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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 1204 by gross, Sat Jun 23 11:43:12 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          
116           super(PDECoefficient, self).__init__()
117         self.what=where         self.what=where
118         self.pattern=pattern         self.pattern=pattern
119         self.altering=altering         self.altering=altering
# Line 68  class PDECoefficient: Line 125  class PDECoefficient:
125         """         """
126         self.value=escript.Data()         self.value=escript.Data()
127    
128      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
129         """         """
130         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
131    
132         @param domain:         @param domain: domain on which the PDE uses the coefficient
133         """         @type domain: L{Domain<escript.Domain>}
134         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
135         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
136         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
137         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
138           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
139           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
140           """
141           if self.what==self.INTERIOR:
142                return escript.Function(domain)
143           elif self.what==self.INTERIOR_REDUCED:
144                return escript.ReducedFunction(domain)
145           elif self.what==self.BOUNDARY:
146                return escript.FunctionOnBoundary(domain)
147           elif self.what==self.BOUNDARY_REDUCED:
148                return escript.ReducedFunctionOnBoundary(domain)
149           elif self.what==self.CONTACT:
150                return escript.FunctionOnContactZero(domain)
151           elif self.what==self.CONTACT_REDUCED:
152                return escript.ReducedFunctionOnContactZero(domain)
153           elif self.what==self.SOLUTION:
154                if reducedEquationOrder and reducedSolutionOrder:
155                    return escript.ReducedSolution(domain)
156                else:
157                    return escript.Solution(domain)
158           elif self.what==self.REDUCED:
159                return escript.ReducedSolution(domain)
160    
161      def getValue(self):      def getValue(self):
162         """         """
163         returns the value of the coefficient:         returns the value of the coefficient
164    
165           @return:  value of the coefficient
166           @rtype:  L{Data<escript.Data>}
167         """         """
168         return self.value         return self.value
169        
170      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  
171         """         """
172           set the value of the coefficient to a new value
173    
174           @param domain: domain on which the PDE uses the coefficient
175           @type domain: L{Domain<escript.Domain>}
176           @param numEquations: number of equations of the PDE
177           @type numEquations: C{int}
178           @param numSolutions: number of components of the PDE solution
179           @type numSolutions: C{int}
180           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
181           @type reducedEquationOrder: C{bool}
182           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
183           @type reducedSolutionOrder: C{bool}
184           @param newValue: number of components of the PDE solution
185           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
186           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
187           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
188           """
189           if newValue==None:
190               newValue=escript.Data()
191           elif isinstance(newValue,escript.Data):
192               if not newValue.isEmpty():
193                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
194                    try:
195                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
196                    except:
197                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
198           else:
199               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
200           if not newValue.isEmpty():
201               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
202                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
203         self.value=newValue         self.value=newValue
204        
205      def isAlteringOperator(self):      def isAlteringOperator(self):
206          """          """
207      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
208    
209            @return:  True if the operator of the PDE is changed when the coefficient is changed
210            @rtype:  C{bool}
211      """      """
212          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
213              return not None              return not None
# Line 102  class PDECoefficient: Line 216  class PDECoefficient:
216    
217      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
218          """          """
219      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
220    
221        @rtype:  C{bool}
222            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
223      """      """
224          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
225              return not None              return not None
226          else:          else:
227              return None              return None
228    
229      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
230         """         """
231         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
232    
233         @param shape:         @param domain: domain on which the PDE uses the coefficient
234         @param dim:         @type domain: L{Domain<escript.Domain>}
235           @param shape: suggested shape of the coefficient
236           @type shape: C{tuple} of C{int} values
237           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
238                     If no appropriate numbers could be identified, C{None} is returned
239           @rtype: C{tuple} of two C{int} values or C{None}
240         """         """
241           dim=domain.getDim()
242         if len(shape)>0:         if len(shape)>0:
243             num=max(shape)+1             num=max(shape)+1
244         else:         else:
245             num=1             num=1
246         search=[]         search=[]
247         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
248            for e in range(num):            for u in range(num):
249               search.append((e,u))               for e in range(num):
250         search.sort(_CompTuple2)                  search.append((e,u))
251         for item in search:            search.sort(self.__CompTuple2)
252               s=self.buildShape(item[0],item[1],dim)            for item in search:
253                 s=self.getShape(domain,item[0],item[1])
254               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
255                   return (1,1)                   return (1,1)
256               else:               else:
257                   if s==shape: return item                   if s==shape: return item
258           elif self.definesNumEquation():
259              for e in range(num,0,-1):
260                 s=self.getShape(domain,e,0)
261                 if len(s)==0 and len(shape)==0:
262                     return (1,None)
263                 else:
264                     if s==shape: return (e,None)
265    
266           elif self.definesNumSolutions():
267              for u in range(num,0,-1):
268                 s=self.getShape(domain,0,u)
269                 if len(s)==0 and len(shape)==0:
270                     return (None,1)
271                 else:
272                     if s==shape: return (None,u)
273         return None         return None
274        def definesNumSolutions(self):
275           """
276           checks if the coefficient allows to estimate the number of solution components
277    
278      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
279          """         @rtype: C{bool}
280      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
281           for i in self.pattern:
282                 if i==self.BY_SOLUTION: return True
283           return False
284    
285      @param e:      def definesNumEquation(self):
286      @param u:         """
287      @param dim:         checks if the coefficient allows to estimate the number of equations
288      """  
289          s=()         @return: True if the coefficient allows an estimate of the number of equations
290          for i in self.pattern:         @rtype: C{bool}
291               if i==self.EQUATION:         """
292                  if e>1: s=s+(e,)         for i in self.pattern:
293               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
294                  if u>1: s=s+(u,)         return False
295    
296        def __CompTuple2(self,t1,t2):
297          """
298          Compare two tuples of possible number of equations and number of solutions
299    
300          @param t1: The first tuple
301          @param t2: The second tuple
302    
303          """
304    
305          dif=t1[0]+t1[1]-(t2[0]+t2[1])
306          if dif<0: return 1
307          elif dif>0: return -1
308          else: return 0
309    
310        def getShape(self,domain,numEquations=1,numSolutions=1):
311           """
312           builds the required shape of the coefficient
313    
314           @param domain: domain on which the PDE uses the coefficient
315           @type domain: L{Domain<escript.Domain>}
316           @param numEquations: number of equations of the PDE
317           @type numEquations: C{int}
318           @param numSolutions: number of components of the PDE solution
319           @type numSolutions: C{int}
320           @return: shape of the coefficient
321           @rtype: C{tuple} of C{int} values
322           """
323           dim=domain.getDim()
324           s=()
325           for i in self.pattern:
326                 if i==self.BY_EQUATION:
327                    if numEquations>1: s=s+(numEquations,)
328                 elif i==self.BY_SOLUTION:
329                    if numSolutions>1: s=s+(numSolutions,)
330               else:               else:
331                  s=s+(dim,)                  s=s+(dim,)
332          return s         return s
333    
334  class LinearPDE:  class LinearPDE(object):
335     """     """
336     Class to handle a linear PDE     This class is used to define a general linear, steady, second order PDE
337         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  
338    
339     \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]  
340    
341     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)}
342    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
343    
344     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
345       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
346       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
347       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
348       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
349       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
350       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.
351    
352     \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]  
353    
354     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}
355    
356     \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]  
357    
    """  
    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  
358    
359     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.  
360    
361       @param args:     M{u=r}  where M{q>0}
362       """  
363       # 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.
364       self.COEFFICIENTS={     The constraints override any other condition set by the PDE or the boundary condition.
365         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
366         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The PDE is symmetrical if
367         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
368         "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]
369         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
370         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     For a system of PDEs and a solution with several components the PDE has the form
371         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
372         "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] }
373         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
374         "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.
375         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     The natural boundary conditions take the form:
376         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
377       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]}
378    
379    
380       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>}.
381    
382       Constraints take the form
383    
384       M{u[i]=r[i]}  where  M{q[i]>0}
385    
386       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
387    
388       The system of PDEs is symmetrical if
389    
390            - M{A[i,j,k,l]=A[k,l,i,j]}
391            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
392            - M{B[i,j,k]=C[k,i,j]}
393            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
394            - M{D[i,k]=D[i,k]}
395            - M{D_reduced[i,k]=D_reduced[i,k]}
396            - M{d[i,k]=d[k,i]}
397            - M{d_reduced[i,k]=d_reduced[k,i]}
398    
399       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
400       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
401       defined as
402    
403       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]}
404    
405       For the case of single solution component and single PDE M{J} is defined
406    
407       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
408    
409       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
410       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
411       the contact condition takes the form
412    
413       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]}
414    
415       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
416       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
417       L{jump<util.jump>}.
418       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>}.
419        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>}.
420       In case of a single PDE and a single component solution the contact condition takes the form
421    
422       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
423    
424       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>}
425    
426       @cvar DEFAULT: The default method used to solve the system of linear equations
427       @cvar DIRECT: The direct solver based on LDU factorization
428       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
429       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
430       @cvar CR: The conjugate residual method
431       @cvar CGS: The conjugate gardient square method
432       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
433       @cvar SSOR: The symmetric overrealaxtion method
434       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
435       @cvar ILUT: The incomplete LU factorization preconditioner with will in
436       @cvar JACOBI: The Jacobi preconditioner
437       @cvar GMRES: The Gram-Schmidt minimum residual method
438       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
439       @cvar LUMPING: Matrix lumping.
440       @cvar NO_REORDERING: No matrix reordering allowed
441       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
442       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
443       @cvar PASO: PASO solver package
444       @cvar SCSL: SGI SCSL solver library
445       @cvar MKL: Intel's MKL solver library
446       @cvar UMFPACK: the UMFPACK library
447       @cvar ITERATIVE: The default iterative solver
448       @cvar AMG: algebraic multi grid
449       @cvar RILU: recursive ILU
450    
451       """
452       DEFAULT= 0
453       DIRECT= 1
454       CHOLEVSKY= 2
455       PCG= 3
456       CR= 4
457       CGS= 5
458       BICGSTAB= 6
459       SSOR= 7
460       ILU0= 8
461       ILUT= 9
462       JACOBI= 10
463       GMRES= 11
464       PRES20= 12
465       LUMPING= 13
466       NO_REORDERING= 17
467       MINIMUM_FILL_IN= 18
468       NESTED_DISSECTION= 19
469       SCSL= 14
470       MKL= 15
471       UMFPACK= 16
472       ITERATIVE= 20
473       PASO= 21
474       AMG= 22
475       RILU = 23
476    
477       SMALL_TOLERANCE=1.e-13
478       __PACKAGE_KEY="package"
479       __METHOD_KEY="method"
480       __SYMMETRY_KEY="symmetric"
481       __TOLERANCE_KEY="tolerance"
482       __PRECONDITIONER_KEY="preconditioner"
483    
484    
485       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
486         """
487         initializes a new linear PDE
488    
489         @param domain: domain of the PDE
490         @type domain: L{Domain<escript.Domain>}
491         @param numEquations: number of equations. If numEquations==None the number of equations
492                              is exracted from the PDE coefficients.
493         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
494                              is exracted from the PDE coefficients.
495         @param debug: if True debug informations are printed.
496    
497         """
498         super(LinearPDE, self).__init__()
499         #
500         #   the coefficients of the general PDE:
501         #
502         self.__COEFFICIENTS_OF_GENEARL_PDE={
503           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
504           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
505           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
506           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
507           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
508           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
509           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
510           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
511           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
512           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
513           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
514           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
515           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
516           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
517           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
518           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
519           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
520           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
521           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
522           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
523           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
524           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
525    
526         # COEFFICIENTS can be overwritten by subclasses:
527         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
528         self.__altered_coefficients=False
529       # initialize attributes       # initialize attributes
530       self.__debug=None       self.__debug=debug
531       self.__domain=domain       self.__domain=domain
532       self.__numEquations=numEquations       self.__numEquations=numEquations
533       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
534       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  
535    
536       # set some default values:       # set some default values:
537       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
538       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
539       self.__tolerance=1.e-8       self.__tolerance=1.e-8
540       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
541       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
542         self.__preconditioner=self.DEFAULT
543         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
544       self.__sym=False       self.__sym=False
      self.__lumping=False  
545    
546     def createCoefficient(self, name):       self.resetCoefficients()
547         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
548       # =============================================================================
549       #    general stuff:
550       # =============================================================================
551       def __str__(self):
552         """
553         returns string representation of the PDE
554    
555         @return: a simple representation of the PDE
556         @rtype: C{str}
557         """
558         return "<LinearPDE %d>"%id(self)
559       # =============================================================================
560       #    debug :
561       # =============================================================================
562       def setDebugOn(self):
563       """       """
564       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
565       """       """
566       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
   
    def __del__(self):  
      pass  
567    
568     def getCoefficient(self,name):     def setDebugOff(self):
569         """
570         switches off debugging
571       """       """
572       return the value of the parameter name       self.__debug=None
573    
574       @param name:     def trace(self,text):
575         """
576         print the text message if debugging is swiched on.
577         @param text: message
578         @type text: C{string}
579       """       """
580       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
581    
582     def getCoefficientOfPDE(self,name):     # =============================================================================
583       # some service functions:
584       # =============================================================================
585       def getDomain(self):
586       """       """
587       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.  
588    
589       @param name:       @return: the domain of the PDE
590         @rtype: L{Domain<escript.Domain>}
591       """       """
592       return self.getCoefficient(name)       return self.__domain
593    
594     def hasCoefficient(self,name):     def getDim(self):
595        """       """
596        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
597    
598        @param name:       @return: the spatial dimension of the PDE domain
599        """       @rtype: C{int}
600        return self.COEFFICIENTS.has_key(name)       """
601         return self.getDomain().getDim()
602    
603     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
604       """       """
605       return true if the test functions should use reduced order       returns the number of equations
606    
607         @return: the number of equations
608         @rtype: C{int}
609         @raise UndefinedPDEError: if the number of equations is not be specified yet.
610       """       """
611       return self.__row_function_space       if self.__numEquations==None:
612             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
613         else:
614             return self.__numEquations
615    
616     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
617       """       """
618       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
619    
620         @return: the number of unknowns
621         @rtype: C{int}
622         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
623       """       """
624       return self.__column_function_space       if self.__numSolutions==None:
625            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
626         else:
627            return self.__numSolutions
628    
629     def setValue(self,**coefficients):     def reduceEquationOrder(self):
630        """       """
631        sets new values to coefficients       return status for order reduction for equation
632    
633        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
634        """       @rtype: L{bool}
635        self.__setValue(**coefficients)       """
636               return self.__reduce_equation_order
637    
638     def cleanCoefficients(self):     def reduceSolutionOrder(self):
639       """       """
640       resets all coefficients to default values.       return status for order reduction for the solution
641    
642         @return: return True is reduced interpolation order is used for the represenation of the solution
643         @rtype: L{bool}
644       """       """
645       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
646    
647     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
648       """       """
649       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
650    
651         @return: representation space of equation
652         @rtype: L{FunctionSpace<escript.FunctionSpace>}
653       """       """
654       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
655                   return escript.ReducedSolution(self.getDomain())
656         else:
657             return escript.Solution(self.getDomain())
658    
659     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
660       """       """
661       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
662    
663       @param name:       @return: representation space of solution
664         @rtype: L{FunctionSpace<escript.FunctionSpace>}
665       """       """
666       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
667          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
668       else:       else:
669          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
670    
671     def getFunctionSpaceForCoefficient(self,name):  
672       def getOperator(self):
673       """       """
674       return the atoms of the coefficient name       provides access to the operator of the PDE
675    
676       @param name:       @return: the operator of the PDE
677         @rtype: L{Operator<escript.Operator>}
678       """       """
679       if self.hasCoefficient(name):       m=self.getSystem()[0]
680          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
681             return self.copyConstraint(1./m)
682       else:       else:
683          raise ValueError,"Solution coefficient %s requested"%name           return m
684    
685     def alteredCoefficient(self,name):     def getRightHandSide(self):
686       """       """
687       announce that coefficient name has been changed       provides access to the right hand side of the PDE
688         @return: the right hand side of the PDE
689         @rtype: L{Data<escript.Data>}
690         """
691         r=self.getSystem()[1]
692         if self.isUsingLumping():
693             return self.copyConstraint(r)
694         else:
695             return r
696    
697       @param name:     def applyOperator(self,u=None):
698       """       """
699       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
700          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
701          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}
702                   the current solution is used.
703         @type u: L{Data<escript.Data>} or None
704         @return: image of u
705         @rtype: L{Data<escript.Data>}
706         """
707         if u==None:
708            return self.getOperator()*self.getSolution()
709       else:       else:
710          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
711    
712     # ===== debug ==============================================================     def getResidual(self,u=None):
713     def setDebugOn(self):       """
714         """       return the residual of u or the current solution if u is not present.
715    
716         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
717                   the current solution is used.
718         @type u: L{Data<escript.Data>} or None
719         @return: residual of u
720         @rtype: L{Data<escript.Data>}
721         """
722         return self.applyOperator(u)-self.getRightHandSide()
723    
724       def checkSymmetry(self,verbose=True):
725          """
726          test the PDE for symmetry.
727    
728          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
729          @type verbose: C{bool}
730          @return:  True if the PDE is symmetric.
731          @rtype: L{Data<escript.Data>}
732          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
733          """
734          verbose=verbose or self.__debug
735          out=True
736          if self.getNumSolutions()!=self.getNumEquations():
737             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
738             out=False
739          else:
740             A=self.getCoefficientOfGeneralPDE("A")
741             if not A.isEmpty():
742                tol=util.Lsup(A)*self.SMALL_TOLERANCE
743                if self.getNumSolutions()>1:
744                   for i in range(self.getNumEquations()):
745                      for j in range(self.getDim()):
746                         for k in range(self.getNumSolutions()):
747                            for l in range(self.getDim()):
748                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
749                                   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)
750                                   out=False
751                else:
752                   for j in range(self.getDim()):
753                      for l in range(self.getDim()):
754                         if util.Lsup(A[j,l]-A[l,j])>tol:
755                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
756                            out=False
757             B=self.getCoefficientOfGeneralPDE("B")
758             C=self.getCoefficientOfGeneralPDE("C")
759             if B.isEmpty() and not C.isEmpty():
760                if verbose: print "non-symmetric PDE because B is not present but C is"
761                out=False
762             elif not B.isEmpty() and C.isEmpty():
763                if verbose: print "non-symmetric PDE because C is not present but B is"
764                out=False
765             elif not B.isEmpty() and not C.isEmpty():
766                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
767                if self.getNumSolutions()>1:
768                   for i in range(self.getNumEquations()):
769                       for j in range(self.getDim()):
770                          for k in range(self.getNumSolutions()):
771                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
772                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
773                                  out=False
774                else:
775                   for j in range(self.getDim()):
776                      if util.Lsup(B[j]-C[j])>tol:
777                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
778                         out=False
779             if self.getNumSolutions()>1:
780               D=self.getCoefficientOfGeneralPDE("D")
781               if not D.isEmpty():
782                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
783                 for i in range(self.getNumEquations()):
784                    for k in range(self.getNumSolutions()):
785                      if util.Lsup(D[i,k]-D[k,i])>tol:
786                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
787                          out=False
788               d=self.getCoefficientOfGeneralPDE("d")
789               if not d.isEmpty():
790                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
791                 for i in range(self.getNumEquations()):
792                    for k in range(self.getNumSolutions()):
793                      if util.Lsup(d[i,k]-d[k,i])>tol:
794                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
795                          out=False
796               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
797               if not d_contact.isEmpty():
798                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
799                 for i in range(self.getNumEquations()):
800                    for k in range(self.getNumSolutions()):
801                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
802                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
803                          out=False
804             # and now the reduced coefficients
805             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
806             if not A_reduced.isEmpty():
807                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
808                if self.getNumSolutions()>1:
809                   for i in range(self.getNumEquations()):
810                      for j in range(self.getDim()):
811                         for k in range(self.getNumSolutions()):
812                            for l in range(self.getDim()):
813                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
814                                   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)
815                                   out=False
816                else:
817                   for j in range(self.getDim()):
818                      for l in range(self.getDim()):
819                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
820                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
821                            out=False
822             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
823             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
824             if B_reduced.isEmpty() and not C_reduced.isEmpty():
825                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
826                out=False
827             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
828                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
829                out=False
830             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
831                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
832                if self.getNumSolutions()>1:
833                   for i in range(self.getNumEquations()):
834                       for j in range(self.getDim()):
835                          for k in range(self.getNumSolutions()):
836                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
837                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
838                                  out=False
839                else:
840                   for j in range(self.getDim()):
841                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
842                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
843                         out=False
844             if self.getNumSolutions()>1:
845               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
846               if not D_reduced.isEmpty():
847                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
848                 for i in range(self.getNumEquations()):
849                    for k in range(self.getNumSolutions()):
850                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
851                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
852                          out=False
853               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
854               if not d_reduced.isEmpty():
855                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
856                 for i in range(self.getNumEquations()):
857                    for k in range(self.getNumSolutions()):
858                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
859                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
860                          out=False
861               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
862               if not d_contact_reduced.isEmpty():
863                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869          return out
870    
871       def getSolution(self,**options):
872         """         """
873         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
874    
875     def setDebugOff(self):         @return: the solution
876           @rtype: L{Data<escript.Data>}
877           @param options: solver options
878           @keyword verbose: True to get some information during PDE solution
879           @type verbose: C{bool}
880           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
881                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
882           @keyword iter_max: maximum number of iteration steps allowed.
883           @keyword drop_tolerance: threshold for drupping in L{ILUT}
884           @keyword drop_storage: maximum of allowed memory in L{ILUT}
885           @keyword truncation: maximum number of residuals in L{GMRES}
886           @keyword restart: restart cycle length in L{GMRES}
887         """         """
888           if not self.__solution_isValid:
889              mat,f=self.getSystem()
890              if self.isUsingLumping():
891                 self.__solution=self.copyConstraint(f*mat)
892              else:
893                 options[self.__TOLERANCE_KEY]=self.getTolerance()
894                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
895                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
896                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
897                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
898                 self.trace("PDE is resolved.")
899                 self.trace("solver options: %s"%str(options))
900                 self.__solution=mat.solve(f,options)
901              self.__solution_isValid=True
902           return self.__solution
903    
904       def getFlux(self,u=None):
905         """
906         returns the flux M{J} for a given M{u}
907    
908         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]}
909    
910         or
911    
912         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
913    
914         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
915         @type u: L{Data<escript.Data>} or None
916         @return: flux
917         @rtype: L{Data<escript.Data>}
918         """
919         if u==None: u=self.getSolution()
920         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
921               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
922               -util.self.getCoefficientOfGeneralPDE("X") \
923               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
924               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
925               -util.self.getCoefficientOfGeneralPDE("X_reduced")
926       # =============================================================================
927       #   solver settings:
928       # =============================================================================
929       def setSolverMethod(self,solver=None,preconditioner=None):
930         """         """
931         self.__debug=None         sets a new solver
932    
933           @param solver: sets a new solver method.
934           @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}
935           @param preconditioner: sets a new solver method.
936           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
937           """
938           if solver==None: solve=self.DEFAULT
939           if preconditioner==None: preconditioner=self.DEFAULT
940           if not (solver,preconditioner)==self.getSolverMethod():
941               self.__solver_method=solver
942               self.__preconditioner=preconditioner
943               self.__checkMatrixType()
944               self.trace("New solver is %s"%self.getSolverMethodName())
945    
946     def debug(self):     def getSolverMethodName(self):
947         """         """
948         returns true if the PDE is in the debug mode         returns the name of the solver currently used
949    
950           @return: the name of the solver currently used.
951           @rtype: C{string}
952         """         """
        return self.__debug  
953    
954     #===== Lumping ===========================         m=self.getSolverMethod()
955     def setLumpingOn(self):         p=self.getSolverPackage()
956        """         method=""
957        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
958        """         elif m[0]==self.DIRECT: method= "DIRECT"
959        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
960           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
961           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
962           self.__lumping=True         elif m[0]==self.CR: method= "CR"
963           elif m[0]==self.CGS: method= "CGS"
964           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
965           elif m[0]==self.SSOR: method= "SSOR"
966           elif m[0]==self.GMRES: method= "GMRES"
967           elif m[0]==self.PRES20: method= "PRES20"
968           elif m[0]==self.LUMPING: method= "LUMPING"
969           elif m[0]==self.AMG: method= "AMG"
970           if m[1]==self.DEFAULT: method+="+DEFAULT"
971           elif m[1]==self.JACOBI: method+= "+JACOBI"
972           elif m[1]==self.ILU0: method+= "+ILU0"
973           elif m[1]==self.ILUT: method+= "+ILUT"
974           elif m[1]==self.SSOR: method+= "+SSOR"
975           elif m[1]==self.AMG: method+= "+AMG"
976           elif m[1]==self.RILU: method+= "+RILU"
977           if p==self.DEFAULT: package="DEFAULT"
978           elif p==self.PASO: package= "PASO"
979           elif p==self.MKL: package= "MKL"
980           elif p==self.SCSL: package= "SCSL"
981           elif p==self.UMFPACK: package= "UMFPACK"
982           else : method="unknown"
983           return "%s solver of %s package"%(method,package)
984    
    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  
985    
986     def setLumping(self,flag=False):     def getSolverMethod(self):
987        """         """
988        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
989    
990     def isUsingLumping(self):         @return: the solver method currently be used.
991        """         @rtype: C{int}
992                 """
993        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
994    
995     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
996         """         """
997         sets a new solver         sets a new solver package
998    
999           @param package: sets a new solver method.
1000           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1001         """         """
1002         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1003             self.__solver_method=solver         if not package==self.getSolverPackage():
1004             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1005             self.__checkMatrixType()             self.__checkMatrixType()
1006               self.trace("New solver is %s"%self.getSolverMethodName())
1007    
1008     def getSolverMethod(self):     def getSolverPackage(self):
1009         """         """
1010         returns the solver method         returns the package of the solver
1011    
1012           @return: the solver package currently being used.
1013           @rtype: C{int}
1014         """         """
1015         return self.__solver_method         return self.__solver_package
1016    
1017       def isUsingLumping(self):
1018          """
1019          checks if matrix lumping is used a solver method
1020    
1021          @return: True is lumping is currently used a solver method.
1022          @rtype: C{bool}
1023          """
1024          return self.getSolverMethod()[0]==self.LUMPING
1025    
    #============ tolerance business =========================================================  
1026     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1027         """         """
1028         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1029    
1030           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1031    
1032           defines the stopping criterion.
1033    
1034           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1035                       the system will be resolved.
1036           @type tol: positive C{float}
1037           @raise ValueError: if tolerance is not positive.
1038         """         """
1039         if not tol>0:         if not tol>0:
1040             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1041         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1042         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1043         self.__tolerance=tol         self.__tolerance=tol
1044         return         return
1045    
1046     def getTolerance(self):     def getTolerance(self):
1047         """         """
1048         returns the tolerance set for the solution         returns the tolerance set for the solution
1049    
1050           @return: tolerance currently used.
1051           @rtype: C{float}
1052         """         """
1053         return self.__tolerance         return self.__tolerance
1054    
1055     #===== symmetry  flag ==========================     # =============================================================================
1056       #    symmetry  flag:
1057       # =============================================================================
1058     def isSymmetric(self):     def isSymmetric(self):
1059        """        """
1060        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1061    
1062          @return: True is a symmetric PDE is indicated, otherwise False is returned
1063          @rtype: C{bool}
1064        """        """
1065        return self.__sym        return self.__sym
1066    
1067     def setSymmetryOn(self):     def setSymmetryOn(self):
1068        """        """
1069        sets the symmetry flag to true        sets the symmetry flag.
1070        """        """
1071        if not self.isSymmetric():        if not self.isSymmetric():
1072           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1073           self.__sym=True           self.__sym=True
1074           self.__checkMatrixType()           self.__checkMatrixType()
1075    
1076     def setSymmetryOff(self):     def setSymmetryOff(self):
1077        """        """
1078        sets the symmetry flag to false        removes the symmetry flag.
1079        """        """
1080        if self.isSymmetric():        if self.isSymmetric():
1081           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1082           self.__sym=False           self.__sym=False
1083           self.__checkMatrixType()           self.__checkMatrixType()
1084    
1085     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1086       """        """
1087       sets the symmetry flag to flag        sets the symmetry flag to flag
1088    
1089       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1090       """        @type flag: C{bool}
1091       if flag:        """
1092          self.setSymmetryOn()        if flag:
1093       else:           self.setSymmetryOn()
1094          self.setSymmetryOff()        else:
1095             self.setSymmetryOff()
1096    
1097     #===== order reduction ==========================     # =============================================================================
1098       # function space handling for the equation as well as the solution
1099       # =============================================================================
1100     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1101       """       """
1102       switches to on reduced order       switches on reduced order for solution and equation representation
1103    
1104         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1105       """       """
1106       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1107       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1108    
1109     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1110       """       """
1111       switches to full order       switches off reduced order for solution and equation representation
1112    
1113         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1114       """       """
1115       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1116       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1117    
1118     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1119       """       """
1120       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1121         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1122       @param flag:                    if flag is not present order reduction is switched off
1123         @type flag: C{bool}
1124         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1125       """       """
1126       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1127       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1128    
1129     #===== order reduction solution ==========================  
1130     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1131       """       """
1132       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1133    
1134         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1135       """       """
1136       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1137       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1138           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1139           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1140           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1141             self.__resetSystem()
1142    
1143     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1144       """       """
1145       switches to full order to interpolate solution       switches off reduced order for solution representation
1146    
1147         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1148       """       """
1149       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1150       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1151           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1152           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1153           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1154             self.__resetSystem()
1155    
1156     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1157       """       """
1158       sets order for test functions according to flag       sets order for test functions according to flag
1159    
1160       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1161                      if flag is not present order reduction is switched off
1162         @type flag: C{bool}
1163         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1164       """       """
1165       if flag:       if flag:
1166          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1167       else:       else:
1168          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1169                                                                                                                                                              
    #===== order reduction equation ==========================  
1170     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1171       """       """
1172       switches to reduced order for test functions       switches on reduced order for equation representation
1173    
1174         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1175       """       """
1176       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1177       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1178           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1179           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1180           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1181             self.__resetSystem()
1182    
1183     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1184       """       """
1185       switches to full order for test functions       switches off reduced order for equation representation
1186    
1187         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1188       """       """
1189       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1190       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1191           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1192           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1193           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1194             self.__resetSystem()
1195    
1196     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1197       """       """
1198       sets order for test functions according to flag       sets order for test functions according to flag
1199    
1200       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1201                      if flag is not present order reduction is switched off
1202         @type flag: C{bool}
1203         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1204       """       """
1205       if flag:       if flag:
1206          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1207       else:       else:
1208          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1209                                                                                                                                                              
1210     # ==== initialization =====================================================================     # =============================================================================
1211       # private method:
1212       # =============================================================================
1213       def __checkMatrixType(self):
1214         """
1215         reassess the matrix type and, if a new matrix is needed, resets the system.
1216         """
1217         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1218         if not new_matrix_type==self.__matrix_type:
1219             self.trace("Matrix type is now %d."%new_matrix_type)
1220             self.__matrix_type=new_matrix_type
1221             self.__resetSystem()
1222       #
1223       #   rebuild switches :
1224       #
1225       def __invalidateSolution(self):
1226           """
1227           indicates the PDE has to be resolved if the solution is requested
1228           """
1229           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1230           self.__solution_isValid=False
1231    
1232       def __invalidateOperator(self):
1233           """
1234           indicates the operator has to be rebuilt next time it is used
1235           """
1236           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1237           self.__invalidateSolution()
1238           self.__operator_is_Valid=False
1239    
1240       def __invalidateRightHandSide(self):
1241           """
1242           indicates the right hand side has to be rebuild next time it is used
1243           """
1244           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1245           self.__invalidateSolution()
1246           self.__righthandside_isValid=False
1247    
1248       def __invalidateSystem(self):
1249           """
1250           annonced that everthing has to be rebuild:
1251           """
1252           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1253           self.__invalidateSolution()
1254           self.__invalidateOperator()
1255           self.__invalidateRightHandSide()
1256    
1257       def __resetSystem(self):
1258           """
1259           annonced that everthing has to be rebuild:
1260           """
1261           self.trace("New System is built from scratch.")
1262           self.__operator=escript.Operator()
1263           self.__operator_is_Valid=False
1264           self.__righthandside=escript.Data()
1265           self.__righthandside_isValid=False
1266           self.__solution=escript.Data()
1267           self.__solution_isValid=False
1268       #
1269       #    system initialization:
1270       #
1271     def __getNewOperator(self):     def __getNewOperator(self):
1272         """         """
1273           returns an instance of a new operator
1274         """         """
1275           self.trace("New operator is allocated.")
1276         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1277                             self.getNumEquations(), \                             self.getNumEquations(), \
1278                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1280  class LinearPDE:
1280                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1281                             self.__matrix_type)                             self.__matrix_type)
1282    
1283     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1284         """         """
1285           returns an instance of a new right hand side
1286         """         """
1287         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1288         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1289             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1290         else:         else:
1291             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1292    
1293     def __getNewSolution(self):     def __getNewSolution(self):
1294         """         """
1295           returns an instance of a new solution
1296         """         """
1297         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1298         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1299             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1300         else:         else:
1301             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1302    
1303       def __makeFreshSolution(self):
1304           """
1305           makes sure that the solution is instantiated and returns it initialized by zeros
1306           """
1307           if self.__solution.isEmpty():
1308               self.__solution=self.__getNewSolution()
1309           else:
1310               self.__solution*=0
1311               self.trace("Solution is reset to zero.")
1312           return self.__solution
1313    
1314       def __makeFreshRightHandSide(self):
1315           """
1316           makes sure that the right hand side is instantiated and returns it initialized by zeros
1317           """
1318           if self.__righthandside.isEmpty():
1319               self.__righthandside=self.__getNewRightHandSide()
1320           else:
1321               self.__righthandside.setToZero()
1322               self.trace("Right hand side is reset to zero.")
1323           return self.__righthandside
1324    
1325     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1326         """         """
1327           makes sure that the operator is instantiated and returns it initialized by zeros
1328         """         """
1329         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1330             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1331         else:         else:
1332             self.__operator.setValue(0.)             self.__operator.resetValues()
1333             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1334         return self.__operator         return self.__operator
1335    
1336     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1337     def getDomain(self):         """
1338           applies the constraints defined by q and r to the system
1339           """
1340           if not self.isUsingLumping():
1341              q=self.getCoefficientOfGeneralPDE("q")
1342              r=self.getCoefficientOfGeneralPDE("r")
1343              if not q.isEmpty() and not self.__operator.isEmpty():
1344                 # q is the row and column mask to indicate where constraints are set:
1345                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1346                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1347                 u=self.__getNewSolution()
1348                 if r.isEmpty():
1349                    r_s=self.__getNewSolution()
1350                 else:
1351                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1352                 u.copyWithMask(r_s,col_q)
1353                 if not self.__righthandside.isEmpty():
1354                    self.__righthandside-=self.__operator*u
1355                    self.__righthandside=self.copyConstraint(self.__righthandside)
1356                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1357       # =============================================================================
1358       # function giving access to coefficients of the general PDE:
1359       # =============================================================================
1360       def getCoefficientOfGeneralPDE(self,name):
1361         """
1362         return the value of the coefficient name of the general PDE.
1363    
1364         @note: This method is called by the assembling routine it can be overwritten
1365               to map coefficients of a particular PDE to the general PDE.
1366         @param name: name of the coefficient requested.
1367         @type name: C{string}
1368         @return: the value of the coefficient  name
1369         @rtype: L{Data<escript.Data>}
1370         @raise IllegalCoefficient: if name is not one of coefficients
1371                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1372                      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}.
1373       """       """
1374       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1375            return self.getCoefficient(name)
1376         else:
1377            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1378    
1379       def hasCoefficientOfGeneralPDE(self,name):
1380       """       """
1381       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1382    
1383         @param name: name of the coefficient enquired.
1384         @type name: C{string}
1385         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1386         @rtype: C{bool}
1387    
    def getDim(self):  
1388       """       """
1389       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1390    
1391       def createCoefficientOfGeneralPDE(self,name):
1392       """       """
1393       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1394    
1395     def getNumEquations(self):       @param name: name of the coefficient requested.
1396         @type name: C{string}
1397         @return: a coefficient name initialized to 0.
1398         @rtype: L{Data<escript.Data>}
1399         @raise IllegalCoefficient: if name is not one of coefficients
1400                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1401                      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}.
1402       """       """
1403       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1404            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1405         else:
1406            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1407    
1408       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1409       """       """
1410       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1411           return self.__numEquations  
1412         @param name: name of the coefficient enquired.
1413         @type name: C{string}
1414         @return: the function space to be used for coefficient name
1415         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1416         @raise IllegalCoefficient: if name is not one of coefficients
1417                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1418                      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}.
1419         """
1420         if self.hasCoefficientOfGeneralPDE(name):
1421            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1422       else:       else:
1423           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1424    
1425     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1426       """       """
1427       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1428    
1429         @param name: name of the coefficient enquired.
1430         @type name: C{string}
1431         @return: the shape of the coefficient name
1432         @rtype: C{tuple} of C{int}
1433         @raise IllegalCoefficient: if name is not one of coefficients
1434                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1435                      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}.
1436       """       """
1437       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1438          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1439       else:       else:
1440          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1441    
1442       # =============================================================================
1443       # functions giving access to coefficients of a particular PDE implementation:
1444       # =============================================================================
1445       def getCoefficient(self,name):
1446         """
1447         returns the value of the coefficient name
1448    
1449     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1450        """       @type name: C{string}
1451        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
1452        """       @rtype: L{Data<escript.Data>}
1453        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1454        out=True       """
1455        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1456           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1457           out=False       else:
1458        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  
1459    
1460     def getFlux(self,u):     def hasCoefficient(self,name):
1461         """       """
1462         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1463    
1464         \f[       @param name: name of the coefficient enquired.
1465         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1466         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1467         @rtype: C{bool}
1468         """
1469         return self.COEFFICIENTS.has_key(name)
1470    
1471         @param u: argument of the operator     def createCoefficient(self, name):
1472         """       """
1473         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1474    
1475     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1476         """       @rtype: L{Data<escript.Data>}
1477         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.
1478         """
1479         if self.hasCoefficient(name):
1480            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1481         else:
1482            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1483    
1484         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1485         """       """
1486         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  
1487    
1488         @param u:       @param name: name of the coefficient enquired.
1489         """       @type name: C{string}
1490         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1491         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1492         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1493         """
1494         if self.hasCoefficient(name):
1495            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1496         else:
1497            raise ValueError,"unknown coefficient %s requested"%name
1498       def getShapeOfCoefficient(self,name):
1499         """
1500         return the shape of the coefficient name
1501    
1502         @param name: name of the coefficient enquired.
1503         @type name: C{string}
1504         @return: the shape of the coefficient name
1505         @rtype: C{tuple} of C{int}
1506         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1507         """
1508         if self.hasCoefficient(name):
1509            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1510         else:
1511            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1512    
1513       def resetCoefficients(self):
1514         """
1515         resets all coefficients to there default values.
1516         """
1517         for i in self.COEFFICIENTS.iterkeys():
1518             self.COEFFICIENTS[i].resetValue()
1519    
1520     def __setValue(self,**coefficients):     def alteredCoefficient(self,name):
1521         """
1522         announce that coefficient name has been changed
1523    
1524         @param name: name of the coefficient enquired.
1525         @type name: C{string}
1526         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1527         @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.
1528         """
1529         if self.hasCoefficient(name):
1530            self.trace("Coefficient %s has been altered."%name)
1531            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1532               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1533               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1534         else:
1535            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1536    
1537       def copyConstraint(self,u):
1538        """        """
1539        sets new values to coefficient        copies the constraint into u and returns u.
1540    
1541          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1542          @type u: L{Data<escript.Data>}
1543          @return: the input u modified by the constraints.
1544          @rtype: L{Data<escript.Data>}
1545          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1546          """
1547          q=self.getCoefficientOfGeneralPDE("q")
1548          r=self.getCoefficientOfGeneralPDE("r")
1549          if not q.isEmpty():
1550             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1551             if r.isEmpty():
1552                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1553             else:
1554                 r=escript.Data(r,u.getFunctionSpace())
1555             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1556          return u
1557    
1558        @param coefficients:     def setValue(self,**coefficients):
1559          """
1560          sets new values to coefficients
1561    
1562          @param coefficients: new values assigned to coefficients
1563          @keyword A: value for coefficient A.
1564          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1565          @keyword A_reduced: value for coefficient A_reduced.
1566          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1567          @keyword B: value for coefficient B
1568          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1569          @keyword B_reduced: value for coefficient B_reduced
1570          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1571          @keyword C: value for coefficient C
1572          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1573          @keyword C_reduced: value for coefficient C_reduced
1574          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1575          @keyword D: value for coefficient D
1576          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1577          @keyword D_reduced: value for coefficient D_reduced
1578          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1579          @keyword X: value for coefficient X
1580          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1581          @keyword X_reduced: value for coefficient X_reduced
1582          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1583          @keyword Y: value for coefficient Y
1584          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1585          @keyword Y_reduced: value for coefficient Y_reduced
1586          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1587          @keyword d: value for coefficient d
1588          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1589          @keyword d_reduced: value for coefficient d_reduced
1590          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1591          @keyword y: value for coefficient y
1592          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1593          @keyword d_contact: value for coefficient d_contact
1594          @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>}.
1595          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1596          @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>}.
1597          @keyword y_contact: value for coefficient y_contact
1598          @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>}.
1599          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1600          @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>}.
1601          @keyword r: values prescribed to the solution at the locations of constraints
1602          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1603                   depending of reduced order is used for the solution.
1604          @keyword q: mask for location of constraints
1605          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1606                   depending of reduced order is used for the representation of the equation.
1607          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1608        """        """
1609        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1610        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1611           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1612              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1613        # 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:
1614        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1615           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1616              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1617                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1621  class LinearPDE:
1621                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1622              if s!=None:              if s!=None:
1623                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1624                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1625                  if res==None:                  if res==None:
1626                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1627                  else:                  else:
1628                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1629                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1630        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1631        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1632        # 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:
1633        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1634          if d==None:          try:
1635               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1636          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1637               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1638                  d2=d             self.alteredCoefficient(i)
1639               else:          except IllegalCoefficientFunctionSpace,m:
1640                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1641          else:              i_red=i+"_reduced"
1642                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1643          if not d2.isEmpty():                  try:
1644             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1645                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1646          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1647          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1648          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1649          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1650                          except IllegalCoefficientFunctionSpace,m:
1651        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1652        self.__setHomogeneousConstraintFlag()              else:
1653        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1654            except IllegalCoefficientValue,m:
1655     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1656        """        self.__altered_coefficients=True
1657        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1658        """        if len(coefficients)>0 and not self.isUsingLumping():
1659        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1660        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1661        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1662        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1663           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1664        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1665             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.)  
1666    
1667     def getSystem(self):     def getSystem(self):
1668         """         """
1669         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1670    
1671           @return: the discrete version of the PDE
1672           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1673         """         """
1674         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1675            if self.isUsingLumping():            if self.isUsingLumping():
1676                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1677                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1678                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1679                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1680                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1681                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1682                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1683                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1684                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1685                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1686                   mat=self.__getNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1687                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1688                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1689                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1690                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1691                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1692                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1693                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1694                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1695                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1696                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1697                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1698                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1699                   self.__applyConstraint()                   if not D.isEmpty():
1700                   self.__operator_isValid=True                       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                     if not d.isEmpty():
1707                         if self.getNumSolutions()>1:
1708                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1709                         else:
1710                            d_times_e=d
1711                     else:
1712                        d_times_e=escript.Data()
1713          
1714                     if not D_reduced.isEmpty():
1715                         if self.getNumSolutions()>1:
1716                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1717                         else:
1718                            D_reduced_times_e=D_reduced
1719                     else:
1720                        D_reduced_times_e=escript.Data()
1721                     if not d_reduced.isEmpty():
1722                         if self.getNumSolutions()>1:
1723                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1724                         else:
1725                            d_reduced_times_e=d_reduced
1726                     else:
1727                        d_reduced_times_e=escript.Data()
1728    
1729                     self.__operator=self.__getNewRightHandSide()
1730                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1731                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1732                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1733                     else:
1734                        self.getDomain().addPDEToRHS(self.__operator, \
1735                                                     escript.Data(), \
1736                                                     D_times_e, \
1737                                                     d_times_e,\
1738                                                     escript.Data())
1739                        self.getDomain().addPDEToRHS(self.__operator, \
1740                                                     escript.Data(), \
1741                                                     D_reduced_times_e, \
1742                                                     d_reduced_times_e,\
1743                                                     escript.Data())
1744                     self.__operator=1./self.__operator
1745                     self.trace("New lumped operator has been built.")
1746                     self.__operator_is_Valid=True
1747                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1748                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1749                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1750                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1751                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1752                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1753                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1754                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1755                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1756                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1757                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1758                     self.trace("New right hand side as been built.")
1759                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1760            else:            else:
1761               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."  
1762                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1763                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1764                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1765                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1766                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1767                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1768                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1769                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1770                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1771                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1772                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1773                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1774                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1775                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1776                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1777                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1780                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1781                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1783                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1784                   self.__applyConstraint()                   self.__applyConstraint()
1785                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1786                   self.__operator_isValid=True                   self.trace("New system has been built.")
1787                     self.__operator_is_Valid=True
1788                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1789               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1790                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1791                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1792                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1793                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1794                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1795                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1796                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1798                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1799                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1800                     self.__righthandside=self.copyConstraint(self.__righthandside)
1801                     self.trace("New right hand side has been built.")
1802                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1803               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1804                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1805                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1806                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1807                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1808                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1809                                escript.Data(), \
1810                                escript.Data(), \
1811                                self.getCoefficientOfGeneralPDE("d"), \
1812                                escript.Data(),\
1813                                self.getCoefficientOfGeneralPDE("d_contact"), \
1814                                escript.Data())
1815                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1816                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1817                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1818                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1819                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1820                              escript.Data(), \                              escript.Data(), \
1821                              escript.Data(), \                              escript.Data(), \
1822                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1823                              escript.Data(),\                              escript.Data(),\
1824                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1825                              escript.Data())                              escript.Data())
1826                   self.__applyConstraint()                   self.__applyConstraint()
1827                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1828                     self.__operator_is_Valid=True
1829         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1830    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1831    
1832     def solve(self,**options):  class Poisson(LinearPDE):
1833        """     """
1834        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1835    
1836        @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  
1837    
1838     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  
1839    
1840       M{n[j]*grad(u)[j] = 0 }
1841    
1842       and constraints:
1843    
1844  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())  
1845    
 class AdvectivePDE(LinearPDE):  
1846     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1847    
1848     \f[     def __init__(self,domain,debug=False):
1849     -(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       """
1850     \f]       initializes a new Poisson equation
1851    
1852         @param domain: domain of the PDE
1853         @type domain: L{Domain<escript.Domain>}
1854         @param debug: if True debug informations are printed.
1855    
1856         """
1857         super(Poisson, self).__init__(domain,1,1,debug)
1858         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1859                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1860                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1861         self.setSymmetryOn()
1862    
1863       def setValue(self,**coefficients):
1864         """
1865         sets new values to coefficients
1866    
1867         @param coefficients: new values assigned to coefficients
1868         @keyword f: value for right hand side M{f}
1869         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1870         @keyword q: mask for location of constraints
1871         @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>}
1872                   depending of reduced order is used for the representation of the equation.
1873         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1874         """
1875         super(Poisson, self).setValue(**coefficients)
1876    
1877       def getCoefficientOfGeneralPDE(self,name):
1878         """
1879         return the value of the coefficient name of the general PDE
1880         @param name: name of the coefficient requested.
1881         @type name: C{string}
1882         @return: the value of the coefficient  name
1883         @rtype: L{Data<escript.Data>}
1884         @raise IllegalCoefficient: if name is not one of coefficients
1885                      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}.
1886         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1887         """
1888         if name == "A" :
1889             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1890         elif name == "B" :
1891             return escript.Data()
1892         elif name == "C" :
1893             return escript.Data()
1894         elif name == "D" :
1895             return escript.Data()
1896         elif name == "X" :
1897             return escript.Data()
1898         elif name == "Y" :
1899             return self.getCoefficient("f")
1900         elif name == "d" :
1901             return escript.Data()
1902         elif name == "y" :
1903             return escript.Data()
1904         elif name == "d_contact" :
1905             return escript.Data()
1906         elif name == "y_contact" :
1907             return escript.Data()
1908         elif name == "A_reduced" :
1909             return escript.Data()
1910         elif name == "B_reduced" :
1911             return escript.Data()
1912         elif name == "C_reduced" :
1913             return escript.Data()
1914         elif name == "D_reduced" :
1915             return escript.Data()
1916         elif name == "X_reduced" :
1917             return escript.Data()
1918         elif name == "Y_reduced" :
1919             return self.getCoefficient("f_reduced")
1920         elif name == "d_reduced" :
1921             return escript.Data()
1922         elif name == "y_reduced" :
1923             return escript.Data()
1924         elif name == "d_contact_reduced" :
1925             return escript.Data()
1926         elif name == "y_contact_reduced" :
1927             return escript.Data()
1928         elif name == "r" :
1929             return escript.Data()
1930         elif name == "q" :
1931             return self.getCoefficient("q")
1932         else:
1933            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1934    
1935     with boundary conditons:  class Helmholtz(LinearPDE):
1936       """
1937       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1938    
1939     \f[     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
1940    
1941     and contact conditions     with natural boundary conditons
1942    
1943     \f[     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    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]  
1944    
1945     and constraints:     and constraints:
1946    
1947     \f[     M{u=r} where M{q>0}
1948     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1949     """     """
    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.  
1950    
1951     def setValue(self,**args):     def __init__(self,domain,debug=False):
1952         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1953         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)  
1954    
1955              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1956              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1957                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
1958                 A_max=util.Lsup(length_of_A)  
1959                 if A_max>0:       """
1960                      inv_A=1./(length_of_A+A_max*self.TOL)       super(Helmholtz, self).__init__(domain,1,1,debug)
1961                 else:       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1962                      inv_A=1./self.TOL                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1963                 peclet_number=length_of_Z*h/2*inv_A                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1964                 xi=self.__xi(peclet_number)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1965                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1966                 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),
1967        return self.__Xi                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1968                                  "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1969                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1970         self.setSymmetryOn()
1971    
1972     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
1973       """       """
1974       return the value of the coefficient name of the general PDE       sets new values to coefficients
1975    
1976       @param name:       @param coefficients: new values assigned to coefficients
1977         @keyword omega: value for coefficient M{S{omega}}
1978         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1979         @keyword k: value for coefficeint M{k}
1980         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1981         @keyword f: value for right hand side M{f}
1982         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1983         @keyword alpha: value for right hand side M{S{alpha}}
1984         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1985         @keyword g: value for right hand side M{g}
1986         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1987         @keyword r: prescribed values M{r} for the solution in constraints.
1988         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1989                   depending of reduced order is used for the representation of the equation.
1990         @keyword q: mask for location of constraints
1991         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1992                   depending of reduced order is used for the representation of the equation.
1993         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1994       """       """
1995       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."  
1996    
1997       if name == "A" :     def getCoefficientOfGeneralPDE(self,name):
1998           A=self.getCoefficient("A")       """
1999           B=self.getCoefficient("B")       return the value of the coefficient name of the general PDE
2000           C=self.getCoefficient("C")  
2001           if B.isEmpty() and C.isEmpty():       @param name: name of the coefficient requested.
2002              Aout=A       @type name: C{string}
2003           else:       @return: the value of the coefficient  name
2004              if A.isEmpty():       @rtype: L{Data<escript.Data>}
2005                 Aout=self.createNewCoefficient("A")       @raise IllegalCoefficient: if name is not one of coefficients
2006              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}.
2007                 Aout=A[:]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2008              Xi=self.getXi()       """
2009              if self.getNumEquations()>1:       if name == "A" :
2010                  for i in range(self.getNumEquations()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2011                     for j in range(self.getDim()):       elif name == "B" :
2012                        for k in range(self.getNumSolutions()):           return escript.Data()
2013                           for l in range(self.getDim()):       elif name == "C" :
2014                              if not C.isEmpty() and not B.isEmpty():           return escript.Data()
2015                                 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" :
2016                              elif C.isEmpty():           return self.getCoefficient("omega")
2017                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       elif name == "X" :
2018                              else:           return escript.Data()
2019                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       elif name == "Y" :
2020              else:           return self.getCoefficient("f")
2021                  for j in range(self.getDim()):       elif name == "d" :
2022                     for l in range(self.getDim()):           return self.getCoefficient("alpha")
2023                        if not C.isEmpty() and not B.isEmpty():       elif name == "y" :
2024                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])           return self.getCoefficient("g")
2025                        elif C.isEmpty():       elif name == "d_contact" :
2026                            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")  
2027       elif name == "y_contact" :       elif name == "y_contact" :
2028           return self.getCoefficient("y_contact")           return escript.Data()
2029       elif name == "r" :       elif name == "A_reduced" :
2030             return escript.Data()
2031         elif name == "B_reduced" :
2032             return escript.Data()
2033         elif name == "C_reduced" :
2034             return escript.Data()
2035         elif name == "D_reduced" :
2036             return escript.Data()
2037         elif name == "X_reduced" :
2038             return escript.Data()
2039         elif name == "Y_reduced" :
2040             return self.getCoefficient("f_reduced")
2041         elif name == "d_reduced" :
2042             return escript.Data()
2043         elif name == "y_reduced" :
2044            return self.getCoefficient("g_reduced")
2045         elif name == "d_contact_reduced" :
2046             return escript.Data()
2047         elif name == "y_contact_reduced" :
2048             return escript.Data()
2049         elif name == "r" :
2050           return self.getCoefficient("r")           return self.getCoefficient("r")
2051       elif name == "q" :       elif name == "q" :
2052           return self.getCoefficient("q")           return self.getCoefficient("q")
2053       else:       else:
2054           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2055    
2056  class Poisson(LinearPDE):  class LameEquation(LinearPDE):
2057     """     """
2058     Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
2059    
2060       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] }
2061    
2062       with natural boundary conditons:
2063    
2064     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]  
2065    
2066     and constraints:     and constraints:
2067    
2068     \f[     M{u[i]=r[i]} where M{q[i]>0}
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
2069    
2070     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)  
2071    
2072     def setValue(self,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2073         self._LinearPDE__setValue(f=f,q=q)        super(LameEquation, self).__init__(domain,\
2074                                             domain.getDim(),domain.getDim(),debug)
2075          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2076                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2077                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2078                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2079                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2080                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2081                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2082          self.setSymmetryOn()
2083    
2084       def setValues(self,**coefficients):
2085         """
2086         sets new values to coefficients
2087    
2088         @param coefficients: new values assigned to coefficients
2089         @keyword lame_mu: value for coefficient M{S{mu}}
2090         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2091         @keyword lame_lambda: value for coefficient M{S{lambda}}
2092         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2093         @keyword F: value for internal force M{F}
2094         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2095         @keyword sigma: value for initial stress M{S{sigma}}
2096         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2097         @keyword f: value for extrenal force M{f}
2098         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2099         @keyword r: prescribed values M{r} for the solution in constraints.
2100         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2101                   depending of reduced order is used for the representation of the equation.
2102         @keyword q: mask for location of constraints
2103         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2104                   depending of reduced order is used for the representation of the equation.
2105         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2106         """
2107         super(LameEquation, self).setValues(**coefficients)
2108    
2109     def getCoefficientOfPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2110       """       """
2111       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2112    
2113       @param name:       @param name: name of the coefficient requested.
2114       """       @type name: C{string}
2115       if name == "A" :       @return: the value of the coefficient  name
2116           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @rtype: L{Data<escript.Data>}
2117       elif name == "B" :       @raise IllegalCoefficient: if name is not one of coefficients
2118                      "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}.
2119         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2120         """
2121         if name == "A" :
2122             out =self.createCoefficientOfGeneralPDE("A")
2123             for i in range(self.getDim()):
2124               for j in range(self.getDim()):
2125                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2126                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2127                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2128             return out
2129         elif name == "B" :
2130           return escript.Data()           return escript.Data()
2131       elif name == "C" :       elif name == "C" :
2132           return escript.Data()           return escript.Data()
2133       elif name == "D" :       elif name == "D" :
2134           return escript.Data()           return escript.Data()
2135       elif name == "X" :       elif name == "X" :
2136             return self.getCoefficient("sigma")
2137         elif name == "Y" :
2138             return self.getCoefficient("F")
2139         elif name == "d" :
2140           return escript.Data()           return escript.Data()
2141       elif name == "Y" :       elif name == "y" :
2142           return self.getCoefficient("f")           return self.getCoefficient("f")
2143       elif name == "d" :       elif name == "d_contact" :
2144           return escript.Data()           return escript.Data()
2145       elif name == "y" :       elif name == "y_contact" :
2146           return escript.Data()           return escript.Data()
2147       elif name == "d_contact" :       elif name == "A_reduced" :
2148           return escript.Data()           return escript.Data()
2149       elif name == "y_contact" :       elif name == "B_reduced" :
2150             return escript.Data()
2151         elif name == "C_reduced" :
2152             return escript.Data()
2153         elif name == "D_reduced" :
2154             return escript.Data()
2155         elif name == "X_reduced" :
2156             return escript.Data()
2157         elif name == "Y_reduced" :
2158           return escript.Data()           return escript.Data()
2159       elif name == "r" :       elif name == "d_reduced" :
2160           return escript.Data()           return escript.Data()
2161       elif name == "q" :       elif name == "y_reduced" :
2162             return escript.Data()
2163         elif name == "d_contact_reduced" :
2164             return escript.Data()
2165         elif name == "y_contact_reduced" :
2166             return escript.Data()
2167         elif name == "r" :
2168             return self.getCoefficient("r")
2169         elif name == "q" :
2170           return self.getCoefficient("q")           return self.getCoefficient("q")
2171       else:       else:
2172           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2173    
 # $Log$  
 # 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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