
15    @var __copyright__: copyrights
16    @var __license__: licence agreement
17    @var __url__: url entry point on documentation
18    @var __version__: version
19    @var __date__: date of the version
20  """  """
21    
22  import escript  import escript
23  import util  import util
24  import numarray  import numarray
25    
26    __author__="Lutz Gross, l.gross@uq.edu.au"
27    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28                        http://www.access.edu.au
29                    Primary Business: Queensland, Australia"""
30    __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32    __url__="http://www.iservo.edu.au/esys"
33    __version__="$Revision$"
34    __date__="$Date$"
35    
36    
37  def _CompTuple2(t1,t2):  class IllegalCoefficient(ValueError):
38     """     """
39     Compare two tuples     raised if an illegal coefficient of the general ar particular PDE is requested.
40       """
41       pass
42    
43     \param t1 The first tuple  class IllegalCoefficientValue(ValueError):
44     \param t2 The second tuple     """
45       raised if an incorrect value for a coefficient is used.
46     """     """
47       pass
48    
49     dif=t1[0]+t1[1]-(t2[0]+t2[1])  class IllegalCoefficientFunctionSpace(ValueError):
50     if dif<0: return 1     """
51     elif dif>0: return -1     raised if an incorrect function space for a coefficient is used.
52     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)  
53    
54  def HALF(P):  class UndefinedPDEError(ValueError):
55      return escript.Scalar(0.5,P.getFunctionSpace())     """
56       raised if a PDE is not fully defined yet.
57       """
58       pass
59    
60  class PDECoefficient:  class PDECoefficient(object):
61      """      """
62      A class for PDE coefficients      A class for describing a PDE coefficient
63    
64        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
65        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
66        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
67        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
68        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
69        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
70        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
71        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
72        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
73        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
74        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
75        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
76        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
77        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
78    
79      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
80      INTERIOR=0      INTERIOR=0
81      BOUNDARY=1      BOUNDARY=1
82      CONTACT=2      CONTACT=2
83      CONTINUOUS=3      SOLUTION=3
84      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
85      # 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
86      # number of unknowns.      BY_SOLUTION=6
87      EQUATION=3      BY_DIM=7
88      SOLUTION=4      OPERATOR=10
89      DIM=5      RIGHTHANDSIDE=11
90      # indicator for what is altered if the coefficient is altered:      BOTH=12
91      OPERATOR=5      INTERIOR_REDUCED=13
92      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
93      BOTH=7      CONTACT_REDUCED=15
94      def __init__(self,where,pattern,altering):  
95        def __init__(self, where, pattern, altering):
96         """         """
97         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
98    
99           @param where: describes where the coefficient lives
100           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
101                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
102           @param pattern: describes the shape of the coefficient and how the shape is build for a given
103                  spatial dimension and numbers of equation and solution in then PDE. For instance,
104                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
105                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
106                  on a 2-dimensional domain. In the case of single equation and a single solution component
107                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
108                  the example would be read as (2,).
109           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
110           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
111           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
112           @param reduced: indicates if reduced
113           @type reduced: C{bool}
114         """         """
115           super(PDECoefficient, self).__init__()
116         self.what=where         self.what=where
117         self.pattern=pattern         self.pattern=pattern
118         self.altering=altering         self.altering=altering
# Line 68  class PDECoefficient: Line 124  class PDECoefficient:
124         """         """
125         self.value=escript.Data()         self.value=escript.Data()
126    
127      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
128         """         """
129         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
130    
131         @param domain:         @param domain: domain on which the PDE uses the coefficient
132         """         @type domain: L{Domain<escript.Domain>}
133         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
134         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
135         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
136         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
137           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
138           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
139           """
140           if self.what==self.INTERIOR:
141                return escript.Function(domain)
142           elif self.what==self.INTERIOR_REDUCED:
143                return escript.ReducedFunction(domain)
144           elif self.what==self.BOUNDARY:
145                return escript.FunctionOnBoundary(domain)
146           elif self.what==self.BOUNDARY_REDUCED:
147                return escript.ReducedFunctionOnBoundary(domain)
148           elif self.what==self.CONTACT:
149                return escript.FunctionOnContactZero(domain)
150           elif self.what==self.CONTACT_REDUCED:
151                return escript.ReducedFunctionOnContactZero(domain)
152           elif self.what==self.SOLUTION:
153                if reducedEquationOrder and reducedSolutionOrder:
154                    return escript.ReducedSolution(domain)
155                else:
156                    return escript.Solution(domain)
157           elif self.what==self.REDUCED:
158                return escript.ReducedSolution(domain)
159    
160      def getValue(self):      def getValue(self):
161         """         """
162         returns the value of the coefficient:         returns the value of the coefficient
163    
164           @return:  value of the coefficient
165           @rtype:  L{Data<escript.Data>}
166         """         """
167         return self.value         return self.value
168        
169      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  
170         """         """
171           set the value of the coefficient to a new value
172    
173           @param domain: domain on which the PDE uses the coefficient
174           @type domain: L{Domain<escript.Domain>}
175           @param numEquations: number of equations of the PDE
176           @type numEquations: C{int}
177           @param numSolutions: number of components of the PDE solution
178           @type numSolutions: C{int}
179           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
180           @type reducedEquationOrder: C{bool}
181           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
182           @type reducedSolutionOrder: C{bool}
183           @param newValue: number of components of the PDE solution
184           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
185           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
186           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
187           """
188           if newValue==None:
189               newValue=escript.Data()
190           elif isinstance(newValue,escript.Data):
191               if not newValue.isEmpty():
192                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
193                    try:
194                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
195                    except:
196                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
197           else:
198               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
199           if not newValue.isEmpty():
200               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
201                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
202         self.value=newValue         self.value=newValue
203        
204      def isAlteringOperator(self):      def isAlteringOperator(self):
205          """          """
206      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
207    
208            @return:  True if the operator of the PDE is changed when the coefficient is changed
209            @rtype:  C{bool}
210      """      """
211          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
212              return not None              return not None
# Line 102  class PDECoefficient: Line 215  class PDECoefficient:
215    
216      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
217          """          """
218      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
219    
220        @rtype:  C{bool}
221            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
222      """      """
223          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
224              return not None              return not None
225          else:          else:
226              return None              return None
227    
228      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
229         """         """
230         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
231    
232         @param shape:         @param domain: domain on which the PDE uses the coefficient
233         @param dim:         @type domain: L{Domain<escript.Domain>}
234           @param shape: suggested shape of the coefficient
235           @type shape: C{tuple} of C{int} values
236           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
237                     If no appropriate numbers could be identified, C{None} is returned
238           @rtype: C{tuple} of two C{int} values or C{None}
239         """         """
240           dim=domain.getDim()
241         if len(shape)>0:         if len(shape)>0:
242             num=max(shape)+1             num=max(shape)+1
243         else:         else:
244             num=1             num=1
245         search=[]         search=[]
246         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
247            for e in range(num):            for u in range(num):
248               search.append((e,u))               for e in range(num):
249         search.sort(_CompTuple2)                  search.append((e,u))
250         for item in search:            search.sort(self.__CompTuple2)
251               s=self.buildShape(item[0],item[1],dim)            for item in search:
252                 s=self.getShape(domain,item[0],item[1])
253               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
254                   return (1,1)                   return (1,1)
255               else:               else:
256                   if s==shape: return item                   if s==shape: return item
257           elif self.definesNumEquation():
258              for e in range(num,0,-1):
259                 s=self.getShape(domain,e,0)
260                 if len(s)==0 and len(shape)==0:
261                     return (1,None)
262                 else:
263                     if s==shape: return (e,None)
264    
265           elif self.definesNumSolutions():
266              for u in range(num,0,-1):
267                 s=self.getShape(domain,0,u)
268                 if len(s)==0 and len(shape)==0:
269                     return (None,1)
270                 else:
271                     if s==shape: return (None,u)
272         return None         return None
273        def definesNumSolutions(self):
274           """
275           checks if the coefficient allows to estimate the number of solution components
276    
277      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
278          """         @rtype: C{bool}
279      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
280           for i in self.pattern:
281                 if i==self.BY_SOLUTION: return True
282           return False
283    
284      @param e:      def definesNumEquation(self):
285      @param u:         """
286      @param dim:         checks if the coefficient allows to estimate the number of equations
287      """  
288          s=()         @return: True if the coefficient allows an estimate of the number of equations
289          for i in self.pattern:         @rtype: C{bool}
290               if i==self.EQUATION:         """
291                  if e>1: s=s+(e,)         for i in self.pattern:
292               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
293                  if u>1: s=s+(u,)         return False
294    
295        def __CompTuple2(self,t1,t2):
296          """
297          Compare two tuples of possible number of equations and number of solutions
298    
299          @param t1: The first tuple
300          @param t2: The second tuple
301    
302          """
303    
304          dif=t1[0]+t1[1]-(t2[0]+t2[1])
305          if dif<0: return 1
306          elif dif>0: return -1
307          else: return 0
308    
309        def getShape(self,domain,numEquations=1,numSolutions=1):
310           """
311           builds the required shape of the coefficient
312    
313           @param domain: domain on which the PDE uses the coefficient
314           @type domain: L{Domain<escript.Domain>}
315           @param numEquations: number of equations of the PDE
316           @type numEquations: C{int}
317           @param numSolutions: number of components of the PDE solution
318           @type numSolutions: C{int}
319           @return: shape of the coefficient
320           @rtype: C{tuple} of C{int} values
321           """
322           dim=domain.getDim()
323           s=()
324           for i in self.pattern:
325                 if i==self.BY_EQUATION:
326                    if numEquations>1: s=s+(numEquations,)
327                 elif i==self.BY_SOLUTION:
328                    if numSolutions>1: s=s+(numSolutions,)
329               else:               else:
330                  s=s+(dim,)                  s=s+(dim,)
331          return s         return s
332    
333  class LinearPDE:  class LinearPDE(object):
334     """     """
335     Class to handle a linear PDE     This class is used to define a general linear, steady, second order PDE
336         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  
337    
338     \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]  
339    
340     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)}
341    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
342    
343     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
344       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
345       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
346       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
347       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
348       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
349       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.
350    
351     \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]  
352    
353     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}
354    
355     \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]  
356    
    """  
    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  
357    
358     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.  
359    
360       @param args:     M{u=r}  where M{q>0}
361       """  
362       # 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.
363       self.COEFFICIENTS={     The constraints override any other condition set by the PDE or the boundary condition.
364         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
365         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The PDE is symmetrical if
366         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
367         "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]
368         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
369         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     For a system of PDEs and a solution with several components the PDE has the form
370         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
371         "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] }
372         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
373         "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.
374         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     The natural boundary conditions take the form:
375         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
376       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]}
377    
378    
379       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>}.
380    
381       Constraints take the form
382    
383       M{u[i]=r[i]}  where  M{q[i]>0}
384    
385       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
386    
387       The system of PDEs is symmetrical if
388    
389            - M{A[i,j,k,l]=A[k,l,i,j]}
390            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
391            - M{B[i,j,k]=C[k,i,j]}
392            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
393            - M{D[i,k]=D[i,k]}
394            - M{D_reduced[i,k]=D_reduced[i,k]}
395            - M{d[i,k]=d[k,i]}
396            - M{d_reduced[i,k]=d_reduced[k,i]}
397    
398       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
399       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
400       defined as
401    
402       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]}
403    
404       For the case of single solution component and single PDE M{J} is defined
405    
406       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
407    
408       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
409       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
410       the contact condition takes the form
411    
412       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]}
413    
414       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
415       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
416       L{jump<util.jump>}.
417       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>}.
418        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>}.
419       In case of a single PDE and a single component solution the contact condition takes the form
420    
421       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
422    
423       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>}
424    
425       @cvar DEFAULT: The default method used to solve the system of linear equations
426       @cvar DIRECT: The direct solver based on LDU factorization
427       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
428       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
429       @cvar CR: The conjugate residual method
430       @cvar CGS: The conjugate gardient square method
431       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
432       @cvar SSOR: The symmetric overrealaxtion method
433       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
434       @cvar ILUT: The incomplete LU factorization preconditioner with will in
435       @cvar JACOBI: The Jacobi preconditioner
436       @cvar GMRES: The Gram-Schmidt minimum residual method
437       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
438       @cvar LUMPING: Matrix lumping.
439       @cvar NO_REORDERING: No matrix reordering allowed
440       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
441       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
442       @cvar PASO: PASO solver package
443       @cvar SCSL: SGI SCSL solver library
444       @cvar MKL: Intel's MKL solver library
445       @cvar UMFPACK: the UMFPACK library
446       @cvar ITERATIVE: The default iterative solver
447       @cvar AMG: algebraic multi grid
448       @cvar RILU: recursive ILU
449    
450       """
451       DEFAULT= 0
452       DIRECT= 1
453       CHOLEVSKY= 2
454       PCG= 3
455       CR= 4
456       CGS= 5
457       BICGSTAB= 6
458       SSOR= 7
459       ILU0= 8
460       ILUT= 9
461       JACOBI= 10
462       GMRES= 11
463       PRES20= 12
464       LUMPING= 13
465       NO_REORDERING= 17
466       MINIMUM_FILL_IN= 18
467       NESTED_DISSECTION= 19
468       SCSL= 14
469       MKL= 15
470       UMFPACK= 16
471       ITERATIVE= 20
472       PASO= 21
473       AMG= 22
474       RILU = 23
475    
476       SMALL_TOLERANCE=1.e-13
477       __PACKAGE_KEY="package"
478       __METHOD_KEY="method"
479       __SYMMETRY_KEY="symmetric"
480       __TOLERANCE_KEY="tolerance"
481       __PRECONDITIONER_KEY="preconditioner"
482    
483    
484       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
485         """
486         initializes a new linear PDE
487    
488         @param domain: domain of the PDE
489         @type domain: L{Domain<escript.Domain>}
490         @param numEquations: number of equations. If numEquations==None the number of equations
491                              is exracted from the PDE coefficients.
492         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
493                              is exracted from the PDE coefficients.
494         @param debug: if True debug informations are printed.
495    
496         """
497         super(LinearPDE, self).__init__()
498         #
499         #   the coefficients of the general PDE:
500         #
501         self.__COEFFICIENTS_OF_GENEARL_PDE={
502           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
503           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
504           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
505           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
506           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
507           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
508           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
509           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
510           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
511           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
512           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
513           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
514           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
515           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
516           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
517           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
518           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
519           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
520           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
522           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
523           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
524    
525         # COEFFICIENTS can be overwritten by subclasses:
526         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
527         self.__altered_coefficients=False
528       # initialize attributes       # initialize attributes
529       self.__debug=None       self.__debug=debug
530       self.__domain=domain       self.__domain=domain
531       self.__numEquations=numEquations       self.__numEquations=numEquations
532       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
533       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  
534    
535       # set some default values:       # set some default values:
536       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
537       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
538       self.__tolerance=1.e-8       self.__tolerance=1.e-8
539       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
540       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
541         self.__preconditioner=self.DEFAULT
542         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
543       self.__sym=False       self.__sym=False
      self.__lumping=False  
544    
545     def createCoefficient(self, name):       self.resetCoefficients()
546         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
547       # =============================================================================
548       #    general stuff:
549       # =============================================================================
550       def __str__(self):
551         """
552         returns string representation of the PDE
553    
554         @return: a simple representation of the PDE
555         @rtype: C{str}
556         """
557         return "<LinearPDE %d>"%id(self)
558       # =============================================================================
559       #    debug :
560       # =============================================================================
561       def setDebugOn(self):
562       """       """
563       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
564       """       """
565       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
   
    def __del__(self):  
      pass  
566    
567     def getCoefficient(self,name):     def setDebugOff(self):
568       """       """
569       return the value of the parameter name       switches off debugging
570         """
571         self.__debug=None
572    
573       @param name:     def trace(self,text):
574         """
575         print the text message if debugging is swiched on.
576         @param text: message
577         @type text: C{string}
578       """       """
579       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
580    
581     def getCoefficientOfPDE(self,name):     # =============================================================================
582       # some service functions:
583       # =============================================================================
584       def getDomain(self):
585       """       """
586       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.  
587    
588       @param name:       @return: the domain of the PDE
589         @rtype: L{Domain<escript.Domain>}
590       """       """
591       return self.getCoefficient(name)       return self.__domain
592    
593     def hasCoefficient(self,name):     def getDim(self):
594        """       """
595        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
596    
597        @param name:       @return: the spatial dimension of the PDE domain
598        """       @rtype: C{int}
599        return self.COEFFICIENTS.has_key(name)       """
600         return self.getDomain().getDim()
601    
602     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
603       """       """
604       return true if the test functions should use reduced order       returns the number of equations
605    
606         @return: the number of equations
607         @rtype: C{int}
608         @raise UndefinedPDEError: if the number of equations is not be specified yet.
609       """       """
610       return self.__row_function_space       if self.__numEquations==None:
611             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
612         else:
613             return self.__numEquations
614    
615     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
616       """       """
617       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
618    
619         @return: the number of unknowns
620         @rtype: C{int}
621         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
622       """       """
623       return self.__column_function_space       if self.__numSolutions==None:
624            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
625         else:
626            return self.__numSolutions
627    
628     def setValue(self,**coefficients):     def reduceEquationOrder(self):
629        """       """
630        sets new values to coefficients       return status for order reduction for equation
631    
632        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
633        """       @rtype: L{bool}
634        self.__setValue(**coefficients)       """
635               return self.__reduce_equation_order
636    
637     def cleanCoefficients(self):     def reduceSolutionOrder(self):
638       """       """
639       resets all coefficients to default values.       return status for order reduction for the solution
640    
641         @return: return True is reduced interpolation order is used for the represenation of the solution
642         @rtype: L{bool}
643       """       """
644       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
645    
646     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
647       """       """
648       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
649    
650         @return: representation space of equation
651         @rtype: L{FunctionSpace<escript.FunctionSpace>}
652       """       """
653       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
654                   return escript.ReducedSolution(self.getDomain())
655         else:
656             return escript.Solution(self.getDomain())
657    
658     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
659       """       """
660       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
661    
662       @param name:       @return: representation space of solution
663         @rtype: L{FunctionSpace<escript.FunctionSpace>}
664       """       """
665       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
666          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
667       else:       else:
668          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
669    
670     def getFunctionSpaceForCoefficient(self,name):  
671       def getOperator(self):
672       """       """
673       return the atoms of the coefficient name       provides access to the operator of the PDE
674    
675       @param name:       @return: the operator of the PDE
676         @rtype: L{Operator<escript.Operator>}
677       """       """
678       if self.hasCoefficient(name):       m=self.getSystem()[0]
679          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
680             return self.copyConstraint(1./m)
681       else:       else:
682          raise ValueError,"Solution coefficient %s requested"%name           return m
683    
684     def alteredCoefficient(self,name):     def getRightHandSide(self):
685       """       """
686       announce that coefficient name has been changed       provides access to the right hand side of the PDE
687         @return: the right hand side of the PDE
688         @rtype: L{Data<escript.Data>}
689         """
690         r=self.getSystem()[1]
691         if self.isUsingLumping():
692             return self.copyConstraint(r)
693         else:
694             return r
695    
696       @param name:     def applyOperator(self,u=None):
697       """       """
698       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
699          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
700          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}
701                   the current solution is used.
702         @type u: L{Data<escript.Data>} or None
703         @return: image of u
704         @rtype: L{Data<escript.Data>}
705         """
706         if u==None:
707            return self.getOperator()*self.getSolution()
708       else:       else:
709          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
710    
711     # ===== debug ==============================================================     def getResidual(self,u=None):
712     def setDebugOn(self):       """
713         """       return the residual of u or the current solution if u is not present.
714    
715         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
716                   the current solution is used.
717         @type u: L{Data<escript.Data>} or None
718         @return: residual of u
719         @rtype: L{Data<escript.Data>}
720         """
721         return self.applyOperator(u)-self.getRightHandSide()
722    
723       def checkSymmetry(self,verbose=True):
724          """
725          test the PDE for symmetry.
726    
727          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
728          @type verbose: C{bool}
729          @return:  True if the PDE is symmetric.
730          @rtype: L{Data<escript.Data>}
731          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
732          """
733          verbose=verbose or self.__debug
734          out=True
735          if self.getNumSolutions()!=self.getNumEquations():
736             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
737             out=False
738          else:
739             A=self.getCoefficientOfGeneralPDE("A")
740             if not A.isEmpty():
741                tol=util.Lsup(A)*self.SMALL_TOLERANCE
742                if self.getNumSolutions()>1:
743                   for i in range(self.getNumEquations()):
744                      for j in range(self.getDim()):
745                         for k in range(self.getNumSolutions()):
746                            for l in range(self.getDim()):
747                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
748                                   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)
749                                   out=False
750                else:
751                   for j in range(self.getDim()):
752                      for l in range(self.getDim()):
753                         if util.Lsup(A[j,l]-A[l,j])>tol:
754                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
755                            out=False
756             B=self.getCoefficientOfGeneralPDE("B")
757             C=self.getCoefficientOfGeneralPDE("C")
758             if B.isEmpty() and not C.isEmpty():
759                if verbose: print "non-symmetric PDE because B is not present but C is"
760                out=False
761             elif not B.isEmpty() and C.isEmpty():
762                if verbose: print "non-symmetric PDE because C is not present but B is"
763                out=False
764             elif not B.isEmpty() and not C.isEmpty():
765                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
766                if self.getNumSolutions()>1:
767                   for i in range(self.getNumEquations()):
768                       for j in range(self.getDim()):
769                          for k in range(self.getNumSolutions()):
770                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
771                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
772                                  out=False
773                else:
774                   for j in range(self.getDim()):
775                      if util.Lsup(B[j]-C[j])>tol:
776                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
777                         out=False
778             if self.getNumSolutions()>1:
779               D=self.getCoefficientOfGeneralPDE("D")
780               if not D.isEmpty():
781                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
782                 for i in range(self.getNumEquations()):
783                    for k in range(self.getNumSolutions()):
784                      if util.Lsup(D[i,k]-D[k,i])>tol:
785                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
786                          out=False
787               d=self.getCoefficientOfGeneralPDE("d")
788               if not d.isEmpty():
789                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
790                 for i in range(self.getNumEquations()):
791                    for k in range(self.getNumSolutions()):
792                      if util.Lsup(d[i,k]-d[k,i])>tol:
793                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
794                          out=False
795               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
796               if not d_contact.isEmpty():
797                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
798                 for i in range(self.getNumEquations()):
799                    for k in range(self.getNumSolutions()):
800                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
801                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
802                          out=False
803             # and now the reduced coefficients
804             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
805             if not A_reduced.isEmpty():
806                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
807                if self.getNumSolutions()>1:
808                   for i in range(self.getNumEquations()):
809                      for j in range(self.getDim()):
810                         for k in range(self.getNumSolutions()):
811                            for l in range(self.getDim()):
812                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
813                                   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)
814                                   out=False
815                else:
816                   for j in range(self.getDim()):
817                      for l in range(self.getDim()):
818                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
819                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
820                            out=False
821             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
822             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
823             if B_reduced.isEmpty() and not C_reduced.isEmpty():
824                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
825                out=False
826             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
827                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
828                out=False
829             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
830                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
831                if self.getNumSolutions()>1:
832                   for i in range(self.getNumEquations()):
833                       for j in range(self.getDim()):
834                          for k in range(self.getNumSolutions()):
835                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
836                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
837                                  out=False
838                else:
839                   for j in range(self.getDim()):
840                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
841                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
842                         out=False
843             if self.getNumSolutions()>1:
844               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
845               if not D_reduced.isEmpty():
846                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
847                 for i in range(self.getNumEquations()):
848                    for k in range(self.getNumSolutions()):
849                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
850                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
851                          out=False
852               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
853               if not d_reduced.isEmpty():
854                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
855                 for i in range(self.getNumEquations()):
856                    for k in range(self.getNumSolutions()):
857                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
858                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
859                          out=False
860               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
861               if not d_contact_reduced.isEmpty():
862                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
863                 for i in range(self.getNumEquations()):
864                    for k in range(self.getNumSolutions()):
865                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
866                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
867                          out=False
868          return out
869    
870       def getSolution(self,**options):
871         """         """
872         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
873    
874     def setDebugOff(self):         @return: the solution
875           @rtype: L{Data<escript.Data>}
876           @param options: solver options
877           @keyword verbose: True to get some information during PDE solution
878           @type verbose: C{bool}
879           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
880                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
881           @keyword iter_max: maximum number of iteration steps allowed.
882           @keyword drop_tolerance: threshold for drupping in L{ILUT}
883           @keyword drop_storage: maximum of allowed memory in L{ILUT}
884           @keyword truncation: maximum number of residuals in L{GMRES}
885           @keyword restart: restart cycle length in L{GMRES}
886         """         """
887           if not self.__solution_isValid:
888              mat,f=self.getSystem()
889              if self.isUsingLumping():
890                 self.__solution=self.copyConstraint(f*mat)
891              else:
892                 options[self.__TOLERANCE_KEY]=self.getTolerance()
893                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
894                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
895                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
896                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
897                 self.trace("PDE is resolved.")
898                 self.trace("solver options: %s"%str(options))
899                 self.__solution=mat.solve(f,options)
900              self.__solution_isValid=True
901           return self.__solution
902    
903       def getFlux(self,u=None):
904         """
905         returns the flux M{J} for a given M{u}
906    
907         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]}
908    
909         or
910    
911         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
912    
913         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
914         @type u: L{Data<escript.Data>} or None
915         @return: flux
916         @rtype: L{Data<escript.Data>}
917         """
918         if u==None: u=self.getSolution()
919         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
920               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
921               -util.self.getCoefficientOfGeneralPDE("X") \
922               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
923               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
924               -util.self.getCoefficientOfGeneralPDE("X_reduced")
925       # =============================================================================
926       #   solver settings:
927       # =============================================================================
928       def setSolverMethod(self,solver=None,preconditioner=None):
929         """         """
930         self.__debug=None         sets a new solver
931    
932           @param solver: sets a new solver method.
933           @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{PRES20}, L{LUMPING}, L{AMG}
934           @param preconditioner: sets a new solver method.
935           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
936           """
937           if solver==None: solve=self.DEFAULT
938           if preconditioner==None: preconditioner=self.DEFAULT
939           if not (solver,preconditioner)==self.getSolverMethod():
940               self.__solver_method=solver
941               self.__preconditioner=preconditioner
942               self.__checkMatrixType()
943               self.trace("New solver is %s"%self.getSolverMethodName())
944    
945     def debug(self):     def getSolverMethodName(self):
946         """         """
947         returns true if the PDE is in the debug mode         returns the name of the solver currently used
948    
949           @return: the name of the solver currently used.
950           @rtype: C{string}
951         """         """
        return self.__debug  
952    
953     #===== Lumping ===========================         m=self.getSolverMethod()
954     def setLumpingOn(self):         p=self.getSolverPackage()
955        """         method=""
956        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
957        """         elif m[0]==self.DIRECT: method= "DIRECT"
958        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
959           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
960           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
961           self.__lumping=True         elif m[0]==self.CR: method= "CR"
962           elif m[0]==self.CGS: method= "CGS"
963           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
964           elif m[0]==self.SSOR: method= "SSOR"
965           elif m[0]==self.GMRES: method= "GMRES"
966           elif m[0]==self.PRES20: method= "PRES20"
967           elif m[0]==self.LUMPING: method= "LUMPING"
968           elif m[0]==self.AMG: method= "AMG"
969           if m[1]==self.DEFAULT: method+="+DEFAULT"
970           elif m[1]==self.JACOBI: method+= "+JACOBI"
971           elif m[1]==self.ILU0: method+= "+ILU0"
972           elif m[1]==self.ILUT: method+= "+ILUT"
973           elif m[1]==self.SSOR: method+= "+SSOR"
974           elif m[1]==self.AMG: method+= "+AMG"
975           elif m[1]==self.RILU: method+= "+RILU"
976           if p==self.DEFAULT: package="DEFAULT"
977           elif p==self.PASO: package= "PASO"
978           elif p==self.MKL: package= "MKL"
979           elif p==self.SCSL: package= "SCSL"
980           elif p==self.UMFPACK: package= "UMFPACK"
981           else : method="unknown"
982           return "%s solver of %s package"%(method,package)
983    
    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  
984    
985     def setLumping(self,flag=False):     def getSolverMethod(self):
986        """         """
987        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
988    
989     def isUsingLumping(self):         @return: the solver method currently be used.
990        """         @rtype: C{int}
991                 """
992        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
993    
994     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
995         """         """
996         sets a new solver         sets a new solver package
997    
998           @param package: sets a new solver method.
999           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1000         """         """
1001         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1002             self.__solver_method=solver         if not package==self.getSolverPackage():
1003             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1004             self.__checkMatrixType()             self.__checkMatrixType()
1005               self.trace("New solver is %s"%self.getSolverMethodName())
1006    
1007     def getSolverMethod(self):     def getSolverPackage(self):
1008         """         """
1009         returns the solver method         returns the package of the solver
1010    
1011           @return: the solver package currently being used.
1012           @rtype: C{int}
1013         """         """
1014         return self.__solver_method         return self.__solver_package
1015    
1016       def isUsingLumping(self):
1017          """
1018          checks if matrix lumping is used a solver method
1019    
1020          @return: True is lumping is currently used a solver method.
1021          @rtype: C{bool}
1022          """
1023          return self.getSolverMethod()[0]==self.LUMPING
1024    
    #============ tolerance business =========================================================  
1025     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1026         """         """
1027         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1028    
1029           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1030    
1031           defines the stopping criterion.
1032    
1033           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1034                       the system will be resolved.
1035           @type tol: positive C{float}
1036           @raise ValueError: if tolerance is not positive.
1037         """         """
1038         if not tol>0:         if not tol>0:
1039             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1040         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1041         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1042         self.__tolerance=tol         self.__tolerance=tol
1043         return         return
1044    
1045     def getTolerance(self):     def getTolerance(self):
1046         """         """
1047         returns the tolerance set for the solution         returns the tolerance set for the solution
1048    
1049           @return: tolerance currently used.
1050           @rtype: C{float}
1051         """         """
1052         return self.__tolerance         return self.__tolerance
1053    
1054     #===== symmetry  flag ==========================     # =============================================================================
1055       #    symmetry  flag:
1056       # =============================================================================
1057     def isSymmetric(self):     def isSymmetric(self):
1058        """        """
1059        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1060    
1061          @return: True is a symmetric PDE is indicated, otherwise False is returned
1062          @rtype: C{bool}
1063        """        """
1064        return self.__sym        return self.__sym
1065    
1066     def setSymmetryOn(self):     def setSymmetryOn(self):
1067        """        """
1068        sets the symmetry flag to true        sets the symmetry flag.
1069        """        """
1070        if not self.isSymmetric():        if not self.isSymmetric():
1071           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1072           self.__sym=True           self.__sym=True
1073           self.__checkMatrixType()           self.__checkMatrixType()
1074    
1075     def setSymmetryOff(self):     def setSymmetryOff(self):
1076        """        """
1077        sets the symmetry flag to false        removes the symmetry flag.
1078        """        """
1079        if self.isSymmetric():        if self.isSymmetric():
1080           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1081           self.__sym=False           self.__sym=False
1082           self.__checkMatrixType()           self.__checkMatrixType()
1083    
1084     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1085       """        """
1086       sets the symmetry flag to flag        sets the symmetry flag to flag
1087    
1088       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1089       """        @type flag: C{bool}
1090       if flag:        """
1091          self.setSymmetryOn()        if flag:
1092       else:           self.setSymmetryOn()
1093          self.setSymmetryOff()        else:
1094             self.setSymmetryOff()
1095    
1096     #===== order reduction ==========================     # =============================================================================
1097       # function space handling for the equation as well as the solution
1098       # =============================================================================
1099     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1100       """       """
1101       switches to on reduced order       switches on reduced order for solution and equation representation
1102    
1103         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1104       """       """
1105       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1106       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1107    
1108     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1109       """       """
1110       switches to full order       switches off reduced order for solution and equation representation
1111    
1112         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1113       """       """
1114       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1115       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1116    
1117     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1118       """       """
1119       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1120         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1121       @param flag:                    if flag is not present order reduction is switched off
1122         @type flag: C{bool}
1123         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1124       """       """
1125       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1126       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1127    
1128     #===== order reduction solution ==========================  
1129     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1130       """       """
1131       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1132    
1133         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1134       """       """
1135       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1136       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1137           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1138           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1139           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1140             self.__resetSystem()
1141    
1142     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1143       """       """
1144       switches to full order to interpolate solution       switches off reduced order for solution representation
1145    
1146         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1147       """       """
1148       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1149       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1150           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1151           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1152           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1153             self.__resetSystem()
1154    
1155     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1156       """       """
1157       sets order for test functions according to flag       sets order for test functions according to flag
1158    
1159       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1160                      if flag is not present order reduction is switched off
1161         @type flag: C{bool}
1162         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1163       """       """
1164       if flag:       if flag:
1165          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1166       else:       else:
1167          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1168                                                                                                                                                              
    #===== order reduction equation ==========================  
1169     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1170       """       """
1171       switches to reduced order for test functions       switches on reduced order for equation representation
1172    
1173         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1174       """       """
1175       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1176       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1177           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1178           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1179           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1180             self.__resetSystem()
1181    
1182     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1183       """       """
1184       switches to full order for test functions       switches off reduced order for equation representation
1185    
1186         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1187       """       """
1188       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1189       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1190           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1191           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1192           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1193             self.__resetSystem()
1194    
1195     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1196       """       """
1197       sets order for test functions according to flag       sets order for test functions according to flag
1198    
1199       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1200                      if flag is not present order reduction is switched off
1201         @type flag: C{bool}
1202         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1203       """       """
1204       if flag:       if flag:
1205          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1206       else:       else:
1207          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1208                                                                                                                                                              
1209     # ==== initialization =====================================================================     # =============================================================================
1210       # private method:
1211       # =============================================================================
1212       def __checkMatrixType(self):
1213         """
1214         reassess the matrix type and, if a new matrix is needed, resets the system.
1215         """
1216         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1217         if not new_matrix_type==self.__matrix_type:
1218             self.trace("Matrix type is now %d."%new_matrix_type)
1219             self.__matrix_type=new_matrix_type
1220             self.__resetSystem()
1221       #
1222       #   rebuild switches :
1223       #
1224       def __invalidateSolution(self):
1225           """
1226           indicates the PDE has to be resolved if the solution is requested
1227           """
1228           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1229           self.__solution_isValid=False
1230    
1231       def __invalidateOperator(self):
1232           """
1233           indicates the operator has to be rebuilt next time it is used
1234           """
1235           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1236           self.__invalidateSolution()
1237           self.__operator_is_Valid=False
1238    
1239       def __invalidateRightHandSide(self):
1240           """
1241           indicates the right hand side has to be rebuild next time it is used
1242           """
1243           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1244           self.__invalidateSolution()
1245           self.__righthandside_isValid=False
1246    
1247       def __invalidateSystem(self):
1248           """
1249           annonced that everthing has to be rebuild:
1250           """
1251           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1252           self.__invalidateSolution()
1253           self.__invalidateOperator()
1254           self.__invalidateRightHandSide()
1255    
1256       def __resetSystem(self):
1257           """
1258           annonced that everthing has to be rebuild:
1259           """
1260           self.trace("New System is built from scratch.")
1261           self.__operator=escript.Operator()
1262           self.__operator_is_Valid=False
1263           self.__righthandside=escript.Data()
1264           self.__righthandside_isValid=False
1265           self.__solution=escript.Data()
1266           self.__solution_isValid=False
1267       #
1268       #    system initialization:
1269       #
1270     def __getNewOperator(self):     def __getNewOperator(self):
1271         """         """
1272           returns an instance of a new operator
1273         """         """
1274           self.trace("New operator is allocated.")
1275         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1276                             self.getNumEquations(), \                             self.getNumEquations(), \
1277                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1279  class LinearPDE:
1279                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1280                             self.__matrix_type)                             self.__matrix_type)
1281    
1282     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1283         """         """
1284           returns an instance of a new right hand side
1285         """         """
1286         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1287         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1288             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1289         else:         else:
1290             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1291    
1292     def __getNewSolution(self):     def __getNewSolution(self):
1293         """         """
1294           returns an instance of a new solution
1295         """         """
1296         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1297         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1298             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1299         else:         else:
1300             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1301    
1302       def __makeFreshSolution(self):
1303           """
1304           makes sure that the solution is instantiated and returns it initialized by zeros
1305           """
1306           if self.__solution.isEmpty():
1307               self.__solution=self.__getNewSolution()
1308           else:
1309               self.__solution*=0
1310               self.trace("Solution is reset to zero.")
1311           return self.__solution
1312    
1313       def __makeFreshRightHandSide(self):
1314           """
1315           makes sure that the right hand side is instantiated and returns it initialized by zeros
1316           """
1317           if self.__righthandside.isEmpty():
1318               self.__righthandside=self.__getNewRightHandSide()
1319           else:
1320               self.__righthandside.setToZero()
1321               self.trace("Right hand side is reset to zero.")
1322           return self.__righthandside
1323    
1324     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1325         """         """
1326           makes sure that the operator is instantiated and returns it initialized by zeros
1327         """         """
1328         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1329             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1330         else:         else:
1331             self.__operator.setValue(0.)             self.__operator.resetValues()
1332             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1333         return self.__operator         return self.__operator
1334    
1335     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1336     def getDomain(self):         """
1337           applies the constraints defined by q and r to the system
1338           """
1339           if not self.isUsingLumping():
1340              q=self.getCoefficientOfGeneralPDE("q")
1341              r=self.getCoefficientOfGeneralPDE("r")
1342              if not q.isEmpty() and not self.__operator.isEmpty():
1343                 # q is the row and column mask to indicate where constraints are set:
1344                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1345                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1346                 u=self.__getNewSolution()
1347                 if r.isEmpty():
1348                    r_s=self.__getNewSolution()
1349                 else:
1350                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1351                 u.copyWithMask(r_s,col_q)
1352                 if not self.__righthandside.isEmpty():
1353                    self.__righthandside-=self.__operator*u
1354                    self.__righthandside=self.copyConstraint(self.__righthandside)
1355                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1356       # =============================================================================
1357       # function giving access to coefficients of the general PDE:
1358       # =============================================================================
1359       def getCoefficientOfGeneralPDE(self,name):
1360         """
1361         return the value of the coefficient name of the general PDE.
1362    
1363         @note: This method is called by the assembling routine it can be overwritten
1364               to map coefficients of a particular PDE to the general PDE.
1365         @param name: name of the coefficient requested.
1366         @type name: C{string}
1367         @return: the value of the coefficient  name
1368         @rtype: L{Data<escript.Data>}
1369         @raise IllegalCoefficient: if name is not one of coefficients
1370                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1371                      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}.
1372       """       """
1373       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1374            return self.getCoefficient(name)
1375         else:
1376            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1377    
1378       def hasCoefficientOfGeneralPDE(self,name):
1379       """       """
1380       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1381    
1382         @param name: name of the coefficient enquired.
1383         @type name: C{string}
1384         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1385         @rtype: C{bool}
1386    
    def getDim(self):  
1387       """       """
1388       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1389    
1390       def createCoefficientOfGeneralPDE(self,name):
1391       """       """
1392       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1393    
1394     def getNumEquations(self):       @param name: name of the coefficient requested.
1395         @type name: C{string}
1396         @return: a coefficient name initialized to 0.
1397         @rtype: L{Data<escript.Data>}
1398         @raise IllegalCoefficient: if name is not one of coefficients
1399                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1400                      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}.
1401       """       """
1402       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1403            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1404         else:
1405            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1406    
1407       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1408       """       """
1409       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1410           return self.__numEquations  
1411         @param name: name of the coefficient enquired.
1412         @type name: C{string}
1413         @return: the function space to be used for coefficient name
1414         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1415         @raise IllegalCoefficient: if name is not one of coefficients
1416                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1417                      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}.
1418         """
1419         if self.hasCoefficientOfGeneralPDE(name):
1420            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1421       else:       else:
1422           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1423    
1424     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1425       """       """
1426       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1427    
1428         @param name: name of the coefficient enquired.
1429         @type name: C{string}
1430         @return: the shape of the coefficient name
1431         @rtype: C{tuple} of C{int}
1432         @raise IllegalCoefficient: if name is not one of coefficients
1433                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1434                      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}.
1435       """       """
1436       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1437          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1438       else:       else:
1439          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1440    
1441       # =============================================================================
1442       # functions giving access to coefficients of a particular PDE implementation:
1443       # =============================================================================
1444       def getCoefficient(self,name):
1445         """
1446         returns the value of the coefficient name
1447    
1448     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1449        """       @type name: C{string}
1450        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
1451        """       @rtype: L{Data<escript.Data>}
1452        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1453        out=True       """
1454        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1455           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1456           out=False       else:
1457        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  
1458    
1459     def getFlux(self,u):     def hasCoefficient(self,name):
1460         """       """
1461         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1462    
1463         \f[       @param name: name of the coefficient enquired.
1464         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1465         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1466         @rtype: C{bool}
1467         """
1468         return self.COEFFICIENTS.has_key(name)
1469    
1470         @param u: argument of the operator     def createCoefficient(self, name):
1471         """       """
1472         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1473    
1474     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1475         """       @rtype: L{Data<escript.Data>}
1476         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.
1477         """
1478         if self.hasCoefficient(name):
1479            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1480         else:
1481            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1482    
1483         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1484         """       """
1485         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  
1486    
1487         @param u:       @param name: name of the coefficient enquired.
1488         """       @type name: C{string}
1489         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1490         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1491         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1492         """
1493         if self.hasCoefficient(name):
1494            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1495         else:
1496            raise ValueError,"unknown coefficient %s requested"%name
1497       def getShapeOfCoefficient(self,name):
1498         """
1499         return the shape of the coefficient name
1500    
1501         @param name: name of the coefficient enquired.
1502         @type name: C{string}
1503         @return: the shape of the coefficient name
1504         @rtype: C{tuple} of C{int}
1505         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1506         """
1507         if self.hasCoefficient(name):
1508            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1509         else:
1510            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1511    
1512     def __setValue(self,**coefficients):     def resetCoefficients(self):
1513         """
1514         resets all coefficients to there default values.
1515         """
1516         for i in self.COEFFICIENTS.iterkeys():
1517             self.COEFFICIENTS[i].resetValue()
1518    
1519       def alteredCoefficient(self,name):
1520         """
1521         announce that coefficient name has been changed
1522    
1523         @param name: name of the coefficient enquired.
1524         @type name: C{string}
1525         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1526         @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.
1527         """
1528         if self.hasCoefficient(name):
1529            self.trace("Coefficient %s has been altered."%name)
1530            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1531               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1532               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1533         else:
1534            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1535    
1536       def copyConstraint(self,u):
1537        """        """
1538        sets new values to coefficient        copies the constraint into u and returns u.
1539    
1540        @param coefficients:        @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1541          @type u: L{Data<escript.Data>}
1542          @return: the input u modified by the constraints.
1543          @rtype: L{Data<escript.Data>}
1544          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1545          """
1546          q=self.getCoefficientOfGeneralPDE("q")
1547          r=self.getCoefficientOfGeneralPDE("r")
1548          if not q.isEmpty():
1549             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1550             if r.isEmpty():
1551                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1552             else:
1553                 r=escript.Data(r,u.getFunctionSpace())
1554             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1555          return u
1556    
1557       def setValue(self,**coefficients):
1558          """
1559          sets new values to coefficients
1560    
1561          @param coefficients: new values assigned to coefficients
1562          @keyword A: value for coefficient A.
1563          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1564          @keyword A_reduced: value for coefficient A_reduced.
1565          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1566          @keyword B: value for coefficient B
1567          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1568          @keyword B_reduced: value for coefficient B_reduced
1569          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1570          @keyword C: value for coefficient C
1571          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1572          @keyword C_reduced: value for coefficient C_reduced
1573          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1574          @keyword D: value for coefficient D
1575          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1576          @keyword D_reduced: value for coefficient D_reduced
1577          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1578          @keyword X: value for coefficient X
1579          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1580          @keyword X_reduced: value for coefficient X_reduced
1581          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1582          @keyword Y: value for coefficient Y
1583          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584          @keyword Y_reduced: value for coefficient Y_reduced
1585          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1586          @keyword d: value for coefficient d
1587          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1588          @keyword d_reduced: value for coefficient d_reduced
1589          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1590          @keyword y: value for coefficient y
1591          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1592          @keyword d_contact: value for coefficient d_contact
1593          @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>}.
1594          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1595          @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>}.
1596          @keyword y_contact: value for coefficient y_contact
1597          @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>}.
1598          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1599          @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>}.
1600          @keyword r: values prescribed to the solution at the locations of constraints
1601          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1602                   depending of reduced order is used for the solution.
1603          @keyword q: mask for location of constraints
1604          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1605                   depending of reduced order is used for the representation of the equation.
1606          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1607        """        """
1608        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1609        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1610           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1611              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1612        # 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:
1613        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1614           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1615              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1616                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1620  class LinearPDE:
1620                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1621              if s!=None:              if s!=None:
1622                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1623                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1624                  if res==None:                  if res==None:
1625                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1626                  else:                  else:
1627                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1628                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1629        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1630        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1631        # 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:
1632        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1633          if d==None:          try:
1634               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1635          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1636               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1637                  d2=d             self.alteredCoefficient(i)
1638               else:          except IllegalCoefficientFunctionSpace,m:
1639                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1640          else:              i_red=i+"_reduced"
1641                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1642          if not d2.isEmpty():                  try:
1643             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1644                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1645          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1646          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1647          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1648          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1649                          except IllegalCoefficientFunctionSpace,m:
1650        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1651        self.__setHomogeneousConstraintFlag()              else:
1652        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1653            except IllegalCoefficientValue,m:
1654     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1655        """        self.__altered_coefficients=True
1656        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1657        """        if len(coefficients)>0 and not self.isUsingLumping():
1658        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1659        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1660        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1661        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1662           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1663        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1664             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.)  
1665    
1666     def getSystem(self):     def getSystem(self):
1667         """         """
1668         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1669    
1670           @return: the discrete version of the PDE
1671           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1672         """         """
1673         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1674            if self.isUsingLumping():            if self.isUsingLumping():
1675                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1676                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1677                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1678                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1679                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1680                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1681                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1682                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1683                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1684                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1685                   mat=self.__getNewOperator()                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1686                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1687                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1688                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1689                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1690                             self.getCoefficientOfPDE("D"), \                   D=self.getCoefficientOfGeneralPDE("D")
1691                             escript.Data(), \                   if not D.isEmpty():
1692                             escript.Data(), \                       if self.getNumSolutions()>1:
1693                             self.getCoefficientOfPDE("d"), \                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1694                             escript.Data(),\                       else:
1695                             self.getCoefficientOfPDE("d_contact"), \                          D_times_e=D
1696                             escript.Data())                   else:
1697                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                      D_times_e=escript.Data()
1698                   self.__applyConstraint()                   d=self.getCoefficientOfGeneralPDE("d")
1699                   self.__operator_isValid=True                   if not d.isEmpty():
1700                         if self.getNumSolutions()>1:
1701                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1702                         else:
1703                            d_times_e=d
1704                     else:
1705                        d_times_e=escript.Data()
1706                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1707                     if not d_contact.isEmpty():
1708                         if self.getNumSolutions()>1:
1709                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1710                         else:
1711                            d_contact_times_e=d_contact
1712                     else:
1713                        d_contact_times_e=escript.Data()
1714        
1715                     self.__operator=self.__getNewRightHandSide()
1716                     self.getDomain().addPDEToRHS(self.__operator, \
1717                                                  escript.Data(), \
1718                                                  D_times_e, \
1719                                                  d_times_e,\
1720                                                  d_contact_times_e)
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     if not D_reduced.isEmpty():
1723                         if self.getNumSolutions()>1:
1724                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1725                         else:
1726                            D_reduced_times_e=D_reduced
1727                     else:
1728                        D_reduced_times_e=escript.Data()
1729                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1730                     if not d_reduced.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_reduced_times_e=d_reduced
1735                     else:
1736                        d_reduced_times_e=escript.Data()
1737                     d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
1738                     if not d_contact_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            d_contact_reduced_times_e=util.matrixmult(d_contact_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            d_contact_reduced_times_e=d_contact_reduced
1743                     else:
1744                        d_contact_reduced_times_e=escript.Data()
1745        
1746                     self.__operator=self.__getNewRightHandSide()
1747                     self.getDomain().addPDEToRHS(self.__operator, \
1748                                                  escript.Data(), \
1749                                                  D_times_e, \
1750                                                  d_times_e,\
1751                                                  d_contact_times_e)
1752                     self.getDomain().addPDEToRHS(self.__operator, \
1753                                                  escript.Data(), \
1754                                                  D_reduced_times_e, \
1755                                                  d_reduced_times_e,\
1756                                                  d_contact_reduced_times_e)
1757                     self.__operator=1./self.__operator
1758                     self.trace("New lumped operator has been built.")
1759                     self.__operator_is_Valid=True
1760                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1761                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1762                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1763                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1764                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1765                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1766                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1767                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1768                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1769                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1770                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1771                     self.trace("New right hand side as been built.")
1772                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1773            else:            else:
1774               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."  
1775                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1776                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1777                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1778                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1779                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1780                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1781                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1782                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1783                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1784                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1785                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1786                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1787                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1788                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1789                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1790                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1791                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1792                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1793                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1797                   self.__applyConstraint()                   self.__applyConstraint()
1798                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1799                   self.__operator_isValid=True                   self.trace("New system has been built.")
1800                     self.__operator_is_Valid=True
1801                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1802               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1803                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1804                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1805                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1806                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1807                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1808                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1809                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1811                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1812                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1813                     self.__righthandside=self.copyConstraint(self.__righthandside)
1814                     self.trace("New right hand side has been built.")
1815                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1816               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1817                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1818                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1819                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1820                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1821                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1822                                escript.Data(), \
1823                                escript.Data(), \
1824                                self.getCoefficientOfGeneralPDE("d"), \
1825                                escript.Data(),\
1826                                self.getCoefficientOfGeneralPDE("d_contact"), \
1827                                escript.Data())
1828                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1829                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1830                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1831                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1832                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1833                              escript.Data(), \                              escript.Data(), \
1834                              escript.Data(), \                              escript.Data(), \
1835                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1836                              escript.Data(),\                              escript.Data(),\
1837                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1838                              escript.Data())                              escript.Data())
1839                   self.__applyConstraint()                   self.__applyConstraint()
1840                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1841                     self.__operator_is_Valid=True
1842         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1843    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1844    
1845     def solve(self,**options):  class Poisson(LinearPDE):
1846        """     """
1847        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1848    
1849        @param options:     M{-grad(grad(u)[j])[j] = f}
       """  
       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  
1850    
1851     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
   
        @param options:  
        """  
        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  
1852    
1853       M{n[j]*grad(u)[j] = 0 }
1854    
1855       and constraints:
1856    
1857  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())  
1858    
 class AdvectivePDE(LinearPDE):  
1859     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1860    
1861     \f[     def __init__(self,domain,debug=False):
1862     -(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       """
1863     \f]       initializes a new Poisson equation
1864    
1865     with boundary conditons:       @param domain: domain of the PDE
1866         @type domain: L{Domain<escript.Domain>}
1867         @param debug: if True debug informations are printed.
1868    
1869     \f[       """
1870     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)
1871     \f]       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1872                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1873                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1874         self.setSymmetryOn()
1875    
1876     and contact conditions     def setValue(self,**coefficients):
1877         """
1878         sets new values to coefficients
1879    
1880     \f[       @param coefficients: new values assigned to coefficients
1881     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}
1882     \f]       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1883         @keyword q: mask for location of constraints
1884         @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>}
1885                   depending of reduced order is used for the representation of the equation.
1886         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1887         """
1888         super(Poisson, self).setValue(**coefficients)
1889    
1890       def getCoefficientOfGeneralPDE(self,name):
1891         """
1892         return the value of the coefficient name of the general PDE
1893         @param name: name of the coefficient requested.
1894         @type name: C{string}
1895         @return: the value of the coefficient  name
1896         @rtype: L{Data<escript.Data>}
1897         @raise IllegalCoefficient: if name is not one of coefficients
1898                      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}.
1899         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1900         """
1901         if name == "A" :
1902             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1903         elif name == "B" :
1904             return escript.Data()
1905         elif name == "C" :
1906             return escript.Data()
1907         elif name == "D" :
1908             return escript.Data()
1909         elif name == "X" :
1910             return escript.Data()
1911         elif name == "Y" :
1912             return self.getCoefficient("f")
1913         elif name == "d" :
1914             return escript.Data()
1915         elif name == "y" :
1916             return escript.Data()
1917         elif name == "d_contact" :
1918             return escript.Data()
1919         elif name == "y_contact" :
1920             return escript.Data()
1921         elif name == "A_reduced" :
1922             return escript.Data()
1923         elif name == "B_reduced" :
1924             return escript.Data()
1925         elif name == "C_reduced" :
1926             return escript.Data()
1927         elif name == "D_reduced" :
1928             return escript.Data()
1929         elif name == "X_reduced" :
1930             return escript.Data()
1931         elif name == "Y_reduced" :
1932             return self.getCoefficient("f_reduced")
1933         elif name == "d_reduced" :
1934             return escript.Data()
1935         elif name == "y_reduced" :
1936             return escript.Data()
1937         elif name == "d_contact_reduced" :
1938             return escript.Data()
1939         elif name == "y_contact_reduced" :
1940             return escript.Data()
1941         elif name == "r" :
1942             return escript.Data()
1943         elif name == "q" :
1944             return self.getCoefficient("q")
1945         else:
1946            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1947    
1948    class Helmholtz(LinearPDE):
1949       """
1950       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1951    
1952       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1953    
1954       with natural boundary conditons
1955    
1956       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1957    
1958     and constraints:     and constraints:
1959    
1960     \f[     M{u=r} where M{q>0}
1961     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1962     """     """
    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.  
1963    
1964     def setValue(self,**args):     def __init__(self,domain,debug=False):
1965         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1966         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)  
1967    
1968              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1969              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1970                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
1971                 A_max=util.Lsup(length_of_A)  
1972                 if A_max>0:       """
1973                      inv_A=1./(length_of_A+A_max*self.TOL)       super(Helmholtz, self).__init__(domain,1,1,debug)
1974                 else:       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1975                      inv_A=1./self.TOL                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1976                 peclet_number=length_of_Z*h/2*inv_A                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1977                 xi=self.__xi(peclet_number)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1978                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1979                 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),
1980        return self.__Xi                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1981                                  "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1982                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1983         self.setSymmetryOn()
1984    
1985     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
1986       """       """
1987       return the value of the coefficient name of the general PDE       sets new values to coefficients
1988    
1989       @param name:       @param coefficients: new values assigned to coefficients
1990         @keyword omega: value for coefficient M{S{omega}}
1991         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1992         @keyword k: value for coefficeint M{k}
1993         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1994         @keyword f: value for right hand side M{f}
1995         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1996         @keyword alpha: value for right hand side M{S{alpha}}
1997         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1998         @keyword g: value for right hand side M{g}
1999         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2000         @keyword r: prescribed values M{r} for the solution in constraints.
2001         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2002                   depending of reduced order is used for the representation of the equation.
2003         @keyword q: mask for location of constraints
2004         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2005                   depending of reduced order is used for the representation of the equation.
2006         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2007       """       """
2008       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."  
2009    
2010       if name == "A" :     def getCoefficientOfGeneralPDE(self,name):
2011           A=self.getCoefficient("A")       """
2012           B=self.getCoefficient("B")       return the value of the coefficient name of the general PDE
2013           C=self.getCoefficient("C")  
2014           if B.isEmpty() and C.isEmpty():       @param name: name of the coefficient requested.
2015              Aout=A       @type name: C{string}
2016           else:       @return: the value of the coefficient  name
2017              if A.isEmpty():       @rtype: L{Data<escript.Data>}
2018                 Aout=self.createNewCoefficient("A")       @raise IllegalCoefficient: if name is not one of coefficients
2019              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}.
2020                 Aout=A[:]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2021              Xi=self.getXi()       """
2022              if self.getNumEquations()>1:       if name == "A" :
2023                  for i in range(self.getNumEquations()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2024                     for j in range(self.getDim()):       elif name == "B" :
2025                        for k in range(self.getNumSolutions()):           return escript.Data()
2026                           for l in range(self.getDim()):       elif name == "C" :
2027                              if not C.isEmpty() and not B.isEmpty():           return escript.Data()
2028                                 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" :
2029                              elif C.isEmpty():           return self.getCoefficient("omega")
2030                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       elif name == "X" :
2031                              else:           return escript.Data()
2032                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       elif name == "Y" :
2033              else:           return self.getCoefficient("f")
2034                  for j in range(self.getDim()):       elif name == "d" :
2035                     for l in range(self.getDim()):           return self.getCoefficient("alpha")
2036                        if not C.isEmpty() and not B.isEmpty():       elif name == "y" :
2037                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])           return self.getCoefficient("g")
2038                        elif C.isEmpty():       elif name == "d_contact" :
2039                            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")  
2040       elif name == "y_contact" :       elif name == "y_contact" :
2041           return self.getCoefficient("y_contact")           return escript.Data()
2042       elif name == "r" :       elif name == "A_reduced" :
2043             return escript.Data()
2044         elif name == "B_reduced" :
2045             return escript.Data()
2046         elif name == "C_reduced" :
2047             return escript.Data()
2048         elif name == "D_reduced" :
2049             return escript.Data()
2050         elif name == "X_reduced" :
2051             return escript.Data()
2052         elif name == "Y_reduced" :
2053             return self.getCoefficient("f_reduced")
2054         elif name == "d_reduced" :
2055             return escript.Data()
2056         elif name == "y_reduced" :
2057            return self.getCoefficient("g_reduced")
2058         elif name == "d_contact_reduced" :
2059             return escript.Data()
2060         elif name == "y_contact_reduced" :
2061             return escript.Data()
2062         elif name == "r" :
2063           return self.getCoefficient("r")           return self.getCoefficient("r")
2064       elif name == "q" :       elif name == "q" :
2065           return self.getCoefficient("q")           return self.getCoefficient("q")
2066       else:       else:
2067           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2068    
2069  class Poisson(LinearPDE):  class LameEquation(LinearPDE):
2070     """     """
2071     Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
2072    
2073       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] }
2074    
2075       with natural boundary conditons:
2076    
2077     class to define a linear PDE of the form     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[  
    -u_{,jj} = f  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
2078    
2079     and constraints:     and constraints:
2080    
2081     \f[     M{u[i]=r[i]} where M{q[i]>0}
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
2082    
2083     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)  
2084    
2085     def setValue(self,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2086         self._LinearPDE__setValue(f=f,q=q)        super(LameEquation, self).__init__(domain,\
2087                                             domain.getDim(),domain.getDim(),debug)
2088          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2089                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2090                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2091                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2092                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2093                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2094                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2095          self.setSymmetryOn()
2096    
2097       def setValues(self,**coefficients):
2098         """
2099         sets new values to coefficients
2100    
2101         @param coefficients: new values assigned to coefficients
2102         @keyword lame_mu: value for coefficient M{S{mu}}
2103         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2104         @keyword lame_lambda: value for coefficient M{S{lambda}}
2105         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2106         @keyword F: value for internal force M{F}
2107         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2108         @keyword sigma: value for initial stress M{S{sigma}}
2109         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2110         @keyword f: value for extrenal force M{f}
2111         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2112         @keyword r: prescribed values M{r} for the solution in constraints.
2113         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2114                   depending of reduced order is used for the representation of the equation.
2115         @keyword q: mask for location of constraints
2116         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2117                   depending of reduced order is used for the representation of the equation.
2118         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2119         """
2120         super(LameEquation, self).setValues(**coefficients)
2121    
2122     def getCoefficientOfPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2123       """       """
2124       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2125    
2126       @param name:       @param name: name of the coefficient requested.
2127       """       @type name: C{string}
2128       if name == "A" :       @return: the value of the coefficient  name
2129           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @rtype: L{Data<escript.Data>}
2130       elif name == "B" :       @raise IllegalCoefficient: if name is not one of coefficients
2131                      "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}.
2132         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2133         """
2134         if name == "A" :
2135             out =self.createCoefficientOfGeneralPDE("A")
2136             for i in range(self.getDim()):
2137               for j in range(self.getDim()):
2138                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2139                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2140                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2141             return out
2142         elif name == "B" :
2143           return escript.Data()           return escript.Data()
2144       elif name == "C" :       elif name == "C" :
2145           return escript.Data()           return escript.Data()
2146       elif name == "D" :       elif name == "D" :
2147           return escript.Data()           return escript.Data()
2148       elif name == "X" :       elif name == "X" :
2149             return self.getCoefficient("sigma")
2150         elif name == "Y" :
2151             return self.getCoefficient("F")
2152         elif name == "d" :
2153           return escript.Data()           return escript.Data()
2154       elif name == "Y" :       elif name == "y" :
2155           return self.getCoefficient("f")           return self.getCoefficient("f")
2156       elif name == "d" :       elif name == "d_contact" :
2157           return escript.Data()           return escript.Data()
2158       elif name == "y" :       elif name == "y_contact" :
2159           return escript.Data()           return escript.Data()
2160       elif name == "d_contact" :       elif name == "A_reduced" :
2161           return escript.Data()           return escript.Data()
2162       elif name == "y_contact" :       elif name == "B_reduced" :
2163             return escript.Data()
2164         elif name == "C_reduced" :
2165             return escript.Data()
2166         elif name == "D_reduced" :
2167             return escript.Data()
2168         elif name == "X_reduced" :
2169             return escript.Data()
2170         elif name == "Y_reduced" :
2171           return escript.Data()           return escript.Data()
2172       elif name == "r" :       elif name == "d_reduced" :
2173           return escript.Data()           return escript.Data()
2174       elif name == "q" :       elif name == "y_reduced" :
2175             return escript.Data()
2176         elif name == "d_contact_reduced" :
2177             return escript.Data()
2178         elif name == "y_contact_reduced" :
2179             return escript.Data()
2180         elif name == "r" :
2181             return self.getCoefficient("r")
2182         elif name == "q" :
2183           return self.getCoefficient("q")           return self.getCoefficient("q")
2184       else:       else:
2185           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2186    
 # $Log$  
 # Revision 1.8  2005/06/09 05:37:59  jgs  
 # Merge of development branch back to main trunk on 2005-06-09  
 #  
 # Revision 1.7  2005/05/06 04:26:10  jgs  
 # Merge of development branch back to main trunk on 2005-05-06  
 #  
 # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
 # Fixed up some docstrings.  Moved module-level functions to top of file so  
 # that epydoc and doxygen can pick them up properly.  
 #  
 # Revision 1.1.2.22  2005/05/12 11:41:30  gross  
 # some basic Models have been added  
 #  
 # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
 # file so that the AdvectivePDE class is picked up by doxygen.  Some  
 # reformatting of docstrings.  Addition of code to make equations come out  
 # as proper LaTeX.  
 #  
 # Revision 1.1.2.20  2005/04/15 07:09:08  gross  
 # some problems with functionspace and linearPDEs fixed.  
 #  
 # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
 # bug in SystemPattern fixed.  
 #  
 # Revision 1.1.2.18  2005/02/08 06:16:45  gross  
 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
 #  
 # Revision 1.1.2.17  2005/02/08 05:56:19  gross  
 # Reference Number handling added  
 #  
 # Revision 1.1.2.16  2005/02/07 04:41:28  gross  
 # some function exposed to python to make mesh merging running  
 #  
 # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
 # timeseries add and ESySParameter.py renames esysXML.py for consistence  
 #  
 # Revision 1.1.2.14  2005/02/01 06:44:10  gross  
 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working  
 #  
 # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
 # updates in the documentation  
 #  
 # Revision 1.1.2.12  2005/01/12 01:28:04  matt  
 # Added createCoefficient method for linearPDEs.  
 #  
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # 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  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  
 #  

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