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trunk/esys2/escript/py_src/linearPDEs.py revision 110 by jgs, Mon Feb 14 04:14:42 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1639 by gross, Mon Jul 14 08:55:25 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4  ## @file linearPDEs.py  #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
19    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
20    solver capabilities in itself but hands the PDE over to
21    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
22    The general interface is provided through the L{LinearPDE} class. The
23    L{AdvectivePDE} which is derived from the L{LinearPDE} class
24    provides an interface to PDE dominated by its advective terms. The L{Poisson},
25    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26    classs which are also derived form the L{LinearPDE} class should be used
27    to define of solve these sepecial PDEs.
28    
29    @var __author__: name of author
30    @var __copyright__: copyrights
31    @var __license__: licence agreement
32    @var __url__: url entry point on documentation
33    @var __version__: version
34    @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
41    
42    __author__="Lutz Gross, l.gross@uq.edu.au"
43    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
44                        http://www.access.edu.au
45                    Primary Business: Queensland, Australia"""
46    __license__="""Licensed under the Open Software License version 3.0
47                 http://www.opensource.org/licenses/osl-3.0.php"""
48    __url__="http://www.iservo.edu.au/esys"
49    __version__="$Revision$"
50    __date__="$Date$"
51    
52    
53    class IllegalCoefficient(ValueError):
54       """
55       raised if an illegal coefficient of the general ar particular PDE is requested.
56       """
57       pass
58    
59    class IllegalCoefficientValue(ValueError):
60       """
61       raised if an incorrect value for a coefficient is used.
62       """
63       pass
64    
65  def _CompTuple2(t1,t2):  class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68     """     """
    @brief  
69    
70     @param t1  class UndefinedPDEError(ValueError):
71     @param t2     """
72       raised if a PDE is not fully defined yet.
73     """     """
74     dif=t1[0]+t1[1]-(t2[0]+t2[1])     pass
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
75    
76  class PDECoefficient:  class PDECoefficient(object):
77      """      """
78      @brief      A class for describing a PDE coefficient
79    
80        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
89        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
90        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
91        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
92        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
93        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
94    
95      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
96      INTERIOR=0      INTERIOR=0
97      BOUNDARY=1      BOUNDARY=1
98      CONTACT=2      CONTACT=2
99      CONTINUOUS=3      SOLUTION=3
100      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
101      # 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
102      # number of unknowns.      BY_SOLUTION=6
103      EQUATION=3      BY_DIM=7
104      SOLUTION=4      OPERATOR=10
105      DIM=5      RIGHTHANDSIDE=11
106      # indicator for what is altered if the coefficient is altered:      BOTH=12
107      OPERATOR=5      INTERIOR_REDUCED=13
108      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
109      BOTH=7      CONTACT_REDUCED=15
110      def __init__(self,where,pattern,altering):  
111         """      def __init__(self, where, pattern, altering):
112         @brief Initialise a PDE Coefficient type         """
113           Initialise a PDE Coefficient type
114    
115           @param where: describes where the coefficient lives
116           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118           @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                  spatial dimension and numbers of equation and solution in then PDE. For instance,
120                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
121                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
122                  on a 2-dimensional domain. In the case of single equation and a single solution component
123                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
124                  the example would be read as (2,).
125           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131           super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
133         self.pattern=pattern         self.pattern=pattern
134         self.altering=altering         self.altering=altering
# Line 53  class PDECoefficient: Line 136  class PDECoefficient:
136    
137      def resetValue(self):      def resetValue(self):
138         """         """
139         @brief resets coefficient value to default         resets coefficient value to default
140         """         """
141         self.value=escript.Data()         self.value=escript.Data()
142    
143      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
144         """         """
145         @brief defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
146    
147         @param domain         @param domain: domain on which the PDE uses the coefficient
148         """         @type domain: L{Domain<escript.Domain>}
149         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
150         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
151         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
152         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
153           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
154           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
155           """
156           if self.what==self.INTERIOR:
157                return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160           elif self.what==self.BOUNDARY:
161                return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164           elif self.what==self.CONTACT:
165                return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168           elif self.what==self.SOLUTION:
169                if reducedEquationOrder and reducedSolutionOrder:
170                    return escript.ReducedSolution(domain)
171                else:
172                    return escript.Solution(domain)
173           elif self.what==self.REDUCED:
174                return escript.ReducedSolution(domain)
175    
176      def getValue(self):      def getValue(self):
177         """         """
178         @brief returns the value of the coefficient:         returns the value of the coefficient
179    
180           @return:  value of the coefficient
181           @rtype:  L{Data<escript.Data>}
182         """         """
183         return self.value         return self.value
184        
185      def setValue(self,newValue):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
        """  
        @brief set the value of the coefficient to new value  
186         """         """
187           set the value of the coefficient to a new value
188    
189           @param domain: domain on which the PDE uses the coefficient
190           @type domain: L{Domain<escript.Domain>}
191           @param numEquations: number of equations of the PDE
192           @type numEquations: C{int}
193           @param numSolutions: number of components of the PDE solution
194           @type numSolutions: C{int}
195           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
196           @type reducedEquationOrder: C{bool}
197           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
198           @type reducedSolutionOrder: C{bool}
199           @param newValue: number of components of the PDE solution
200           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203           """
204           if newValue==None:
205               newValue=escript.Data()
206           elif isinstance(newValue,escript.Data):
207               if not newValue.isEmpty():
208                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                    try:
210                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                    except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213           else:
214               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215           if not newValue.isEmpty():
216               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
217                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
218         self.value=newValue         self.value=newValue
219        
220      def isAlteringOperator(self):      def isAlteringOperator(self):
221          """          """
222      @brief 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
223    
224            @return:  True if the operator of the PDE is changed when the coefficient is changed
225            @rtype:  C{bool}
226      """      """
227          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
228              return not None              return not None
# Line 91  class PDECoefficient: Line 231  class PDECoefficient:
231    
232      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
233          """          """
234      @brief 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
235    
236        @rtype:  C{bool}
237            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
238      """      """
239          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
240              return not None              return not None
241          else:          else:
242              return None              return None
243    
244      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
245         """         """
246         @brief 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
247    
248         @param shape         @param domain: domain on which the PDE uses the coefficient
249         @param dim         @type domain: L{Domain<escript.Domain>}
250           @param shape: suggested shape of the coefficient
251           @type shape: C{tuple} of C{int} values
252           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
253                     If no appropriate numbers could be identified, C{None} is returned
254           @rtype: C{tuple} of two C{int} values or C{None}
255         """         """
256           dim=domain.getDim()
257         if len(shape)>0:         if len(shape)>0:
258             num=max(shape)+1             num=max(shape)+1
259         else:         else:
260             num=1             num=1
261         search=[]         search=[]
262         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
263            for e in range(num):            for u in range(num):
264               search.append((e,u))               for e in range(num):
265         search.sort(_CompTuple2)                  search.append((e,u))
266         for item in search:            search.sort(self.__CompTuple2)
267               s=self.buildShape(item[0],item[1],dim)            for item in search:
268                 s=self.getShape(domain,item[0],item[1])
269               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
270                   return (1,1)                   return (1,1)
271               else:               else:
272                   if s==shape: return item                   if s==shape: return item
273           elif self.definesNumEquation():
274              for e in range(num,0,-1):
275                 s=self.getShape(domain,e,0)
276                 if len(s)==0 and len(shape)==0:
277                     return (1,None)
278                 else:
279                     if s==shape: return (e,None)
280    
281           elif self.definesNumSolutions():
282              for u in range(num,0,-1):
283                 s=self.getShape(domain,0,u)
284                 if len(s)==0 and len(shape)==0:
285                     return (None,1)
286                 else:
287                     if s==shape: return (None,u)
288         return None         return None
289        def definesNumSolutions(self):
290           """
291           checks if the coefficient allows to estimate the number of solution components
292    
293      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
294          """         @rtype: C{bool}
295      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
296           for i in self.pattern:
297                 if i==self.BY_SOLUTION: return True
298           return False
299    
300      @param e      def definesNumEquation(self):
301      @param u         """
302      @param dim         checks if the coefficient allows to estimate the number of equations
303      """  
304          s=()         @return: True if the coefficient allows an estimate of the number of equations
305          for i in self.pattern:         @rtype: C{bool}
306               if i==self.EQUATION:         """
307                  if e>1: s=s+(e,)         for i in self.pattern:
308               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
309                  if u>1: s=s+(u,)         return False
310    
311        def __CompTuple2(self,t1,t2):
312          """
313          Compare two tuples of possible number of equations and number of solutions
314    
315          @param t1: The first tuple
316          @param t2: The second tuple
317    
318          """
319    
320          dif=t1[0]+t1[1]-(t2[0]+t2[1])
321          if dif<0: return 1
322          elif dif>0: return -1
323          else: return 0
324    
325        def getShape(self,domain,numEquations=1,numSolutions=1):
326           """
327           builds the required shape of the coefficient
328    
329           @param domain: domain on which the PDE uses the coefficient
330           @type domain: L{Domain<escript.Domain>}
331           @param numEquations: number of equations of the PDE
332           @type numEquations: C{int}
333           @param numSolutions: number of components of the PDE solution
334           @type numSolutions: C{int}
335           @return: shape of the coefficient
336           @rtype: C{tuple} of C{int} values
337           """
338           dim=domain.getDim()
339           s=()
340           for i in self.pattern:
341                 if i==self.BY_EQUATION:
342                    if numEquations>1: s=s+(numEquations,)
343                 elif i==self.BY_SOLUTION:
344                    if numSolutions>1: s=s+(numSolutions,)
345               else:               else:
346                  s=s+(dim,)                  s=s+(dim,)
347          return s         return s
348    
349  class LinearPDE:  class LinearPDE(object):
350     """     """
351     @brief Class to handel a linear PDE     This class is used to define a general linear, steady, second order PDE
352         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  
353    
354       -(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     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
355    
356       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)}
357    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
358    
359      and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361       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
362       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
363       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       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.
366    
367          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     The following natural boundary conditions are considered:
368    
369      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}
370    
371           u_i=r_i where q_i>0     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>}.
372    
    """  
    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  
373    
374     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
      """  
      @brief initializes a new linear PDE.  
375    
376       @param args     M{u=r}  where M{q>0}
377       """  
378       # 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.
379       self.COEFFICIENTS={     The constraints override any other condition set by the PDE or the boundary condition.
380         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
381         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The PDE is symmetrical if
382         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
383         "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]}
384         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
385         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     For a system of PDEs and a solution with several components the PDE has the form
386         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
387         "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] }
388         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
389         "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.
390         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     The natural boundary conditions take the form:
391         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
392       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]}
393    
394    
395       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>}.
396    
397       Constraints take the form
398    
399       M{u[i]=r[i]}  where  M{q[i]>0}
400    
401       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
402    
403       The system of PDEs is symmetrical if
404    
405            - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407            - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409            - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411            - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415       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
416       defined as
417    
418       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]}
419    
420       For the case of single solution component and single PDE M{J} is defined
421    
422       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426       the contact condition takes the form
427    
428       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]}
429    
430       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
431       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432       L{jump<util.jump>}.
433       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>}.
434       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>}.
435       In case of a single PDE and a single component solution the contact condition takes the form
436    
437       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439       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>}
440    
441       @cvar DEFAULT: The default method used to solve the system of linear equations
442       @cvar DIRECT: The direct solver based on LDU factorization
443       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
444       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
445       @cvar CR: The conjugate residual method
446       @cvar CGS: The conjugate gardient square method
447       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
448       @cvar SSOR: The symmetric overrealaxtion method
449       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
450       @cvar ILUT: The incomplete LU factorization preconditioner with will in
451       @cvar JACOBI: The Jacobi preconditioner
452       @cvar GMRES: The Gram-Schmidt minimum residual method
453       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
454       @cvar LUMPING: Matrix lumping.
455       @cvar NO_REORDERING: No matrix reordering allowed
456       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
457       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
458       @cvar PASO: PASO solver package
459       @cvar SCSL: SGI SCSL solver library
460       @cvar MKL: Intel's MKL solver library
461       @cvar UMFPACK: the UMFPACK library
462       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
463       @cvar ITERATIVE: The default iterative solver
464       @cvar AMG: algebraic multi grid
465       @cvar RILU: recursive ILU
466    
467       """
468       DEFAULT= 0
469       DIRECT= 1
470       CHOLEVSKY= 2
471       PCG= 3
472       CR= 4
473       CGS= 5
474       BICGSTAB= 6
475       SSOR= 7
476       ILU0= 8
477       ILUT= 9
478       JACOBI= 10
479       GMRES= 11
480       PRES20= 12
481       LUMPING= 13
482       NO_REORDERING= 17
483       MINIMUM_FILL_IN= 18
484       NESTED_DISSECTION= 19
485       SCSL= 14
486       MKL= 15
487       UMFPACK= 16
488       ITERATIVE= 20
489       PASO= 21
490       AMG= 22
491       RILU = 23
492       TRILINOS = 24
493       NONLINEAR_GMRES = 25
494    
495       SMALL_TOLERANCE=1.e-13
496       __PACKAGE_KEY="package"
497       __METHOD_KEY="method"
498       __SYMMETRY_KEY="symmetric"
499       __TOLERANCE_KEY="tolerance"
500       __PRECONDITIONER_KEY="preconditioner"
501    
502    
503       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
504         """
505         initializes a new linear PDE
506    
507         @param domain: domain of the PDE
508         @type domain: L{Domain<escript.Domain>}
509         @param numEquations: number of equations. If numEquations==None the number of equations
510                              is exracted from the PDE coefficients.
511         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
512                              is exracted from the PDE coefficients.
513         @param debug: if True debug informations are printed.
514    
515         """
516         super(LinearPDE, self).__init__()
517         #
518         #   the coefficients of the general PDE:
519         #
520         self.__COEFFICIENTS_OF_GENEARL_PDE={
521           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
522           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
524           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
525           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
526           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
530           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
534           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
535           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
536           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
540           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
542           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
543    
544         # COEFFICIENTS can be overwritten by subclasses:
545         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
546         self.__altered_coefficients=False
547       # initialize attributes       # initialize attributes
548       self.__debug=None       self.__debug=debug
549       self.__domain=domain       self.__domain=domain
550       self.__numEquations=numEquations       self.__numEquations=numEquations
551       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
552       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  
553    
554       # set some default values:       # set some default values:
555       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
556       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
557       self.__tolerance=1.e-8       self.__tolerance=1.e-8
558       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
559       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
560         self.__preconditioner=self.DEFAULT
561         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
562       self.__sym=False       self.__sym=False
      self.__lumping=False  
563    
564     def createCoefficient(self, name):       self.resetCoefficients()
565         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
566       # =============================================================================
567       #    general stuff:
568       # =============================================================================
569       def __str__(self):
570         """
571         returns string representation of the PDE
572    
573         @return: a simple representation of the PDE
574         @rtype: C{str}
575         """
576         return "<LinearPDE %d>"%id(self)
577       # =============================================================================
578       #    debug :
579       # =============================================================================
580       def setDebugOn(self):
581       """       """
582       @brief create a data object corresponding to coefficient name       switches on debugging
      @param name  
583       """       """
584       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
585    
586     def __del__(self):     def setDebugOff(self):
587       pass       """
588         switches off debugging
    def getCoefficient(self,name):  
589       """       """
590       @brief return the value of the parameter name       self.__debug=None
591    
592       @param name     def trace(self,text):
593       """       """
594       return self.COEFFICIENTS[name].getValue()       print the text message if debugging is swiched on.
595         @param text: message
596         @type text: C{string}
597         """
598         if self.__debug: print "%s: %s"%(str(self),text)
599    
600     def getCoefficientOfPDE(self,name):     # =============================================================================
601       # some service functions:
602       # =============================================================================
603       def getDomain(self):
604       """       """
605       @brief return the value of the coefficient name of the general PDE. This method is called by the assembling routine       returns the domain of the PDE
606              it can be overwritten to map coefficients of a particualr PDE to the general PDE.  
607       @param name       @return: the domain of the PDE
608         @rtype: L{Domain<escript.Domain>}
609       """       """
610       return self.getCoefficient(name)       return self.__domain
611    
612     def hasCoefficient(self,name):     def getDim(self):
613        """       """
614        @brief return true if name is the name of a coefficient       returns the spatial dimension of the PDE
615    
616        @param name       @return: the spatial dimension of the PDE domain
617        """       @rtype: C{int}
618        return self.COEFFICIENTS.has_key(name)       """
619         return self.getDomain().getDim()
620    
621     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
622       """       """
623       @brief return true if the test functions should use reduced order       returns the number of equations
624    
625         @return: the number of equations
626         @rtype: C{int}
627         @raise UndefinedPDEError: if the number of equations is not be specified yet.
628       """       """
629       return self.__row_function_space       if self.__numEquations==None:
630             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
631         else:
632             return self.__numEquations
633    
634     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
635       """       """
636       @brief return true if the interpolation of the solution should use reduced order       returns the number of unknowns
637    
638         @return: the number of unknowns
639         @rtype: C{int}
640         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
641       """       """
642       return self.__column_function_space       if self.__numSolutions==None:
643            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
644         else:
645            return self.__numSolutions
646    
647     def setValue(self,**coefficients):     def reduceEquationOrder(self):
648        """       """
649        @brief sets new values to coefficients       return status for order reduction for equation
650    
651        @param coefficients       @return: return True is reduced interpolation order is used for the represenation of the equation
652        """       @rtype: L{bool}
653        self._setValue(**coefficients)       """
654               return self.__reduce_equation_order
655    
656     def cleanCoefficients(self):     def reduceSolutionOrder(self):
657       """       """
658       @brief resets all coefficients to default values.       return status for order reduction for the solution
659    
660         @return: return True is reduced interpolation order is used for the represenation of the solution
661         @rtype: L{bool}
662       """       """
663       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
664    
665     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
666       """       """
667       @brief returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
668    
669         @return: representation space of equation
670         @rtype: L{FunctionSpace<escript.FunctionSpace>}
671       """       """
672       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
673                   return escript.ReducedSolution(self.getDomain())
674         else:
675             return escript.Solution(self.getDomain())
676    
677     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
678       """       """
679       @brief return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
680    
681       @param name       @return: representation space of solution
682         @rtype: L{FunctionSpace<escript.FunctionSpace>}
683       """       """
684       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
685          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
686       else:       else:
687          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
688    
689     def getFunctionSpaceForCoefficient(self,name):  
690       def getOperator(self):
691       """       """
692       @brief return the atoms of the coefficient name       provides access to the operator of the PDE
693    
694       @param name       @return: the operator of the PDE
695         @rtype: L{Operator<escript.Operator>}
696       """       """
697       if self.hasCoefficient(name):       m=self.getSystem()[0]
698          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
699             return self.copyConstraint(1./m)
700       else:       else:
701          raise ValueError,"Solution coefficient %s requested"%name           return m
702    
703     def alteredCoefficient(self,name):     def getRightHandSide(self):
704       """       """
705       @brief annonced that coefficient name has been changed       provides access to the right hand side of the PDE
706         @return: the right hand side of the PDE
707         @rtype: L{Data<escript.Data>}
708         """
709         r=self.getSystem()[1]
710         if self.isUsingLumping():
711             return self.copyConstraint(r)
712         else:
713             return r
714    
715       @param name     def applyOperator(self,u=None):
716       """       """
717       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
718          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
719          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}
720                   the current solution is used.
721         @type u: L{Data<escript.Data>} or None
722         @return: image of u
723         @rtype: L{Data<escript.Data>}
724         """
725         if u==None:
726            return self.getOperator()*self.getSolution()
727       else:       else:
728          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
729    
730     # ===== debug ==============================================================     def getResidual(self,u=None):
731     def setDebugOn(self):       """
732         """       return the residual of u or the current solution if u is not present.
        @brief  
        """  
        self.__debug=not None  
733    
734     def setDebugOff(self):       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
735                   the current solution is used.
736         @type u: L{Data<escript.Data>} or None
737         @return: residual of u
738         @rtype: L{Data<escript.Data>}
739         """
740         return self.applyOperator(u)-self.getRightHandSide()
741    
742       def checkSymmetry(self,verbose=True):
743          """
744          test the PDE for symmetry.
745    
746          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
747          @type verbose: C{bool}
748          @return:  True if the PDE is symmetric.
749          @rtype: L{Data<escript.Data>}
750          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
751          """
752          verbose=verbose or self.__debug
753          out=True
754          if self.getNumSolutions()!=self.getNumEquations():
755             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
756             out=False
757          else:
758             A=self.getCoefficientOfGeneralPDE("A")
759             if not A.isEmpty():
760                tol=util.Lsup(A)*self.SMALL_TOLERANCE
761                if self.getNumSolutions()>1:
762                   for i in range(self.getNumEquations()):
763                      for j in range(self.getDim()):
764                         for k in range(self.getNumSolutions()):
765                            for l in range(self.getDim()):
766                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
767                                   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)
768                                   out=False
769                else:
770                   for j in range(self.getDim()):
771                      for l in range(self.getDim()):
772                         if util.Lsup(A[j,l]-A[l,j])>tol:
773                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
774                            out=False
775             B=self.getCoefficientOfGeneralPDE("B")
776             C=self.getCoefficientOfGeneralPDE("C")
777             if B.isEmpty() and not C.isEmpty():
778                if verbose: print "non-symmetric PDE because B is not present but C is"
779                out=False
780             elif not B.isEmpty() and C.isEmpty():
781                if verbose: print "non-symmetric PDE because C is not present but B is"
782                out=False
783             elif not B.isEmpty() and not C.isEmpty():
784                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
785                if self.getNumSolutions()>1:
786                   for i in range(self.getNumEquations()):
787                       for j in range(self.getDim()):
788                          for k in range(self.getNumSolutions()):
789                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
790                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
791                                  out=False
792                else:
793                   for j in range(self.getDim()):
794                      if util.Lsup(B[j]-C[j])>tol:
795                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
796                         out=False
797             if self.getNumSolutions()>1:
798               D=self.getCoefficientOfGeneralPDE("D")
799               if not D.isEmpty():
800                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
801                 for i in range(self.getNumEquations()):
802                    for k in range(self.getNumSolutions()):
803                      if util.Lsup(D[i,k]-D[k,i])>tol:
804                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
805                          out=False
806               d=self.getCoefficientOfGeneralPDE("d")
807               if not d.isEmpty():
808                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
809                 for i in range(self.getNumEquations()):
810                    for k in range(self.getNumSolutions()):
811                      if util.Lsup(d[i,k]-d[k,i])>tol:
812                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
813                          out=False
814               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
815               if not d_contact.isEmpty():
816                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
817                 for i in range(self.getNumEquations()):
818                    for k in range(self.getNumSolutions()):
819                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
820                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
821                          out=False
822             # and now the reduced coefficients
823             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
824             if not A_reduced.isEmpty():
825                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
826                if self.getNumSolutions()>1:
827                   for i in range(self.getNumEquations()):
828                      for j in range(self.getDim()):
829                         for k in range(self.getNumSolutions()):
830                            for l in range(self.getDim()):
831                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
832                                   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)
833                                   out=False
834                else:
835                   for j in range(self.getDim()):
836                      for l in range(self.getDim()):
837                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
838                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
839                            out=False
840             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
841             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
842             if B_reduced.isEmpty() and not C_reduced.isEmpty():
843                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
844                out=False
845             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
849                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
850                if self.getNumSolutions()>1:
851                   for i in range(self.getNumEquations()):
852                       for j in range(self.getDim()):
853                          for k in range(self.getNumSolutions()):
854                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
855                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
856                                  out=False
857                else:
858                   for j in range(self.getDim()):
859                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
860                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
861                         out=False
862             if self.getNumSolutions()>1:
863               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
864               if not D_reduced.isEmpty():
865                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
866                 for i in range(self.getNumEquations()):
867                    for k in range(self.getNumSolutions()):
868                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
869                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
870                          out=False
871               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
872               if not d_reduced.isEmpty():
873                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
874                 for i in range(self.getNumEquations()):
875                    for k in range(self.getNumSolutions()):
876                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
877                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
878                          out=False
879               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
880               if not d_contact_reduced.isEmpty():
881                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
882                 for i in range(self.getNumEquations()):
883                    for k in range(self.getNumSolutions()):
884                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
885                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
886                          out=False
887          return out
888    
889       def getSolution(self,**options):
890         """         """
891         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
892    
893           @return: the solution
894           @rtype: L{Data<escript.Data>}
895           @param options: solver options
896           @keyword verbose: True to get some information during PDE solution
897           @type verbose: C{bool}
898           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
899                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
900           @keyword iter_max: maximum number of iteration steps allowed.
901           @keyword drop_tolerance: threshold for drupping in L{ILUT}
902           @keyword drop_storage: maximum of allowed memory in L{ILUT}
903           @keyword truncation: maximum number of residuals in L{GMRES}
904           @keyword restart: restart cycle length in L{GMRES}
905         """         """
906         self.__debug=None         if not self.__solution_isValid:
907              mat,f=self.getSystem()
908              if self.isUsingLumping():
909                 self.__solution=self.copyConstraint(f*mat)
910              else:
911                 options[self.__TOLERANCE_KEY]=self.getTolerance()
912                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
913                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
914                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
915                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
916                 self.trace("PDE is resolved.")
917                 self.trace("solver options: %s"%str(options))
918                 self.__solution=mat.solve(f,options)
919              self.__solution_isValid=True
920           return self.__solution
921    
922       def getFlux(self,u=None):
923         """
924         returns the flux M{J} for a given M{u}
925    
926         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]}
927    
928     def debug(self):       or
929    
930         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
931    
932         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
933         @type u: L{Data<escript.Data>} or None
934         @return: flux
935         @rtype: L{Data<escript.Data>}
936         """
937         if u==None: u=self.getSolution()
938         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
939               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
940               -util.self.getCoefficientOfGeneralPDE("X") \
941               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X_reduced")
944       # =============================================================================
945       #   solver settings:
946       # =============================================================================
947       def setSolverMethod(self,solver=None,preconditioner=None):
948           """
949           sets a new solver
950    
951           @param solver: sets a new solver method.
952           @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}
953           @param preconditioner: sets a new solver method.
954           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
955           """
956           if solver==None: solver=self.__solver_method
957           if preconditioner==None: preconditioner=self.__preconditioner
958           if solver==None: solver=self.DEFAULT
959           if preconditioner==None: preconditioner=self.DEFAULT
960           if not (solver,preconditioner)==self.getSolverMethod():
961               self.__solver_method=solver
962               self.__preconditioner=preconditioner
963               self.__checkMatrixType()
964               self.trace("New solver is %s"%self.getSolverMethodName())
965    
966       def getSolverMethodName(self):
967         """         """
968         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
969    
970           @return: the name of the solver currently used.
971           @rtype: C{string}
972         """         """
        return self.__debug  
973    
974     #===== Lumping ===========================         m=self.getSolverMethod()
975     def setLumpingOn(self):         p=self.getSolverPackage()
976        """         method=""
977        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
978        """         elif m[0]==self.DIRECT: method= "DIRECT"
979        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
980           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
981           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
982           self.__lumping=True         elif m[0]==self.CR: method= "CR"
983           elif m[0]==self.CGS: method= "CGS"
984           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
985           elif m[0]==self.SSOR: method= "SSOR"
986           elif m[0]==self.GMRES: method= "GMRES"
987           elif m[0]==self.PRES20: method= "PRES20"
988           elif m[0]==self.LUMPING: method= "LUMPING"
989           elif m[0]==self.AMG: method= "AMG"
990           if m[1]==self.DEFAULT: method+="+DEFAULT"
991           elif m[1]==self.JACOBI: method+= "+JACOBI"
992           elif m[1]==self.ILU0: method+= "+ILU0"
993           elif m[1]==self.ILUT: method+= "+ILUT"
994           elif m[1]==self.SSOR: method+= "+SSOR"
995           elif m[1]==self.AMG: method+= "+AMG"
996           elif m[1]==self.RILU: method+= "+RILU"
997           if p==self.DEFAULT: package="DEFAULT"
998           elif p==self.PASO: package= "PASO"
999           elif p==self.MKL: package= "MKL"
1000           elif p==self.SCSL: package= "SCSL"
1001           elif p==self.UMFPACK: package= "UMFPACK"
1002           elif p==self.TRILINOS: package= "TRILINOS"
1003           else : method="unknown"
1004           return "%s solver of %s package"%(method,package)
1005    
    def setLumpingOff(self):  
       """  
       @brief switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
1006    
1007     def setLumping(self,flag=False):     def getSolverMethod(self):
1008        """         """
1009        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
1010    
1011     def isUsingLumping(self):         @return: the solver method currently be used.
1012        """         @rtype: C{int}
1013        @brief         """
1014        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
1015    
1016     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
1017         """         """
1018         @brief sets a new solver         sets a new solver package
1019    
1020           @param package: sets a new solver method.
1021           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1022         """         """
1023         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1024             self.__solver_method=solver         if not package==self.getSolverPackage():
1025             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1026             self.__checkMatrixType()             self.__checkMatrixType()
1027               self.trace("New solver is %s"%self.getSolverMethodName())
1028    
1029     def getSolverMethod(self):     def getSolverPackage(self):
1030         """         """
1031         @brief returns the solver method         returns the package of the solver
1032    
1033           @return: the solver package currently being used.
1034           @rtype: C{int}
1035         """         """
1036         return self.__solver_method         return self.__solver_package
1037    
1038       def isUsingLumping(self):
1039          """
1040          checks if matrix lumping is used a solver method
1041    
1042          @return: True is lumping is currently used a solver method.
1043          @rtype: C{bool}
1044          """
1045          return self.getSolverMethod()[0]==self.LUMPING
1046    
    #============ tolerance business =========================================================  
1047     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1048         """         """
1049         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1050    
1051           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1052    
1053           defines the stopping criterion.
1054    
1055           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1056                       the system will be resolved.
1057           @type tol: positive C{float}
1058           @raise ValueError: if tolerance is not positive.
1059         """         """
1060         if not tol>0:         if not tol>0:
1061             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1062         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1063         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1064         self.__tolerance=tol         self.__tolerance=tol
1065         return         return
1066    
1067     def getTolerance(self):     def getTolerance(self):
1068         """         """
1069         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1070    
1071           @return: tolerance currently used.
1072           @rtype: C{float}
1073         """         """
1074         return self.__tolerance         return self.__tolerance
1075    
1076     #===== symmetry  flag ==========================     # =============================================================================
1077       #    symmetry  flag:
1078       # =============================================================================
1079     def isSymmetric(self):     def isSymmetric(self):
1080        """        """
1081        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1082    
1083          @return: True is a symmetric PDE is indicated, otherwise False is returned
1084          @rtype: C{bool}
1085        """        """
1086        return self.__sym        return self.__sym
1087    
1088     def setSymmetryOn(self):     def setSymmetryOn(self):
1089        """        """
1090        @brief sets the symmetry flag to true        sets the symmetry flag.
1091        """        """
1092        if not self.isSymmetric():        if not self.isSymmetric():
1093           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1094           self.__sym=True           self.__sym=True
1095           self.__checkMatrixType()           self.__checkMatrixType()
1096    
1097     def setSymmetryOff(self):     def setSymmetryOff(self):
1098        """        """
1099        @brief sets the symmetry flag to false        removes the symmetry flag.
1100        """        """
1101        if self.isSymmetric():        if self.isSymmetric():
1102           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1103           self.__sym=False           self.__sym=False
1104           self.__checkMatrixType()           self.__checkMatrixType()
1105    
1106     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1107       """        """
1108       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1109    
1110       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1111       """        @type flag: C{bool}
1112       if flag:        """
1113          self.setSymmetryOn()        if flag:
1114       else:           self.setSymmetryOn()
1115          self.setSymmetryOff()        else:
1116             self.setSymmetryOff()
1117    
1118     #===== order reduction ==========================     # =============================================================================
1119       # function space handling for the equation as well as the solution
1120       # =============================================================================
1121     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1122       """       """
1123       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1124    
1125         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1126       """       """
1127       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1128       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1129    
1130     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1131       """       """
1132       @brief switches to full order       switches off reduced order for solution and equation representation
1133    
1134         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1135       """       """
1136       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1137       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1138    
1139     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1140       """       """
1141       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1142         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1143       @param flag                    if flag is not present order reduction is switched off
1144         @type flag: C{bool}
1145         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1146       """       """
1147       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1148       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1149    
1150     #===== order reduction solution ==========================  
1151     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1152       """       """
1153       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1154    
1155         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1156       """       """
1157       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1158       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1159           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1160           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1161           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1162             self.__resetSystem()
1163    
1164     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1165       """       """
1166       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1167    
1168         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1169       """       """
1170       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1171       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1172           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1173           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1174           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1175             self.__resetSystem()
1176    
1177     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1178       """       """
1179       @brief sets order for test functions according to flag       sets order for test functions according to flag
1180    
1181       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1182                      if flag is not present order reduction is switched off
1183         @type flag: C{bool}
1184         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1185       """       """
1186       if flag:       if flag:
1187          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1188       else:       else:
1189          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1190                                                                                                                                                              
    #===== order reduction equation ==========================  
1191     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1192       """       """
1193       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1194    
1195         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1196       """       """
1197       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1198       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1199           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1200           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1201           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1202             self.__resetSystem()
1203    
1204     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1205       """       """
1206       @brief switches to full order for test functions       switches off reduced order for equation representation
1207    
1208         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1209       """       """
1210       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1211       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1212           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1213           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1214           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1215             self.__resetSystem()
1216    
1217     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1218       """       """
1219       @brief sets order for test functions according to flag       sets order for test functions according to flag
1220    
1221       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1222                      if flag is not present order reduction is switched off
1223         @type flag: C{bool}
1224         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1225       """       """
1226       if flag:       if flag:
1227          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1228       else:       else:
1229          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1230                                                                                                                                                              
1231     # ==== initialization =====================================================================     # =============================================================================
1232     def __makeNewOperator(self):     # private method:
1233       # =============================================================================
1234       def __checkMatrixType(self):
1235         """
1236         reassess the matrix type and, if a new matrix is needed, resets the system.
1237         """
1238         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1239         if not new_matrix_type==self.__matrix_type:
1240             self.trace("Matrix type is now %d."%new_matrix_type)
1241             self.__matrix_type=new_matrix_type
1242             self.__resetSystem()
1243       #
1244       #   rebuild switches :
1245       #
1246       def __invalidateSolution(self):
1247           """
1248           indicates the PDE has to be resolved if the solution is requested
1249           """
1250           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1251           self.__solution_isValid=False
1252    
1253       def __invalidateOperator(self):
1254           """
1255           indicates the operator has to be rebuilt next time it is used
1256           """
1257           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1258           self.__invalidateSolution()
1259           self.__operator_is_Valid=False
1260    
1261       def __invalidateRightHandSide(self):
1262         """         """
1263         @brief         indicates the right hand side has to be rebuild next time it is used
1264         """         """
1265           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1266           self.__invalidateSolution()
1267           self.__righthandside_isValid=False
1268    
1269       def __invalidateSystem(self):
1270           """
1271           annonced that everthing has to be rebuild:
1272           """
1273           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1274           self.__invalidateSolution()
1275           self.__invalidateOperator()
1276           self.__invalidateRightHandSide()
1277    
1278       def __resetSystem(self):
1279           """
1280           annonced that everthing has to be rebuild:
1281           """
1282           self.trace("New System is built from scratch.")
1283           self.__operator=escript.Operator()
1284           self.__operator_is_Valid=False
1285           self.__righthandside=escript.Data()
1286           self.__righthandside_isValid=False
1287           self.__solution=escript.Data()
1288           self.__solution_isValid=False
1289       #
1290       #    system initialization:
1291       #
1292       def __getNewOperator(self):
1293           """
1294           returns an instance of a new operator
1295           """
1296           self.trace("New operator is allocated.")
1297         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1298                             self.getNumEquations(), \                             self.getNumEquations(), \
1299                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 545  class LinearPDE: Line 1301  class LinearPDE:
1301                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1302                             self.__matrix_type)                             self.__matrix_type)
1303    
1304     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1305         """         """
1306         @brief         returns an instance of a new right hand side
1307         """         """
1308         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1309           if self.getNumEquations()>1:
1310               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1311           else:
1312               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1313    
1314     def __makeNewSolution(self):     def __getNewSolution(self):
1315         """         """
1316         @brief         returns an instance of a new solution
1317         """         """
1318         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1319           if self.getNumSolutions()>1:
1320               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1321           else:
1322               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1323    
1324     def __getFreshOperator(self):     def __makeFreshSolution(self):
1325         """         """
1326         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1327         """         """
1328         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1329             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1330         else:         else:
1331             self.__operator.setValue(0.)             self.__solution*=0
1332             self.__operator.resetSolver()             self.trace("Solution is reset to zero.")
1333             if self.debug() : print "PDE Debug: Operator reset to zero"         return self.__solution
        return self.__operator  
1334    
1335     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1336         """         """
1337         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1338         """         """
1339         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1340             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1341         else:         else:
1342             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1343             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1344             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1345    
1346     #============ some serivice functions  =====================================================     def __makeFreshOperator(self):
1347     def getDomain(self):         """
1348           makes sure that the operator is instantiated and returns it initialized by zeros
1349           """
1350           if self.__operator.isEmpty():
1351               self.__operator=self.__getNewOperator()
1352           else:
1353               self.__operator.resetValues()
1354               self.trace("Operator reset to zero")
1355           return self.__operator
1356    
1357       def __applyConstraint(self):
1358           """
1359           applies the constraints defined by q and r to the system
1360           """
1361           if not self.isUsingLumping():
1362              q=self.getCoefficientOfGeneralPDE("q")
1363              r=self.getCoefficientOfGeneralPDE("r")
1364              if not q.isEmpty() and not self.__operator.isEmpty():
1365                 # q is the row and column mask to indicate where constraints are set:
1366                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1367                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1368                 u=self.__getNewSolution()
1369                 if r.isEmpty():
1370                    r_s=self.__getNewSolution()
1371                 else:
1372                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1373                 u.copyWithMask(r_s,col_q)
1374                 if not self.__righthandside.isEmpty():
1375                    self.__righthandside-=self.__operator*u
1376                    self.__righthandside=self.copyConstraint(self.__righthandside)
1377                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1378       # =============================================================================
1379       # function giving access to coefficients of the general PDE:
1380       # =============================================================================
1381       def getCoefficientOfGeneralPDE(self,name):
1382         """
1383         return the value of the coefficient name of the general PDE.
1384    
1385         @note: This method is called by the assembling routine it can be overwritten
1386               to map coefficients of a particular PDE to the general PDE.
1387         @param name: name of the coefficient requested.
1388         @type name: C{string}
1389         @return: the value of the coefficient  name
1390         @rtype: L{Data<escript.Data>}
1391         @raise IllegalCoefficient: if name is not one of coefficients
1392                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1393                      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}.
1394       """       """
1395       @brief returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1396            return self.getCoefficient(name)
1397         else:
1398            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1399    
1400       def hasCoefficientOfGeneralPDE(self,name):
1401       """       """
1402       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1403    
1404         @param name: name of the coefficient enquired.
1405         @type name: C{string}
1406         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1407         @rtype: C{bool}
1408    
    def getDim(self):  
1409       """       """
1410       @brief returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1411    
1412       def createCoefficientOfGeneralPDE(self,name):
1413       """       """
1414       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1415    
1416     def getNumEquations(self):       @param name: name of the coefficient requested.
1417         @type name: C{string}
1418         @return: a coefficient name initialized to 0.
1419         @rtype: L{Data<escript.Data>}
1420         @raise IllegalCoefficient: if name is not one of coefficients
1421                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1422                      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}.
1423       """       """
1424       @brief returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1425            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1426         else:
1427            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1428    
1429       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1430       """       """
1431       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1432           return self.__numEquations  
1433         @param name: name of the coefficient enquired.
1434         @type name: C{string}
1435         @return: the function space to be used for coefficient name
1436         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1437         @raise IllegalCoefficient: if name is not one of coefficients
1438                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1439                      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}.
1440         """
1441         if self.hasCoefficientOfGeneralPDE(name):
1442            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1443       else:       else:
1444           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1445    
1446     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1447       """       """
1448       @brief returns the number of unknowns       return the shape of the coefficient name of the general PDE
1449    
1450         @param name: name of the coefficient enquired.
1451         @type name: C{string}
1452         @return: the shape of the coefficient name
1453         @rtype: C{tuple} of C{int}
1454         @raise IllegalCoefficient: if name is not one of coefficients
1455                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1456                      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}.
1457       """       """
1458       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1459          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1460       else:       else:
1461          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1462    
1463       # =============================================================================
1464       # functions giving access to coefficients of a particular PDE implementation:
1465       # =============================================================================
1466       def getCoefficient(self,name):
1467         """
1468         returns the value of the coefficient name
1469    
1470     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1471        """       @type name: C{string}
1472        @brief 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
1473        """       @rtype: L{Data<escript.Data>}
1474        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1475        out=True       """
1476        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1477           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1478           out=False       else:
1479        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  
1480    
1481     def getFlux(self,u):     def hasCoefficient(self,name):
1482         """       """
1483         @brief returns the flux J_ij for a given u       return True if name is the name of a coefficient
1484    
1485              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @param name: name of the coefficient enquired.
1486         @type name: C{string}
1487         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1488         @rtype: C{bool}
1489         """
1490         return self.COEFFICIENTS.has_key(name)
1491    
1492         @param u argument of the operator     def createCoefficient(self, name):
1493         """
1494         create a L{Data<escript.Data>} object corresponding to coefficient name
1495    
1496         """       @return: a coefficient name initialized to 0.
1497         raise SystemError,"getFlux is not implemented yet"       @rtype: L{Data<escript.Data>}
1498         return None       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1499         """
1500         if self.hasCoefficient(name):
1501            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1502         else:
1503            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1504    
1505     def applyOperator(self,u):     def getFunctionSpaceForCoefficient(self,name):
1506         """       """
1507         @brief applies the operator of the PDE to a given solution u in weak from       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1508    
1509         @param u argument of the operator       @param name: name of the coefficient enquired.
1510         @type name: C{string}
1511         @return: the function space to be used for coefficient name
1512         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1513         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1514         """
1515         if self.hasCoefficient(name):
1516            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1517         else:
1518            raise ValueError,"unknown coefficient %s requested"%name
1519       def getShapeOfCoefficient(self,name):
1520         """
1521         return the shape of the coefficient name
1522    
1523         """       @param name: name of the coefficient enquired.
1524         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       @type name: C{string}
1525                                                                                                                                                                   @return: the shape of the coefficient name
1526     def getResidual(self,u):       @rtype: C{tuple} of C{int}
1527         """       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1528         @brief return the residual of u in the weak from       """
1529         if self.hasCoefficient(name):
1530            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1531         else:
1532            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1533    
1534         @param u     def resetCoefficients(self):
1535         """       """
1536         return self.applyOperator(u)-self.getRightHandSide()       resets all coefficients to there default values.
1537         """
1538         for i in self.COEFFICIENTS.iterkeys():
1539             self.COEFFICIENTS[i].resetValue()
1540    
1541       def alteredCoefficient(self,name):
1542         """
1543         announce that coefficient name has been changed
1544    
1545         @param name: name of the coefficient enquired.
1546         @type name: C{string}
1547         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1548         @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.
1549         """
1550         if self.hasCoefficient(name):
1551            self.trace("Coefficient %s has been altered."%name)
1552            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1553               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1554               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1555         else:
1556            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1557    
1558       def copyConstraint(self,u):
1559          """
1560          copies the constraint into u and returns u.
1561    
1562          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1563          @type u: L{Data<escript.Data>}
1564          @return: the input u modified by the constraints.
1565          @rtype: L{Data<escript.Data>}
1566          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1567          """
1568          q=self.getCoefficientOfGeneralPDE("q")
1569          r=self.getCoefficientOfGeneralPDE("r")
1570          if not q.isEmpty():
1571             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1572             if r.isEmpty():
1573                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1574             else:
1575                 r=escript.Data(r,u.getFunctionSpace())
1576             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1577          return u
1578    
1579     def _setValue(self,**coefficients):     def setValue(self,**coefficients):
1580        """        """
1581        @brief sets new values to coefficient        sets new values to coefficients
1582    
1583        @param coefficients        @param coefficients: new values assigned to coefficients
1584          @keyword A: value for coefficient A.
1585          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1586          @keyword A_reduced: value for coefficient A_reduced.
1587          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1588          @keyword B: value for coefficient B
1589          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1590          @keyword B_reduced: value for coefficient B_reduced
1591          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1592          @keyword C: value for coefficient C
1593          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1594          @keyword C_reduced: value for coefficient C_reduced
1595          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1596          @keyword D: value for coefficient D
1597          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1598          @keyword D_reduced: value for coefficient D_reduced
1599          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1600          @keyword X: value for coefficient X
1601          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1602          @keyword X_reduced: value for coefficient X_reduced
1603          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1604          @keyword Y: value for coefficient Y
1605          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1606          @keyword Y_reduced: value for coefficient Y_reduced
1607          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1608          @keyword d: value for coefficient d
1609          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1610          @keyword d_reduced: value for coefficient d_reduced
1611          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1612          @keyword y: value for coefficient y
1613          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1614          @keyword d_contact: value for coefficient d_contact
1615          @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>}.
1616          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1617          @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>}.
1618          @keyword y_contact: value for coefficient y_contact
1619          @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>}.
1620          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1621          @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>}.
1622          @keyword r: values prescribed to the solution at the locations of constraints
1623          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1624                   depending of reduced order is used for the solution.
1625          @keyword q: mask for location of constraints
1626          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                   depending of reduced order is used for the representation of the equation.
1628          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1629        """        """
1630        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1631        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1632           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1633              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1634        # 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:
1635        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1636           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1637              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1638                  s=d.shape                  s=d.shape
# Line 726  class LinearPDE: Line 1642  class LinearPDE:
1642                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1643              if s!=None:              if s!=None:
1644                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1645                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1646                  if res==None:                  if res==None:
1647                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1648                  else:                  else:
1649                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1650                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1651        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1652        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1653        # 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:
1654        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1655          if d==None:          try:
1656               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1657          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1658               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1659                  d2=d             self.alteredCoefficient(i)
1660               else:          except IllegalCoefficientFunctionSpace,m:
1661                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1662          else:              i_red=i+"_reduced"
1663                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1664          if not d2.isEmpty():                  try:
1665             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1666                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1667          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1668          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1669          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1670          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1671                          except IllegalCoefficientFunctionSpace,m:
1672        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673        self.__setHomogeneousConstraintFlag()              else:
1674        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1675            except IllegalCoefficientValue,m:
1676     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677        """        self.__altered_coefficients=True
1678        @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1679        """        if len(coefficients)>0 and not self.isUsingLumping():
1680        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1681        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1682        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1683        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1684           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1685        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1686             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):  
        """  
        @brief 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):  
        """  
        @brief 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):  
        """  
        @brief 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):  
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      @brief 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):  
       """  
       @brief 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):  
        """  
        @brief 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.__makeNewSolution()  
           if r.isEmpty():  
              r_s=self.__makeNewSolution()  
           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.)  
1687    
1688     def getSystem(self):     def getSystem(self):
1689         """         """
1690         @brief return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1691    
1692           @return: the discrete version of the PDE
1693           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1694         """         """
1695         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1696            if self.isUsingLumping():            if self.isUsingLumping():
1697                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1698                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1699                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1700                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1701                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1702                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1703                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1704                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1705                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1706                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1707                   mat=self.__makeNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1708                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1709                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1710                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1711                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1712                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1713                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1714                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1715                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1716                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1717                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1718                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1719                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1720                   self.__applyConstraint()                   if not D.isEmpty():
1721                   self.__operator_isValid=True                       if self.getNumSolutions()>1:
1722                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1723                         else:
1724                            D_times_e=D
1725                     else:
1726                        D_times_e=escript.Data()
1727                     if not d.isEmpty():
1728                         if self.getNumSolutions()>1:
1729                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1730                         else:
1731                            d_times_e=d
1732                     else:
1733                        d_times_e=escript.Data()
1734          
1735                     if not D_reduced.isEmpty():
1736                         if self.getNumSolutions()>1:
1737                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1738                         else:
1739                            D_reduced_times_e=D_reduced
1740                     else:
1741                        D_reduced_times_e=escript.Data()
1742                     if not d_reduced.isEmpty():
1743                         if self.getNumSolutions()>1:
1744                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1745                         else:
1746                            d_reduced_times_e=d_reduced
1747                     else:
1748                        d_reduced_times_e=escript.Data()
1749    
1750                     self.__operator=self.__getNewRightHandSide()
1751                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1752                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1753                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1754                     else:
1755                        self.getDomain().addPDEToRHS(self.__operator, \
1756                                                     escript.Data(), \
1757                                                     D_times_e, \
1758                                                     d_times_e,\
1759                                                     escript.Data())
1760                        self.getDomain().addPDEToRHS(self.__operator, \
1761                                                     escript.Data(), \
1762                                                     D_reduced_times_e, \
1763                                                     d_reduced_times_e,\
1764                                                     escript.Data())
1765                     self.__operator=1./self.__operator
1766                     self.trace("New lumped operator has been built.")
1767                     self.__operator_is_Valid=True
1768                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1769                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1770                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1771                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1772                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1773                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1774                                 self.getCoefficientOfPDE("y_contact"))                   self.getDomain().addPDEToRHS(self.__righthandside, \
1775                   self.__copyConstraint()                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1776                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1778                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1779                     self.trace("New right hand side as been built.")
1780                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1781            else:            else:
1782               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1783                   if self.debug() : print "PDE Debug: New system is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1784                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("A"), \
1785                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1786                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1787                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1788                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1789                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1790                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1791                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1792                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1793                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y_contact"))
1794                                 self.getCoefficientOfPDE("y_contact"))                   self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1795                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1805                   self.__applyConstraint()                   self.__applyConstraint()
1806                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1807                   self.__operator_isValid=True                   self.trace("New system has been built.")
1808                     self.__operator_is_Valid=True
1809                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1810               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1811                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1812                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1813                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1814                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1815                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1816                                 self.getCoefficientOfPDE("y_contact"))                   self.getDomain().addPDEToRHS(self.__righthandside, \
1817                   self.__copyConstraint()                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1818                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1820                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1821                     self.__righthandside=self.copyConstraint(self.__righthandside)
1822                     self.trace("New right hand side has been built.")
1823                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1824               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1825                   if self.debug() : print "PDE Debug: New operator is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1826                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),escript.Data(), \                              self.getCoefficientOfGeneralPDE("A"), \
1827                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("B"), \
1828                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("C"), \
1829                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("D"), \
1830                              self.getCoefficientOfPDE("D"), \                              escript.Data(), \
1831                                escript.Data(), \
1832                                self.getCoefficientOfGeneralPDE("d"), \
1833                                escript.Data(),\
1834                                self.getCoefficientOfGeneralPDE("d_contact"), \
1835                                escript.Data())
1836                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1837                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1840                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1841                              escript.Data(), \                              escript.Data(), \
1842                              escript.Data(), \                              escript.Data(), \
1843                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1844                              escript.Data(),\                              escript.Data(),\
1845                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1846                              escript.Data())                              escript.Data())
1847                   self.__applyConstraint()                   self.__applyConstraint()
1848                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1849                     self.__operator_is_Valid=True
1850         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        @brief returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1851    
    def getRightHandSide(self):  
        """  
        @brief returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1852    
1853     def solve(self,**options):  class Poisson(LinearPDE):
1854        """     """
1855        @brief solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1856    
1857        @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  
1858    
1859     def getSolution(self,**options):     with natural boundary conditons
        """  
        @brief returns the solution of the PDE  
1860    
1861         @param options     M{n[j]*grad(u)[j] = 0 }
        """  
        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  
1862    
1863       and constraints:
1864    
1865       M{u=0} where M{q>0}
1866    
1867  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)  
 def HALF(P): return escript.Scalar(0.5,P.getFunctionSpace())  
1868    
1869       def __init__(self,domain,debug=False):
1870         """
1871         initializes a new Poisson equation
1872    
1873  class AdvectivePDE(LinearPDE):       @param domain: domain of the PDE
1874     """       @type domain: L{Domain<escript.Domain>}
1875     @brief Class to handel a linear PDE domineated by advective terms:       @param debug: if True debug informations are printed.
     
    class to define a linear PDE of the form  
1876    
1877       -(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       """
1878         super(Poisson, self).__init__(domain,1,1,debug)
1879         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1881                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1882         self.setSymmetryOn()
1883    
1884       with boundary conditons:     def setValue(self,**coefficients):
1885         """
1886         sets new values to coefficients
1887    
1888          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       @param coefficients: new values assigned to coefficients
1889         @keyword f: value for right hand side M{f}
1890         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1891         @keyword q: mask for location of constraints
1892         @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>}
1893                   depending of reduced order is used for the representation of the equation.
1894         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1895         """
1896         super(Poisson, self).setValue(**coefficients)
1897    
1898       def getCoefficientOfGeneralPDE(self,name):
1899         """
1900         return the value of the coefficient name of the general PDE
1901         @param name: name of the coefficient requested.
1902         @type name: C{string}
1903         @return: the value of the coefficient  name
1904         @rtype: L{Data<escript.Data>}
1905         @raise IllegalCoefficient: if name is not one of coefficients
1906                      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}.
1907         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1908         """
1909         if name == "A" :
1910             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1911         elif name == "B" :
1912             return escript.Data()
1913         elif name == "C" :
1914             return escript.Data()
1915         elif name == "D" :
1916             return escript.Data()
1917         elif name == "X" :
1918             return escript.Data()
1919         elif name == "Y" :
1920             return self.getCoefficient("f")
1921         elif name == "d" :
1922             return escript.Data()
1923         elif name == "y" :
1924             return escript.Data()
1925         elif name == "d_contact" :
1926             return escript.Data()
1927         elif name == "y_contact" :
1928             return escript.Data()
1929         elif name == "A_reduced" :
1930             return escript.Data()
1931         elif name == "B_reduced" :
1932             return escript.Data()
1933         elif name == "C_reduced" :
1934             return escript.Data()
1935         elif name == "D_reduced" :
1936             return escript.Data()
1937         elif name == "X_reduced" :
1938             return escript.Data()
1939         elif name == "Y_reduced" :
1940             return self.getCoefficient("f_reduced")
1941         elif name == "d_reduced" :
1942             return escript.Data()
1943         elif name == "y_reduced" :
1944             return escript.Data()
1945         elif name == "d_contact_reduced" :
1946             return escript.Data()
1947         elif name == "y_contact_reduced" :
1948             return escript.Data()
1949         elif name == "r" :
1950             return escript.Data()
1951         elif name == "q" :
1952             return self.getCoefficient("q")
1953         else:
1954            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1955    
1956      and contact conditions  class Helmholtz(LinearPDE):
1957       """
1958       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1959    
1960          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1961    
1962      and constraints:     with natural boundary conditons
1963    
1964           u_i=r_i where q_i>0     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1965    
1966     """     and constraints:
    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.  
1967    
1968     def setValue(self,**args):     M{u=r} where M{q>0}
        if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()  
        self._setValue(**args)  
             
    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)  
1969    
1970              Z_max=util.Lsup(length_of_Z)     """
             if Z_max>0.:  
                length_of_A=util.length(A)  
                A_max=util.Lsup(length_of_A)  
                if A_max>0:  
                     inv_A=1./(length_of_A+A_max*self.TOL)  
                else:  
                     inv_A=1./self.TOL  
                peclet_number=length_of_Z*h/2*inv_A  
                xi=self.__xi(peclet_number)  
                self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)  
                print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)  
       return self.__Xi  
         
1971    
1972     def getCoefficientOfPDE(self,name):     def __init__(self,domain,debug=False):
1973       """       """
1974       @brief return the value of the coefficient name of the general PDE       initializes a new Poisson equation
1975       @param name  
1976         @param domain: domain of the PDE
1977         @type domain: L{Domain<escript.Domain>}
1978         @param debug: if True debug informations are printed.
1979    
1980         """
1981         super(Helmholtz, self).__init__(domain,1,1,debug)
1982         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1984                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1990                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1991         self.setSymmetryOn()
1992    
1993       def setValue(self,**coefficients):
1994       """       """
1995       if not self.getNumEquations() == self.getNumSolutions():       sets new values to coefficients
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
1996    
1997       if name == "A" :       @param coefficients: new values assigned to coefficients
1998           A=self.getCoefficient("A")       @keyword omega: value for coefficient M{S{omega}}
1999           B=self.getCoefficient("B")       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000           C=self.getCoefficient("C")       @keyword k: value for coefficeint M{k}
2001           if B.isEmpty() and C.isEmpty():       @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002              Aout=A       @keyword f: value for right hand side M{f}
2003           else:       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2004              if A.isEmpty():       @keyword alpha: value for right hand side M{S{alpha}}
2005                 Aout=self.createNewCoefficient("A")       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006              else:       @keyword g: value for right hand side M{g}
2007                 Aout=A[:]       @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2008              Xi=self.getXi()       @keyword r: prescribed values M{r} for the solution in constraints.
2009              if self.getNumEquations()>1:       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2010                  for i in range(self.getNumEquations()):                 depending of reduced order is used for the representation of the equation.
2011                     for j in range(self.getDim()):       @keyword q: mask for location of constraints
2012                        for k in range(self.getNumSolutions()):       @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                           for l in range(self.getDim()):                 depending of reduced order is used for the representation of the equation.
2014                              if not C.isEmpty() and not B.isEmpty():       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
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])       """
2016                              elif C.isEmpty():       super(Helmholtz, self).setValue(**coefficients)
2017                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
2018                              else:     def getCoefficientOfGeneralPDE(self,name):
2019                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       """
2020              else:       return the value of the coefficient name of the general PDE
2021                  for j in range(self.getDim()):  
2022                     for l in range(self.getDim()):       @param name: name of the coefficient requested.
2023                        if not C.isEmpty() and not B.isEmpty():       @type name: C{string}
2024                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])       @return: the value of the coefficient  name
2025                        elif C.isEmpty():       @rtype: L{Data<escript.Data>}
2026                            Aout[j,l]+=Xi*B[j]*B[l]       @raise IllegalCoefficient: if name is not one of coefficients
2027                        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}.
2028                            Aout[j,l]+=Xi*C[j]*C[l]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2029           return Aout       """
2030       elif name == "B" :       if name == "A" :
2031           B=self.getCoefficient("B")           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2032           C=self.getCoefficient("C")       elif name == "B" :
2033           D=self.getCoefficient("D")           return escript.Data()
2034           if C.isEmpty() or D.isEmpty():       elif name == "C" :
2035              Bout=B           return escript.Data()
2036           else:       elif name == "D" :
2037              Xi=self.getXi()           return self.getCoefficient("omega")
2038              if B.isEmpty():       elif name == "X" :
2039                  Bout=self.createNewCoefficient("B")           return escript.Data()
2040              else:       elif name == "Y" :
2041                  Bout=B[:]           return self.getCoefficient("f")
2042              if self.getNumEquations()>1:       elif name == "d" :
2043                 for k in range(self.getNumSolutions()):           return self.getCoefficient("alpha")
2044                    for p in range(self.getNumEquations()):       elif name == "y" :
2045                       tmp=Xi*D[p,k]           return self.getCoefficient("g")
2046                       for i in range(self.getNumEquations()):       elif name == "d_contact" :
2047                          for j in range(self.getDim()):           return escript.Data()
                            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")  
2048       elif name == "y_contact" :       elif name == "y_contact" :
2049           return self.getCoefficient("y_contact")           return escript.Data()
2050       elif name == "r" :       elif name == "A_reduced" :
2051             return escript.Data()
2052         elif name == "B_reduced" :
2053             return escript.Data()
2054         elif name == "C_reduced" :
2055             return escript.Data()
2056         elif name == "D_reduced" :
2057             return escript.Data()
2058         elif name == "X_reduced" :
2059             return escript.Data()
2060         elif name == "Y_reduced" :
2061             return self.getCoefficient("f_reduced")
2062         elif name == "d_reduced" :
2063             return escript.Data()
2064         elif name == "y_reduced" :
2065            return self.getCoefficient("g_reduced")
2066         elif name == "d_contact_reduced" :
2067             return escript.Data()
2068         elif name == "y_contact_reduced" :
2069             return escript.Data()
2070         elif name == "r" :
2071           return self.getCoefficient("r")           return self.getCoefficient("r")
2072       elif name == "q" :       elif name == "q" :
2073           return self.getCoefficient("q")           return self.getCoefficient("q")
2074       else:       else:
2075           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2076    
2077  class Poisson(LinearPDE):  class LameEquation(LinearPDE):
    """  
    @brief Class to define a Poisson equstion problem:  
                                                                                                                                                               
    class to define a linear PDE of the form  
                                                                                                                                                               
         -u_{,jj} = f  
                                                                                                                                                               
      with boundary conditons:  
                                                                                                                                                               
         n_j*u_{,j} = 0  
                                                                                                                                                               
     and constraints:  
                                                                                                                                                               
          u=0 where q>0  
                                                                                                                                                               
2078     """     """
2079       Class to define a Lame equation problem:
2080    
2081     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     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] }
        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)  
2082    
2083     def setValue(self,f=escript.Data(),q=escript.Data()):     with natural boundary conditons:
        self._setValue(f=f,q=q)  
2084    
2085     def getCoefficientOfPDE(self,name):     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] }
2086       """  
2087       @brief return the value of the coefficient name of the general PDE     and constraints:
2088       @param name  
2089       """     M{u[i]=r[i]} where M{q[i]>0}
2090       if name == "A" :  
2091           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))     """
2092       elif name == "B" :  
2093       def __init__(self,domain,debug=False):
2094          super(LameEquation, self).__init__(domain,\
2095                                             domain.getDim(),domain.getDim(),debug)
2096          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2097                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2098                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2100                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2101                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2102                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2103          self.setSymmetryOn()
2104    
2105       def setValues(self,**coefficients):
2106         """
2107         sets new values to coefficients
2108    
2109         @param coefficients: new values assigned to coefficients
2110         @keyword lame_mu: value for coefficient M{S{mu}}
2111         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112         @keyword lame_lambda: value for coefficient M{S{lambda}}
2113         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2114         @keyword F: value for internal force M{F}
2115         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2116         @keyword sigma: value for initial stress M{S{sigma}}
2117         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2118         @keyword f: value for extrenal force M{f}
2119         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2120         @keyword r: prescribed values M{r} for the solution in constraints.
2121         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2122                   depending of reduced order is used for the representation of the equation.
2123         @keyword q: mask for location of constraints
2124         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2127         """
2128         super(LameEquation, self).setValues(**coefficients)
2129    
2130       def getCoefficientOfGeneralPDE(self,name):
2131         """
2132         return the value of the coefficient name of the general PDE
2133    
2134         @param name: name of the coefficient requested.
2135         @type name: C{string}
2136         @return: the value of the coefficient  name
2137         @rtype: L{Data<escript.Data>}
2138         @raise IllegalCoefficient: if name is not one of coefficients
2139                      "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}.
2140         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2141         """
2142         if name == "A" :
2143             out =self.createCoefficientOfGeneralPDE("A")
2144             for i in range(self.getDim()):
2145               for j in range(self.getDim()):
2146                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2147                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2148                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2149             return out
2150         elif name == "B" :
2151           return escript.Data()           return escript.Data()
2152       elif name == "C" :       elif name == "C" :
2153           return escript.Data()           return escript.Data()
2154       elif name == "D" :       elif name == "D" :
2155           return escript.Data()           return escript.Data()
2156       elif name == "X" :       elif name == "X" :
2157             return self.getCoefficient("sigma")
2158         elif name == "Y" :
2159             return self.getCoefficient("F")
2160         elif name == "d" :
2161           return escript.Data()           return escript.Data()
2162       elif name == "Y" :       elif name == "y" :
2163           return self.getCoefficient("f")           return self.getCoefficient("f")
2164       elif name == "d" :       elif name == "d_contact" :
2165           return escript.Data()           return escript.Data()
2166       elif name == "y" :       elif name == "y_contact" :
2167           return escript.Data()           return escript.Data()
2168       elif name == "d_contact" :       elif name == "A_reduced" :
2169           return escript.Data()           return escript.Data()
2170       elif name == "y_contact" :       elif name == "B_reduced" :
2171             return escript.Data()
2172         elif name == "C_reduced" :
2173             return escript.Data()
2174         elif name == "D_reduced" :
2175             return escript.Data()
2176         elif name == "X_reduced" :
2177           return escript.Data()           return escript.Data()
2178       elif name == "r" :       elif name == "Y_reduced" :
2179           return escript.Data()           return escript.Data()
2180       elif name == "q" :       elif name == "d_reduced" :
2181             return escript.Data()
2182         elif name == "y_reduced" :
2183             return escript.Data()
2184         elif name == "d_contact_reduced" :
2185             return escript.Data()
2186         elif name == "y_contact_reduced" :
2187             return escript.Data()
2188         elif name == "r" :
2189             return self.getCoefficient("r")
2190         elif name == "q" :
2191           return self.getCoefficient("q")           return self.getCoefficient("q")
2192       else:       else:
2193           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2194    
2195    def LinearSinglePDE(domain,debug=False):
2196       """
2197       defines a single linear PDEs
2198    
2199       @param domain: domain of the PDE
2200       @type domain: L{Domain<escript.Domain>}
2201       @param debug: if True debug informations are printed.
2202       @rtype: L{LinearPDE}
2203       """
2204       return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2205    
2206    def LinearPDESystem(domain,debug=False):
2207       """
2208       defines a system of linear PDEs
2209    
2210       @param domain: domain of the PDE
2211       @type domain: L{Domain<escript.Domain>}
2212       @param debug: if True debug informations are printed.
2213       @rtype: L{LinearPDE}
2214       """
2215       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2216    
2217    class TransportPDE(object):
2218         """
2219         Warning: This is still a very experimental. The class is still changing!
2220    
2221         Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2222        
2223         u=r where q>0
2224        
2225         all coefficients are constant over time.
2226    
2227         typical usage:
2228    
2229             p=TransportPDE(dom)
2230             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2231             p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2232             t=0
2233             dt=0.1
2234             while (t<1.):
2235                  u=p.solve(dt)
2236    
2237         """
2238         def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2239            self.__domain=domain
2240            self.__num_equations=num_equations
2241            self.__useSUPG=useSUPG
2242            self.__trace=trace
2243            self.__theta=theta
2244            self.__matrix_type=0
2245            self.__reduced=True
2246            self.__reassemble=True
2247            if self.__useSUPG:
2248               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2249               self.__pde.setSymmetryOn()
2250               self.__pde.setReducedOrderOn()
2251            else:
2252               self.__transport_problem=self.__getNewTransportProblem()
2253            self.setTolerance()
2254            self.__M=escript.Data()
2255            self.__A=escript.Data()
2256            self.__B=escript.Data()
2257            self.__C=escript.Data()
2258            self.__D=escript.Data()
2259            self.__X=escript.Data()
2260            self.__Y=escript.Data()
2261            self.__d=escript.Data()
2262            self.__y=escript.Data()
2263            self.__d_contact=escript.Data()
2264            self.__y_contact=escript.Data()
2265            self.__r=escript.Data()
2266            self.__q=escript.Data()
2267    
2268         def trace(self,text):
2269                 if self.__trace: print text
2270         def getSafeTimeStepSize(self):
2271            if self.__useSUPG:
2272                if self.__reassemble:
2273                   h=self.__domain.getSize()
2274                   dt=None
2275                   if not self.__A.isEmpty():
2276                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2277                      if dt == None:
2278                         dt = dt2
2279                      else:
2280                         dt=1./(1./dt+1./dt2)
2281                   if not self.__B.isEmpty():
2282                      dt2=util.inf(h*self.__M/util.length(self.__B))
2283                      if dt == None:
2284                         dt = dt2
2285                      else:
2286                         dt=1./(1./dt+1./dt2)
2287                   if not  self.__C.isEmpty():
2288                      dt2=util.inf(h*self.__M/util.length(self.__C))
2289                      if dt == None:
2290                         dt = dt2
2291                      else:
2292                         dt=1./(1./dt+1./dt2)
2293                   if not self.__D.isEmpty():
2294                      dt2=util.inf(self.__M/util.length(self.__D))
2295                      if dt == None:
2296                         dt = dt2
2297                      else:
2298                         dt=1./(1./dt+1./dt2)
2299                   self.__dt = dt/2
2300                return self.__dt
2301            else:
2302                return self.__getTransportProblem().getSafeTimeStepSize()
2303         def getDomain(self):
2304            return self.__domain
2305         def getTheta(self):
2306            return self.__theta
2307         def getNumEquations(self):
2308            return self.__num_equations
2309         def setReducedOn(self):
2310              if not self.reduced():
2311                  if self.__useSUPG:
2312                     self.__pde.setReducedOrderOn()
2313                  else:
2314                     self.__transport_problem=self.__getNewTransportProblem()
2315              self.__reduced=True
2316         def setReducedOff(self):
2317              if self.reduced():
2318                  if self.__useSUPG:
2319                     self.__pde.setReducedOrderOff()
2320                  else:
2321                     self.__transport_problem=self.__getNewTransportProblem()
2322              self.__reduced=False
2323         def reduced(self):
2324             return self.__reduced
2325         def getFunctionSpace(self):
2326            if self.reduced():
2327               return escript.ReducedSolution(self.getDomain())
2328            else:
2329               return escript.Solution(self.getDomain())
2330    
2331         def setTolerance(self,tol=1.e-8):
2332            self.__tolerance=tol
2333            if self.__useSUPG:
2334                  self.__pde.setTolerance(self.__tolerance)
2335    
2336         def __getNewTransportProblem(self):
2337           """
2338           returns an instance of a new operator
2339           """
2340           self.trace("New Transport problem is allocated.")
2341           return self.getDomain().newTransportProblem( \
2342                                   self.getTheta(),
2343                                   self.getNumEquations(), \
2344                                   self.getFunctionSpace(), \
2345                                   self.__matrix_type)
2346              
2347         def __getNewSolutionVector(self):
2348             if self.getNumEquations() ==1 :
2349                    out=escript.Data(0.0,(),self.getFunctionSpace())
2350             else:
2351                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2352             return out
2353    
2354         def __getTransportProblem(self):
2355           if self.__reassemble:
2356                 self.__source=self.__getNewSolutionVector()
2357                 self.__transport_problem.reset()
2358                 self.getDomain().addPDEToTransportProblem(
2359                             self.__transport_problem,
2360                             self.__source,
2361                             self.__M,
2362                             self.__A,
2363                             self.__B,
2364                             self.__C,
2365                             self.__D,
2366                             self.__X,
2367                             self.__Y,
2368                             self.__d,
2369                             self.__y,
2370                             self.__d_contact,
2371                             self.__y_contact)
2372                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2373                 self.__reassemble=False
2374           return self.__transport_problem
2375         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2376                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2377                 if not M==None:
2378                      self.__reassemble=True
2379                      self.__M=M
2380                 if not A==None:
2381                      self.__reassemble=True
2382                      self.__A=A
2383                 if not B==None:
2384                      self.__reassemble=True
2385                      self.__B=B
2386                 if not C==None:
2387                      self.__reassemble=True
2388                      self.__C=C
2389                 if not D==None:
2390                      self.__reassemble=True
2391                      self.__D=D
2392                 if not X==None:
2393                      self.__reassemble=True
2394                      self.__X=X
2395                 if not Y==None:
2396                      self.__reassemble=True
2397                      self.__Y=Y
2398                 if not d==None:
2399                      self.__reassemble=True
2400                      self.__d=d
2401                 if not y==None:
2402                      self.__reassemble=True
2403                      self.__y=y
2404                 if not d_contact==None:
2405                      self.__reassemble=True
2406                      self.__d_contact=d_contact
2407                 if not y_contact==None:
2408                      self.__reassemble=True
2409                      self.__y_contact=y_contact
2410                 if not q==None:
2411                      self.__reassemble=True
2412                      self.__q=q
2413                 if not r==None:
2414                      self.__reassemble=True
2415                      self.__r=r
2416    
2417         def setInitialSolution(self,u):
2418                 if self.__useSUPG:
2419                     self.__u=util.interpolate(u,self.getFunctionSpace())
2420                 else:
2421                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2422    
2423         def solve(self,dt,**kwarg):
2424               if self.__useSUPG:
2425                    if self.__reassemble:
2426                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2427                        self.__reassemble=False
2428                    dt2=self.getSafeTimeStepSize()
2429                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2430                    dt2=dt/nn
2431                    nnn=0
2432                    u=self.__u
2433                    self.trace("number of substeps is %d."%nn)
2434                    while nnn<nn :
2435                        self.__setSUPG(u,u,dt2/2)
2436                        u_half=self.__pde.getSolution(verbose=True)
2437                        self.__setSUPG(u,u_half,dt2)
2438                        u=self.__pde.getSolution(verbose=True)
2439                        nnn+=1
2440                    self.__u=u
2441                    return self.__u
2442               else:
2443                   kwarg["tolerance"]=self.__tolerance
2444                   tp=self.__getTransportProblem()
2445                   return tp.solve(self.__source,dt,kwarg)
2446         def __setSUPG(self,u0,u,dt):
2447                g=util.grad(u)
2448                X=0
2449                Y=self.__M*u0
2450                X=0
2451                self.__pde.setValue(r=u0)
2452                if not self.__A.isEmpty():
2453                   X=X+dt*util.matrixmult(self.__A,g)
2454                if not self.__B.isEmpty():
2455                   X=X+dt*self.__B*u
2456                if not  self.__C.isEmpty():
2457                   Y=Y+dt*util.inner(self.__C,g)
2458                if not self.__D.isEmpty():
2459                   Y=Y+dt*self.__D*u
2460                if not self.__X.isEmpty():
2461                   X=X+dt*self.__X
2462                if not self.__Y.isEmpty():
2463                   Y=Y+dt*self.__Y
2464                self.__pde.setValue(X=X,Y=Y)
2465                if not self.__y.isEmpty():
2466                   self.__pde.setValue(y=dt*self.__y)
2467                if not self.__y_contact.isEmpty():
2468                   self.__pde.setValue(y=dt*self.__y_contact)
2469                self.__pde.setValue(r=u0)

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