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trunk/esys2/escript/py_src/linearPDEs.py revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC temp/escript/py_src/linearPDEs.py revision 1387 by trankine, Fri Jan 11 07:45:26 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 escript  import escript
38  import util  import util
39  import numarray  import numarray
40    
41  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
42       """  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
43       @brief Return the Domain which is equal to the input domain (if not None)                      http://www.access.edu.au
44       and is the domain of all Data objects in the dictionary data.                  Primary Business: Queensland, Australia"""
45       An exception is raised if this is not possible  __license__="""Licensed under the Open Software License version 3.0
46                 http://www.opensource.org/licenses/osl-3.0.php"""
47       @param domain  __url__="http://www.iservo.edu.au/esys"
48       @param data  __version__="$Revision$"
49       """  __date__="$Date$"
50       # get the domain used by any Data object in the list data:  
51       data_domain=None  
52       for d in data.itervalues():  class IllegalCoefficient(ValueError):
53            if isinstance(d,escript.Data):     """
54               if not d.isEmpty(): data_domain=d.getDomain()     raised if an illegal coefficient of the general ar particular PDE is requested.
55       # check if domain and data_domain are identical?     """
56       if domain == None:     pass
          if data_domain == None:  
               raise ValueError,"Undefined PDE domain. Specify a domain or use a Data class object as coefficient"  
      else:  
          if data_domain == None:  
               data_domain=domain  
          else:  
            if not data_domain == domain:  
                  raise ValueError,"Domain of coefficients doesnot match specified domain"  
      # now we check if all Data class object coefficients are defined on data_domain:  
      for i,d in data.iteritems():  
          if isinstance(d,escript.Data):  
             if not d.isEmpty():  
                if not data_domain==d.getDomain():  
                  raise ValueError,"Illegal domain for coefficient %s."%i  
      # done:  
      return data_domain  
   
 def identifyNumEquationsAndSolutions(dim,coef={}):  
      # get number of equations and number of unknowns:  
      numEquations=0  
      numSolutions=0  
      for i in coef.iterkeys():  
         if not coef[i].isEmpty():  
            res=_PDECoefficientTypes[i].estimateNumEquationsAndNumSolutions(coef[i].getShape(),dim)  
            if res==None:  
                raise ValueError,"Illegal shape %s of coefficient %s"%(coef[i].getShape().__str__(),i)  
            else:  
                numEquations=max(numEquations,res[0])  
                numSolutions=max(numSolutions,res[1])  
      return numEquations,numSolutions  
   
   
 def _CompTuple2(t1,t2):  
    """  
    @brief  
   
    @param t1  
    @param t2  
    """  
    dif=t1[0]+t1[1]-(t2[0]+t2[1])  
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
57    
58  class PDECoefficientType:  class IllegalCoefficientValue(ValueError):
59       """
60       raised if an incorrect value for a coefficient is used.
61       """
62       pass
63    
64    class IllegalCoefficientFunctionSpace(ValueError):
65       """
66       raised if an incorrect function space for a coefficient is used.
67       """
68    
69    class UndefinedPDEError(ValueError):
70       """
71       raised if a PDE is not fully defined yet.
72       """
73       pass
74    
75    class PDECoefficient(object):
76      """      """
77      @brief      A class for describing a PDE coefficient
78    
79        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
80        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
81        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
82        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
83        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
84        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
85        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
86        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
87        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
88        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
89        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
90        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
91        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
92        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
93    
94      """      """
     # identifier for location of Data objects defining coefficients  
95      INTERIOR=0      INTERIOR=0
96      BOUNDARY=1      BOUNDARY=1
97      CONTACT=2      CONTACT=2
98      CONTINUOUS=3      SOLUTION=3
99      # identifier in the pattern of coefficients:      REDUCED=4
100      # 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
101      # number of unknowns.      BY_SOLUTION=6
102      EQUATION=3      BY_DIM=7
103      SOLUTION=4      OPERATOR=10
104      DIM=5      RIGHTHANDSIDE=11
105      # indicator for what is altered if the coefficient is altered:      BOTH=12
106      OPERATOR=5      INTERIOR_REDUCED=13
107      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
108      BOTH=7      CONTACT_REDUCED=15
109      def __init__(self,where,pattern,altering):  
110         """      def __init__(self, where, pattern, altering):
111         @brief Initialise a PDE Coefficient type         """
112           Initialise a PDE Coefficient type
113    
114           @param where: describes where the coefficient lives
115           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
116                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
117           @param pattern: describes the shape of the coefficient and how the shape is build for a given
118                  spatial dimension and numbers of equation and solution in then PDE. For instance,
119                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
120                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
121                  on a 2-dimensional domain. In the case of single equation and a single solution component
122                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
123                  the example would be read as (2,).
124           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
125           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
126           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
127           @param reduced: indicates if reduced
128           @type reduced: C{bool}
129         """         """
130           super(PDECoefficient, self).__init__()
131         self.what=where         self.what=where
132         self.pattern=pattern         self.pattern=pattern
133         self.altering=altering         self.altering=altering
134           self.resetValue()
135    
136      def getFunctionSpace(self,domain):      def resetValue(self):
137         """         """
138         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
139         """         """
140         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
141         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
142         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
143         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
144           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
145    
146           @param domain: domain on which the PDE uses the coefficient
147           @type domain: L{Domain<escript.Domain>}
148           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
149           @type reducedEquationOrder: C{bool}
150           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
151           @type reducedSolutionOrder: C{bool}
152           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
153           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
154           """
155           if self.what==self.INTERIOR:
156                return escript.Function(domain)
157           elif self.what==self.INTERIOR_REDUCED:
158                return escript.ReducedFunction(domain)
159           elif self.what==self.BOUNDARY:
160                return escript.FunctionOnBoundary(domain)
161           elif self.what==self.BOUNDARY_REDUCED:
162                return escript.ReducedFunctionOnBoundary(domain)
163           elif self.what==self.CONTACT:
164                return escript.FunctionOnContactZero(domain)
165           elif self.what==self.CONTACT_REDUCED:
166                return escript.ReducedFunctionOnContactZero(domain)
167           elif self.what==self.SOLUTION:
168                if reducedEquationOrder and reducedSolutionOrder:
169                    return escript.ReducedSolution(domain)
170                else:
171                    return escript.Solution(domain)
172           elif self.what==self.REDUCED:
173                return escript.ReducedSolution(domain)
174    
175        def getValue(self):
176           """
177           returns the value of the coefficient
178    
179           @return:  value of the coefficient
180           @rtype:  L{Data<escript.Data>}
181           """
182           return self.value
183    
184        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
185           """
186           set the value of the coefficient to a new value
187    
188           @param domain: domain on which the PDE uses the coefficient
189           @type domain: L{Domain<escript.Domain>}
190           @param numEquations: number of equations of the PDE
191           @type numEquations: C{int}
192           @param numSolutions: number of components of the PDE solution
193           @type numSolutions: C{int}
194           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
195           @type reducedEquationOrder: C{bool}
196           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
197           @type reducedSolutionOrder: C{bool}
198           @param newValue: number of components of the PDE solution
199           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
200           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
201           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
202           """
203           if newValue==None:
204               newValue=escript.Data()
205           elif isinstance(newValue,escript.Data):
206               if not newValue.isEmpty():
207                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
208                    try:
209                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
210                    except:
211                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
212           else:
213               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
214           if not newValue.isEmpty():
215               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
216                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
217           self.value=newValue
218    
219      def isAlteringOperator(self):      def isAlteringOperator(self):
220          """          """
221      @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
222    
223            @return:  True if the operator of the PDE is changed when the coefficient is changed
224            @rtype:  C{bool}
225      """      """
226          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
227              return not None              return not None
# Line 119  class PDECoefficientType: Line 230  class PDECoefficientType:
230    
231      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
232          """          """
233      @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
234    
235        @rtype:  C{bool}
236            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
237      """      """
238          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
239              return not None              return not None
240          else:          else:
241              return None              return None
242    
243      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
244         """         """
245         @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
246    
247         @param shape         @param domain: domain on which the PDE uses the coefficient
248         @param dim         @type domain: L{Domain<escript.Domain>}
249           @param shape: suggested shape of the coefficient
250           @type shape: C{tuple} of C{int} values
251           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
252                     If no appropriate numbers could be identified, C{None} is returned
253           @rtype: C{tuple} of two C{int} values or C{None}
254         """         """
255           dim=domain.getDim()
256         if len(shape)>0:         if len(shape)>0:
257             num=max(shape)+1             num=max(shape)+1
258         else:         else:
259             num=1             num=1
260         search=[]         search=[]
261         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
262            for e in range(num):            for u in range(num):
263               search.append((e,u))               for e in range(num):
264         search.sort(_CompTuple2)                  search.append((e,u))
265         for item in search:            search.sort(self.__CompTuple2)
266               s=self.buildShape(item[0],item[1],dim)            for item in search:
267                 s=self.getShape(domain,item[0],item[1])
268               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
269                   return (1,1)                   return (1,1)
270               else:               else:
271                   if s==shape: return item                   if s==shape: return item
272           elif self.definesNumEquation():
273              for e in range(num,0,-1):
274                 s=self.getShape(domain,e,0)
275                 if len(s)==0 and len(shape)==0:
276                     return (1,None)
277                 else:
278                     if s==shape: return (e,None)
279    
280           elif self.definesNumSolutions():
281              for u in range(num,0,-1):
282                 s=self.getShape(domain,0,u)
283                 if len(s)==0 and len(shape)==0:
284                     return (None,1)
285                 else:
286                     if s==shape: return (None,u)
287         return None         return None
288        def definesNumSolutions(self):
289           """
290           checks if the coefficient allows to estimate the number of solution components
291    
292      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
293          """         @rtype: C{bool}
294      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
295           for i in self.pattern:
296                 if i==self.BY_SOLUTION: return True
297           return False
298    
299      @param e      def definesNumEquation(self):
300      @param u         """
301      @param dim         checks if the coefficient allows to estimate the number of equations
302      """  
303          s=()         @return: True if the coefficient allows an estimate of the number of equations
304          for i in self.pattern:         @rtype: C{bool}
305               if i==self.EQUATION:         """
306                  if e>1: s=s+(e,)         for i in self.pattern:
307               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
308                  if u>1: s=s+(u,)         return False
309    
310        def __CompTuple2(self,t1,t2):
311          """
312          Compare two tuples of possible number of equations and number of solutions
313    
314          @param t1: The first tuple
315          @param t2: The second tuple
316    
317          """
318    
319          dif=t1[0]+t1[1]-(t2[0]+t2[1])
320          if dif<0: return 1
321          elif dif>0: return -1
322          else: return 0
323    
324        def getShape(self,domain,numEquations=1,numSolutions=1):
325           """
326           builds the required shape of the coefficient
327    
328           @param domain: domain on which the PDE uses the coefficient
329           @type domain: L{Domain<escript.Domain>}
330           @param numEquations: number of equations of the PDE
331           @type numEquations: C{int}
332           @param numSolutions: number of components of the PDE solution
333           @type numSolutions: C{int}
334           @return: shape of the coefficient
335           @rtype: C{tuple} of C{int} values
336           """
337           dim=domain.getDim()
338           s=()
339           for i in self.pattern:
340                 if i==self.BY_EQUATION:
341                    if numEquations>1: s=s+(numEquations,)
342                 elif i==self.BY_SOLUTION:
343                    if numSolutions>1: s=s+(numSolutions,)
344               else:               else:
345                  s=s+(dim,)                  s=s+(dim,)
346          return s         return s
347    
348  _PDECoefficientTypes={  class LinearPDE(object):
 "A"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "B"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "C"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "D"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "X"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM),PDECoefficientType.RIGHTHANDSIDE),  
 "Y"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "r"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "q"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.SOLUTION,),PDECoefficientType.BOTH),  
 }  
   
 class LinearPDE:  
349     """     """
350     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
351         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  
352    
353       -(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:
354    
355       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)}
356    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
357    
358      and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
359       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
360       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
361       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
362       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
363       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
364       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.
365    
366          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:
367    
368      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}
369    
370           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>}.
371    
    """  
    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  
372    
373     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.  
374    
375       @param args     M{u=r}  where M{q>0}
376       """  
377       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
378       The constraints override any other condition set by the PDE or the boundary condition.
379    
380       The PDE is symmetrical if
381    
382       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]}
383    
384       For a system of PDEs and a solution with several components the PDE has the form
385    
386       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] }
387    
388       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.
389       The natural boundary conditions take the form:
390    
391       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]}
392    
393    
394       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>}.
395    
396       Constraints take the form
397    
398       M{u[i]=r[i]}  where  M{q[i]>0}
399    
400       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
401    
402       The system of PDEs is symmetrical if
403    
404            - M{A[i,j,k,l]=A[k,l,i,j]}
405            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
406            - M{B[i,j,k]=C[k,i,j]}
407            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
408            - M{D[i,k]=D[i,k]}
409            - M{D_reduced[i,k]=D_reduced[i,k]}
410            - M{d[i,k]=d[k,i]}
411            - M{d_reduced[i,k]=d_reduced[k,i]}
412    
413       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
414       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
415       defined as
416    
417       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]}
418    
419       For the case of single solution component and single PDE M{J} is defined
420    
421       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
422    
423       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
424       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
425       the contact condition takes the form
426    
427       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]}
428    
429       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
430       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
431       L{jump<util.jump>}.
432       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>}.
433       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>}.
434       In case of a single PDE and a single component solution the contact condition takes the form
435    
436       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
437    
438       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>}
439    
440       @cvar DEFAULT: The default method used to solve the system of linear equations
441       @cvar DIRECT: The direct solver based on LDU factorization
442       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
443       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
444       @cvar CR: The conjugate residual method
445       @cvar CGS: The conjugate gardient square method
446       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
447       @cvar SSOR: The symmetric overrealaxtion method
448       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449       @cvar ILUT: The incomplete LU factorization preconditioner with will in
450       @cvar JACOBI: The Jacobi preconditioner
451       @cvar GMRES: The Gram-Schmidt minimum residual method
452       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
453       @cvar LUMPING: Matrix lumping.
454       @cvar NO_REORDERING: No matrix reordering allowed
455       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
456       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
457       @cvar PASO: PASO solver package
458       @cvar SCSL: SGI SCSL solver library
459       @cvar MKL: Intel's MKL solver library
460       @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462       @cvar ITERATIVE: The default iterative solver
463       @cvar AMG: algebraic multi grid
464       @cvar RILU: recursive ILU
465    
466       """
467       DEFAULT= 0
468       DIRECT= 1
469       CHOLEVSKY= 2
470       PCG= 3
471       CR= 4
472       CGS= 5
473       BICGSTAB= 6
474       SSOR= 7
475       ILU0= 8
476       ILUT= 9
477       JACOBI= 10
478       GMRES= 11
479       PRES20= 12
480       LUMPING= 13
481       NO_REORDERING= 17
482       MINIMUM_FILL_IN= 18
483       NESTED_DISSECTION= 19
484       SCSL= 14
485       MKL= 15
486       UMFPACK= 16
487       ITERATIVE= 20
488       PASO= 21
489       AMG= 22
490       RILU = 23
491       TRILINOS = 24
492    
493       SMALL_TOLERANCE=1.e-13
494       __PACKAGE_KEY="package"
495       __METHOD_KEY="method"
496       __SYMMETRY_KEY="symmetric"
497       __TOLERANCE_KEY="tolerance"
498       __PRECONDITIONER_KEY="preconditioner"
499    
500    
501       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
502         """
503         initializes a new linear PDE
504    
505         @param domain: domain of the PDE
506         @type domain: L{Domain<escript.Domain>}
507         @param numEquations: number of equations. If numEquations==None the number of equations
508                              is exracted from the PDE coefficients.
509         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
510                              is exracted from the PDE coefficients.
511         @param debug: if True debug informations are printed.
512    
513         """
514         super(LinearPDE, self).__init__()
515         #
516         #   the coefficients of the general PDE:
517         #
518         self.__COEFFICIENTS_OF_GENEARL_PDE={
519           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
520           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
522           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
524           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
525           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
530           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
534           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
540           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
541    
542         # COEFFICIENTS can be overwritten by subclasses:
543         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
544         self.__altered_coefficients=False
545       # initialize attributes       # initialize attributes
546       self.__debug=None       self.__debug=debug
547       self.__domain=domain       self.__domain=domain
548       self.__numEquations=numEquations       self.__numEquations=numEquations
549       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
550       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  
551    
552       # set some default values:       # set some default values:
553       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
554       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
555       self.__tolerance=1.e-8       self.__tolerance=1.e-8
556       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
557       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
558         self.__preconditioner=self.DEFAULT
559         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
560       self.__sym=False       self.__sym=False
      self.__lumping=False  
561    
562     def getCoefficient(self,name):       self.resetCoefficients()
563         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
564       # =============================================================================
565       #    general stuff:
566       # =============================================================================
567       def __str__(self):
568         """
569         returns string representation of the PDE
570    
571         @return: a simple representation of the PDE
572         @rtype: C{str}
573         """
574         return "<LinearPDE %d>"%id(self)
575       # =============================================================================
576       #    debug :
577       # =============================================================================
578       def setDebugOn(self):
579         """
580         switches on debugging
581       """       """
582       @brief return the value of the coefficient name       self.__debug=not None
583    
584       @param name     def setDebugOff(self):
585         """
586         switches off debugging
587       """       """
588       return self.__coefficient[name]       self.__debug=None
589    
590     def setValue(self,**coefficients):     def trace(self,text):
591        """       """
592        @brief sets new values to coefficients       print the text message if debugging is swiched on.
593         @param text: message
594         @type text: C{string}
595         """
596         if self.__debug: print "%s: %s"%(str(self),text)
597    
598        @param coefficients     # =============================================================================
599        """     # some service functions:
600        self._setValue(**coefficients)     # =============================================================================
601             def getDomain(self):
602         """
603         returns the domain of the PDE
604    
605     def _setValue(self,**coefficients):       @return: the domain of the PDE
606        """       @rtype: L{Domain<escript.Domain>}
607        @brief sets new values to coefficients       """
608         return self.__domain
609    
610        @param coefficients     def getDim(self):
611        """       """
612               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
613    
614        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
615        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
616           for i in self.__coefficient.iterkeys():       """
617               if alteredCoefficients.has_key(i) and not alteredCoefficients[i].isEmpty():       return self.getDomain().getDim()
                  if not self.getShapeOfCoefficient(i)==alteredCoefficients[i].getShape():  
                     raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),alteredCoefficients[i].getShape())  
              else:  
                  if not self.__coefficient[i].isEmpty():  
                     if not self.getShapeOfCoefficient(i)==self.__coefficient[i].getShape():  
                        raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),self.__coefficient[i].getShape())  
       # overwrite new values:  
       for i,d in alteredCoefficients.iteritems():  
          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
          self.__coefficient[i]=d  
          self.alteredCoefficient(i)  
   
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if not "q" in alteredCoefficients and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def cleanCoefficients(self):  
      """  
      @brief resets all coefficients to default values.  
      """  
      self.__coefficient={}  
      for i in _PDECoefficientTypes.iterkeys():  
          self.__coefficient[i]=escript.Data()  
618    
619     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
620       """       """
621       @brief return the shape of the coefficient name       returns the number of equations
622    
623       @param name       @return: the number of equations
624         @rtype: C{int}
625         @raise UndefinedPDEError: if the number of equations is not be specified yet.
626       """       """
627       if self.hasCoefficient(name):       if self.__numEquations==None:
628          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
629       else:       else:
630          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
631    
632     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
633       """       """
634       @brief return the atoms of the coefficient name       returns the number of unknowns
635    
636       @param name       @return: the number of unknowns
637         @rtype: C{int}
638         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
639       """       """
640       if self.hasCoefficient(name):       if self.__numSolutions==None:
641          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
642       else:       else:
643          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
644    
645     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
646       """       """
647       @brief annonced that coefficient name has been changed       return status for order reduction for equation
648    
649       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
650         @rtype: L{bool}
651       """       """
652       if self.hasCoefficient(name):       return self.__reduce_equation_order
         if _PDECoefficientTypes[name].isAlteringOperator(): self.__rebuildOperator()  
         if _PDECoefficientTypes[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()  
      else:  
         raise ValueError,"Solution coefficient %s requested"%name  
653    
654     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
655        """       """
656        @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.       return status for order reduction for the solution
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty() and not r.isEmpty():  
          print (q*r).Lsup(), 1.e-13*r.Lsup()  
          if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False  
       if self.debug():  
            if self.__homogeneous_constraint:  
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
   
    def hasCoefficient(self,name):  
       """  
       @brief return true if name is the name of a coefficient  
657    
658        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
659        """       @rtype: L{bool}
660        return self.__coefficient.has_key(name)       """
661         return self.__reduce_solution_order
662    
663     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
664       """       """
665       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
666    
667         @return: representation space of equation
668         @rtype: L{FunctionSpace<escript.FunctionSpace>}
669       """       """
670       return self.__row_function_space       if self.reduceEquationOrder():
671             return escript.ReducedSolution(self.getDomain())
672         else:
673             return escript.Solution(self.getDomain())
674    
675     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
676       """       """
677       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
678    
679         @return: representation space of solution
680         @rtype: L{FunctionSpace<escript.FunctionSpace>}
681       """       """
682       return self.__column_function_space       if self.reduceSolutionOrder():
683             return escript.ReducedSolution(self.getDomain())
684         else:
685             return escript.Solution(self.getDomain())
686    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
687    
688     def setDebugOff(self):     def getOperator(self):
689         """       """
690         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
691    
692     def debug(self):       @return: the operator of the PDE
693         """       @rtype: L{Operator<escript.Operator>}
694         @brief returns true if the PDE is in the debug mode       """
695         """       m=self.getSystem()[0]
696         return self.__debug       if self.isUsingLumping():
697             return self.copyConstraint(1./m)
698         else:
699             return m
700    
701     #===== Lumping ===========================     def getRightHandSide(self):
702     def setLumpingOn(self):       """
703        """       provides access to the right hand side of the PDE
704        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
705        """       @rtype: L{Data<escript.Data>}
706        if not self.isUsingLumping():       """
707           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
708           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
709           self.__rebuildOperator()           return self.copyConstraint(r)
710           self.__lumping=True       else:
711             return r
712    
713     def setLumpingOff(self):     def applyOperator(self,u=None):
714        """       """
715        @brief switches off matrix lumping       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
716    
717     def setLumping(self,flag=False):       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
718        """                 the current solution is used.
719        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
720        """       @return: image of u
721        if flag:       @rtype: L{Data<escript.Data>}
722           self.setLumpingOn()       """
723        else:       if u==None:
724           self.setLumpingOff()          return self.getOperator()*self.getSolution()
725         else:
726            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
727    
728     def isUsingLumping(self):     def getResidual(self,u=None):
729         """
730         return the residual of u or the current solution if u is not present.
731    
732         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
733                   the current solution is used.
734         @type u: L{Data<escript.Data>} or None
735         @return: residual of u
736         @rtype: L{Data<escript.Data>}
737         """
738         return self.applyOperator(u)-self.getRightHandSide()
739    
740       def checkSymmetry(self,verbose=True):
741        """        """
742        @brief        test the PDE for symmetry.
743    
744          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
745          @type verbose: C{bool}
746          @return:  True if the PDE is symmetric.
747          @rtype: L{Data<escript.Data>}
748          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
749        """        """
750        return self.__lumping        verbose=verbose or self.__debug
751          out=True
752          if self.getNumSolutions()!=self.getNumEquations():
753             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
754             out=False
755          else:
756             A=self.getCoefficientOfGeneralPDE("A")
757             if not A.isEmpty():
758                tol=util.Lsup(A)*self.SMALL_TOLERANCE
759                if self.getNumSolutions()>1:
760                   for i in range(self.getNumEquations()):
761                      for j in range(self.getDim()):
762                         for k in range(self.getNumSolutions()):
763                            for l in range(self.getDim()):
764                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
765                                   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)
766                                   out=False
767                else:
768                   for j in range(self.getDim()):
769                      for l in range(self.getDim()):
770                         if util.Lsup(A[j,l]-A[l,j])>tol:
771                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
772                            out=False
773             B=self.getCoefficientOfGeneralPDE("B")
774             C=self.getCoefficientOfGeneralPDE("C")
775             if B.isEmpty() and not C.isEmpty():
776                if verbose: print "non-symmetric PDE because B is not present but C is"
777                out=False
778             elif not B.isEmpty() and C.isEmpty():
779                if verbose: print "non-symmetric PDE because C is not present but B is"
780                out=False
781             elif not B.isEmpty() and not C.isEmpty():
782                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
783                if self.getNumSolutions()>1:
784                   for i in range(self.getNumEquations()):
785                       for j in range(self.getDim()):
786                          for k in range(self.getNumSolutions()):
787                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
788                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
789                                  out=False
790                else:
791                   for j in range(self.getDim()):
792                      if util.Lsup(B[j]-C[j])>tol:
793                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
794                         out=False
795             if self.getNumSolutions()>1:
796               D=self.getCoefficientOfGeneralPDE("D")
797               if not D.isEmpty():
798                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
799                 for i in range(self.getNumEquations()):
800                    for k in range(self.getNumSolutions()):
801                      if util.Lsup(D[i,k]-D[k,i])>tol:
802                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
803                          out=False
804               d=self.getCoefficientOfGeneralPDE("d")
805               if not d.isEmpty():
806                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
807                 for i in range(self.getNumEquations()):
808                    for k in range(self.getNumSolutions()):
809                      if util.Lsup(d[i,k]-d[k,i])>tol:
810                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
811                          out=False
812               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
813               if not d_contact.isEmpty():
814                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
815                 for i in range(self.getNumEquations()):
816                    for k in range(self.getNumSolutions()):
817                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
818                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
819                          out=False
820             # and now the reduced coefficients
821             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
822             if not A_reduced.isEmpty():
823                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
824                if self.getNumSolutions()>1:
825                   for i in range(self.getNumEquations()):
826                      for j in range(self.getDim()):
827                         for k in range(self.getNumSolutions()):
828                            for l in range(self.getDim()):
829                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
830                                   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)
831                                   out=False
832                else:
833                   for j in range(self.getDim()):
834                      for l in range(self.getDim()):
835                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
836                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
837                            out=False
838             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
839             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
840             if B_reduced.isEmpty() and not C_reduced.isEmpty():
841                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
842                out=False
843             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
847                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
848                if self.getNumSolutions()>1:
849                   for i in range(self.getNumEquations()):
850                       for j in range(self.getDim()):
851                          for k in range(self.getNumSolutions()):
852                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
853                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
854                                  out=False
855                else:
856                   for j in range(self.getDim()):
857                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
858                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
859                         out=False
860             if self.getNumSolutions()>1:
861               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
862               if not D_reduced.isEmpty():
863                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
870               if not d_reduced.isEmpty():
871                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
872                 for i in range(self.getNumEquations()):
873                    for k in range(self.getNumSolutions()):
874                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
875                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
876                          out=False
877               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
878               if not d_contact_reduced.isEmpty():
879                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
880                 for i in range(self.getNumEquations()):
881                    for k in range(self.getNumSolutions()):
882                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
883                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
884                          out=False
885          return out
886    
887     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
888         """         """
889         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
890    
891           @return: the solution
892           @rtype: L{Data<escript.Data>}
893           @param options: solver options
894           @keyword verbose: True to get some information during PDE solution
895           @type verbose: C{bool}
896           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
897                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
898           @keyword iter_max: maximum number of iteration steps allowed.
899           @keyword drop_tolerance: threshold for drupping in L{ILUT}
900           @keyword drop_storage: maximum of allowed memory in L{ILUT}
901           @keyword truncation: maximum number of residuals in L{GMRES}
902           @keyword restart: restart cycle length in L{GMRES}
903         """         """
904         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
905              mat,f=self.getSystem()
906              if self.isUsingLumping():
907                 self.__solution=self.copyConstraint(f*mat)
908              else:
909                 options[self.__TOLERANCE_KEY]=self.getTolerance()
910                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
911                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
912                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
913                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
914                 self.trace("PDE is resolved.")
915                 self.trace("solver options: %s"%str(options))
916                 self.__solution=mat.solve(f,options)
917              self.__solution_isValid=True
918           return self.__solution
919    
920       def getFlux(self,u=None):
921         """
922         returns the flux M{J} for a given M{u}
923    
924         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]}
925    
926         or
927    
928         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
929    
930         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
931         @type u: L{Data<escript.Data>} or None
932         @return: flux
933         @rtype: L{Data<escript.Data>}
934         """
935         if u==None: u=self.getSolution()
936         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
937               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
938               -util.self.getCoefficientOfGeneralPDE("X") \
939               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X_reduced")
942       # =============================================================================
943       #   solver settings:
944       # =============================================================================
945       def setSolverMethod(self,solver=None,preconditioner=None):
946           """
947           sets a new solver
948    
949           @param solver: sets a new solver method.
950           @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}
951           @param preconditioner: sets a new solver method.
952           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
953           """
954           if solver==None: solver=self.__solver_method
955           if preconditioner==None: preconditioner=self.__preconditioner
956           if solver==None: solver=self.DEFAULT
957           if preconditioner==None: preconditioner=self.DEFAULT
958           if not (solver,preconditioner)==self.getSolverMethod():
959             self.__solver_method=solver             self.__solver_method=solver
960             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
961             self.__checkMatrixType()             self.__checkMatrixType()
962               self.trace("New solver is %s"%self.getSolverMethodName())
963    
964       def getSolverMethodName(self):
965           """
966           returns the name of the solver currently used
967    
968           @return: the name of the solver currently used.
969           @rtype: C{string}
970           """
971    
972           m=self.getSolverMethod()
973           p=self.getSolverPackage()
974           method=""
975           if m[0]==self.DEFAULT: method="DEFAULT"
976           elif m[0]==self.DIRECT: method= "DIRECT"
977           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
978           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
979           elif m[0]==self.PCG: method= "PCG"
980           elif m[0]==self.CR: method= "CR"
981           elif m[0]==self.CGS: method= "CGS"
982           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
983           elif m[0]==self.SSOR: method= "SSOR"
984           elif m[0]==self.GMRES: method= "GMRES"
985           elif m[0]==self.PRES20: method= "PRES20"
986           elif m[0]==self.LUMPING: method= "LUMPING"
987           elif m[0]==self.AMG: method= "AMG"
988           if m[1]==self.DEFAULT: method+="+DEFAULT"
989           elif m[1]==self.JACOBI: method+= "+JACOBI"
990           elif m[1]==self.ILU0: method+= "+ILU0"
991           elif m[1]==self.ILUT: method+= "+ILUT"
992           elif m[1]==self.SSOR: method+= "+SSOR"
993           elif m[1]==self.AMG: method+= "+AMG"
994           elif m[1]==self.RILU: method+= "+RILU"
995           if p==self.DEFAULT: package="DEFAULT"
996           elif p==self.PASO: package= "PASO"
997           elif p==self.MKL: package= "MKL"
998           elif p==self.SCSL: package= "SCSL"
999           elif p==self.UMFPACK: package= "UMFPACK"
1000           elif p==self.TRILINOS: package= "TRILINOS"
1001           else : method="unknown"
1002           return "%s solver of %s package"%(method,package)
1003    
1004    
1005     def getSolverMethod(self):     def getSolverMethod(self):
1006         """         """
1007         @brief returns the solver method         returns the solver method
1008    
1009           @return: the solver method currently be used.
1010           @rtype: C{int}
1011           """
1012           return self.__solver_method,self.__preconditioner
1013    
1014       def setSolverPackage(self,package=None):
1015           """
1016           sets a new solver package
1017    
1018           @param package: sets a new solver method.
1019           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1020           """
1021           if package==None: package=self.DEFAULT
1022           if not package==self.getSolverPackage():
1023               self.__solver_package=package
1024               self.__checkMatrixType()
1025               self.trace("New solver is %s"%self.getSolverMethodName())
1026    
1027       def getSolverPackage(self):
1028           """
1029           returns the package of the solver
1030    
1031           @return: the solver package currently being used.
1032           @rtype: C{int}
1033         """         """
1034         return self.__solver_method         return self.__solver_package
1035    
1036       def isUsingLumping(self):
1037          """
1038          checks if matrix lumping is used a solver method
1039    
1040          @return: True is lumping is currently used a solver method.
1041          @rtype: C{bool}
1042          """
1043          return self.getSolverMethod()[0]==self.LUMPING
1044    
    #============ tolerance business =========================================================  
1045     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1046         """         """
1047         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1048    
1049           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1050    
1051           defines the stopping criterion.
1052    
1053           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1054                       the system will be resolved.
1055           @type tol: positive C{float}
1056           @raise ValueError: if tolerance is not positive.
1057         """         """
1058         if not tol>0:         if not tol>0:
1059             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1060         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1061         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1062         self.__tolerance=tol         self.__tolerance=tol
1063         return         return
1064    
1065     def getTolerance(self):     def getTolerance(self):
1066         """         """
1067         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1068    
1069           @return: tolerance currently used.
1070           @rtype: C{float}
1071         """         """
1072         return self.__tolerance         return self.__tolerance
1073    
1074     #===== symmetry  flag ==========================     # =============================================================================
1075       #    symmetry  flag:
1076       # =============================================================================
1077     def isSymmetric(self):     def isSymmetric(self):
1078        """        """
1079        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1080    
1081          @return: True is a symmetric PDE is indicated, otherwise False is returned
1082          @rtype: C{bool}
1083        """        """
1084        return self.__sym        return self.__sym
1085    
1086     def setSymmetryOn(self):     def setSymmetryOn(self):
1087        """        """
1088        @brief sets the symmetry flag to true        sets the symmetry flag.
1089        """        """
1090        if not self.isSymmetric():        if not self.isSymmetric():
1091           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1092           self.__sym=True           self.__sym=True
1093           self.__checkMatrixType()           self.__checkMatrixType()
1094    
1095     def setSymmetryOff(self):     def setSymmetryOff(self):
1096        """        """
1097        @brief sets the symmetry flag to false        removes the symmetry flag.
1098        """        """
1099        if self.isSymmetric():        if self.isSymmetric():
1100           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1101           self.__sym=False           self.__sym=False
1102           self.__checkMatrixType()           self.__checkMatrixType()
1103    
1104     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1105       """        """
1106       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1107    
1108       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1109       """        @type flag: C{bool}
1110       if flag:        """
1111          self.setSymmetryOn()        if flag:
1112       else:           self.setSymmetryOn()
1113          self.setSymmetryOff()        else:
1114             self.setSymmetryOff()
1115    
1116     #===== order reduction ==========================     # =============================================================================
1117       # function space handling for the equation as well as the solution
1118       # =============================================================================
1119     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1120       """       """
1121       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1122    
1123         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1124       """       """
1125       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1126       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1127    
1128     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1129       """       """
1130       @brief switches to full order       switches off reduced order for solution and equation representation
1131    
1132         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1133       """       """
1134       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1135       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1136    
1137     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1138       """       """
1139       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1140         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1141       @param flag                    if flag is not present order reduction is switched off
1142         @type flag: C{bool}
1143         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1144       """       """
1145       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1146       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1147    
1148     #===== order reduction solution ==========================  
1149     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1150       """       """
1151       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1152    
1153         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1154       """       """
1155       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1156       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1157           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1158           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1159           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1160             self.__resetSystem()
1161    
1162     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1163       """       """
1164       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1165    
1166         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1167       """       """
1168       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1169       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1170           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1171           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1172           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1173             self.__resetSystem()
1174    
1175     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1176       """       """
1177       @brief sets order for test functions according to flag       sets order for test functions according to flag
1178    
1179       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1180                      if flag is not present order reduction is switched off
1181         @type flag: C{bool}
1182         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1183       """       """
1184       if flag:       if flag:
1185          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1186       else:       else:
1187          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1188                                                                                                                                                              
    #===== order reduction equation ==========================  
1189     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1190       """       """
1191       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1192    
1193         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1194       """       """
1195       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1196       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1197           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1198           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1199           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1200             self.__resetSystem()
1201    
1202     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1203       """       """
1204       @brief switches to full order for test functions       switches off reduced order for equation representation
1205    
1206         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1207       """       """
1208       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1209       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1210           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1211           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1212           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1213             self.__resetSystem()
1214    
1215     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1216       """       """
1217       @brief sets order for test functions according to flag       sets order for test functions according to flag
1218    
1219       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1220                      if flag is not present order reduction is switched off
1221         @type flag: C{bool}
1222         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1223       """       """
1224       if flag:       if flag:
1225          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1226       else:       else:
1227          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1228    
1229     # ==== initialization =====================================================================     # =============================================================================
1230     def __makeNewOperator(self):     # private method:
1231       # =============================================================================
1232       def __checkMatrixType(self):
1233         """
1234         reassess the matrix type and, if a new matrix is needed, resets the system.
1235         """
1236         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1237         if not new_matrix_type==self.__matrix_type:
1238             self.trace("Matrix type is now %d."%new_matrix_type)
1239             self.__matrix_type=new_matrix_type
1240             self.__resetSystem()
1241       #
1242       #   rebuild switches :
1243       #
1244       def __invalidateSolution(self):
1245           """
1246           indicates the PDE has to be resolved if the solution is requested
1247           """
1248           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1249           self.__solution_isValid=False
1250    
1251       def __invalidateOperator(self):
1252           """
1253           indicates the operator has to be rebuilt next time it is used
1254           """
1255           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1256           self.__invalidateSolution()
1257           self.__operator_is_Valid=False
1258    
1259       def __invalidateRightHandSide(self):
1260         """         """
1261         @brief         indicates the right hand side has to be rebuild next time it is used
1262         """         """
1263           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1264           self.__invalidateSolution()
1265           self.__righthandside_isValid=False
1266    
1267       def __invalidateSystem(self):
1268           """
1269           annonced that everthing has to be rebuild:
1270           """
1271           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1272           self.__invalidateSolution()
1273           self.__invalidateOperator()
1274           self.__invalidateRightHandSide()
1275    
1276       def __resetSystem(self):
1277           """
1278           annonced that everthing has to be rebuild:
1279           """
1280           self.trace("New System is built from scratch.")
1281           self.__operator=escript.Operator()
1282           self.__operator_is_Valid=False
1283           self.__righthandside=escript.Data()
1284           self.__righthandside_isValid=False
1285           self.__solution=escript.Data()
1286           self.__solution_isValid=False
1287       #
1288       #    system initialization:
1289       #
1290       def __getNewOperator(self):
1291           """
1292           returns an instance of a new operator
1293           """
1294           self.trace("New operator is allocated.")
1295         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1296                             self.getNumEquations(), \                             self.getNumEquations(), \
1297                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1299  class LinearPDE:
1299                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1300                             self.__matrix_type)                             self.__matrix_type)
1301    
1302     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1303         """         """
1304         @brief         returns an instance of a new right hand side
1305         """         """
1306         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1307           if self.getNumEquations()>1:
1308               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1309           else:
1310               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1311    
1312     def __makeNewSolution(self):     def __getNewSolution(self):
1313         """         """
1314         @brief         returns an instance of a new solution
1315         """         """
1316         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1317           if self.getNumSolutions()>1:
1318               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1319           else:
1320               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1321    
1322     def __getFreshOperator(self):     def __makeFreshSolution(self):
1323         """         """
1324         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1325         """         """
1326         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1327             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1328         else:         else:
1329             self.__operator.setValue(0.)             self.__solution*=0
1330             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1331         return self.__operator         return self.__solution
1332    
1333     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1334         """         """
1335         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1336         """         """
1337         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1338             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1339         else:         else:
1340             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1341             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1342             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
   
    # ==== 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(deep)  
   
1343    
1344     def __rebuildOperator(self,deep=False):     def __makeFreshOperator(self):
1345         """         """
1346         @brief indicates the operator has to be rebuilt next time it is used         makes sure that the operator is instantiated and returns it initialized by zeros
1347         """         """
1348         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if self.__operator.isEmpty():
1349         self.__rebuildSolution(deep)             self.__operator=self.__getNewOperator()
1350         self.__operator_isValid=False         else:
1351         if deep: self.__operator=escript.Operator()             self.__operator.resetValues()
1352               self.trace("Operator reset to zero")
1353           return self.__operator
1354    
1355     def __rebuildRightHandSide(self,deep=False):     def __applyConstraint(self):
1356         """         """
1357         @brief indicates the right hand side has to be rebuild next time it is used         applies the constraints defined by q and r to the system
1358         """         """
1359         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."         if not self.isUsingLumping():
1360         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1361         self.__righthandside_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1362         if not self.__homogeneous_constraint: self.__rebuildOperator()            if not q.isEmpty() and not self.__operator.isEmpty():
1363         if deep: self.__righthandside=escript.Data()               # q is the row and column mask to indicate where constraints are set:
1364                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1365                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1366                 u=self.__getNewSolution()
1367                 if r.isEmpty():
1368                    r_s=self.__getNewSolution()
1369                 else:
1370                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1371                 u.copyWithMask(r_s,col_q)
1372                 if not self.__righthandside.isEmpty():
1373                    self.__righthandside-=self.__operator*u
1374                    self.__righthandside=self.copyConstraint(self.__righthandside)
1375                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1376       # =============================================================================
1377       # function giving access to coefficients of the general PDE:
1378       # =============================================================================
1379       def getCoefficientOfGeneralPDE(self,name):
1380         """
1381         return the value of the coefficient name of the general PDE.
1382    
1383         @note: This method is called by the assembling routine it can be overwritten
1384               to map coefficients of a particular PDE to the general PDE.
1385         @param name: name of the coefficient requested.
1386         @type name: C{string}
1387         @return: the value of the coefficient  name
1388         @rtype: L{Data<escript.Data>}
1389         @raise IllegalCoefficient: if name is not one of coefficients
1390                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1391                      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}.
1392         """
1393         if self.hasCoefficientOfGeneralPDE(name):
1394            return self.getCoefficient(name)
1395         else:
1396            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1397    
1398     def __rebuildSystem(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
1399       """       """
1400       @brief reassess the matrix type and, if needed, initiates an operator rebuild       checks if name is a the name of a coefficient of the general PDE.
1401    
1402         @param name: name of the coefficient enquired.
1403         @type name: C{string}
1404         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1405         @rtype: C{bool}
1406    
1407       """       """
1408       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
      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)  
1409    
1410     #============ assembling =======================================================     def createCoefficientOfGeneralPDE(self,name):
1411     def __copyConstraint(self,u):       """
1412        """       returns a new instance of a coefficient for coefficient name of the general PDE
       @brief copies the constrint condition into u  
       """  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty():  
           if r.isEmpty():  
              r2=escript.Data(0,u.getShape(),u.getFunctionSpace())  
           else:  
              r2=escript.Data(r,u.getFunctionSpace())  
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1413    
1414     def __applyConstraint(self,rhs_update=True):       @param name: name of the coefficient requested.
1415         """       @type name: C{string}
1416         @brief applies the constraints  defined by q and r to the system       @return: a coefficient name initialized to 0.
1417         """       @rtype: L{Data<escript.Data>}
1418         q=self.getCoefficient("q")       @raise IllegalCoefficient: if name is not one of coefficients
1419         r=self.getCoefficient("r")                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1420         if not q.isEmpty() and not self.__operator.isEmpty():                    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}.
1421            # q is the row and column mask to indicate where constraints are set:       """
1422            row_q=escript.Data(q,self.getFunctionSpaceForEquation())       if self.hasCoefficientOfGeneralPDE(name):
1423            col_q=escript.Data(q,self.getFunctionSpaceForSolution())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1424            u=self.__makeNewSolution()       else:
1425            if r.isEmpty():          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if not self.__righthandside.isEmpty() and rhs_update: self.__righthandside-=self.__operator*u  
           self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1426    
1427     def getOperator(self):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1428         """       """
1429         @brief returns the operator of the PDE       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
        """  
        if not self.__operator_isValid:  
            # some Constraints are applying for a lumpled stifness matrix:  
            if self.isUsingLumping():  
               if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():  
                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"  
               if not self.getCoefficient("A").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient A"  
               if not self.getCoefficient("B").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient B"  
               if not self.getCoefficient("C").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient C"  
               if not self.getCoefficient("D").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient D"  
               if self.debug() : print "PDE Debug: New lumped operator is built."  
               mat=self.__makeNewOperator(self)  
            else:  
               if self.debug() : print "PDE Debug: New operator is built."  
               mat=self.__getFreshOperator()  
   
            self.getDomain().addPDEToSystem(mat,escript.Data(), \  
                         self.getCoefficient("A"), \  
                         self.getCoefficient("B"), \  
                         self.getCoefficient("C"), \  
                         self.getCoefficient("D"), \  
                         escript.Data(), \  
                         escript.Data(), \  
                         self.getCoefficient("d"), \  
                         escript.Data(),\  
                         self.getCoefficient("d_contact"), \  
                         escript.Data())  
            if self.isUsingLumping():  
               self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceOfSolution(),True)  
            else:  
               self.__applyConstraint(rhs_update=False)  
            self.__operator_isValid=True  
        return self.__operator  
1430    
1431     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1432         """       @type name: C{string}
1433         @brief returns the right hand side of the PDE       @return: the function space to be used for coefficient name
1434         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1435         @raise IllegalCoefficient: if name is not one of coefficients
1436                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1437                      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}.
1438         """
1439         if self.hasCoefficientOfGeneralPDE(name):
1440            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1441         else:
1442            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1443    
1444         @param ignoreConstraint     def getShapeOfCoefficientOfGeneralPDE(self,name):
1445         """       """
1446         if not self.__righthandside_isValid:       return the shape of the coefficient name of the general PDE
            if self.debug() : print "PDE Debug: New right hand side is built."  
            self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \  
                          self.getCoefficient("X"), \  
                          self.getCoefficient("Y"),\  
                          self.getCoefficient("y"),\  
                          self.getCoefficient("y_contact"))  
            self.__righthandside_isValid=True  
            if ignoreConstraint: self.__copyConstraint(self.__righthandside)  
        return self.__righthandside  
1447    
1448     def getSystem(self):       @param name: name of the coefficient enquired.
1449         """       @type name: C{string}
1450         @brief       @return: the shape of the coefficient name
1451         """       @rtype: C{tuple} of C{int}
1452         if not self.__operator_isValid and not self.__righthandside_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1453            if self.debug() : print "PDE Debug: New PDE is built."                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1454            if self.isUsingLumping():                    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}.
1455                self.getRightHandSide(ignoreConstraint=True)       """
1456                self.getOperator()       if self.hasCoefficientOfGeneralPDE(name):
1457            else:          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1458                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \       else:
1459                              self.getCoefficient("A"), \          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
                             self.getCoefficient("B"), \  
                             self.getCoefficient("C"), \  
                             self.getCoefficient("D"), \  
                             self.getCoefficient("X"), \  
                             self.getCoefficient("Y"), \  
                             self.getCoefficient("d"), \  
                             self.getCoefficient("y"), \  
                             self.getCoefficient("d_contact"), \  
                             self.getCoefficient("y_contact"))  
           self.__operator_isValid=True  
           self.__righthandside_isValid=True  
           self.__applyConstraint()  
           self.__copyConstraint(self.__righthandside)  
        elif not self.__operator_isValid:  
           self.getOperator()  
        elif not self.__righthandside_isValid:  
           self.getRightHandSide()  
        return (self.__operator,self.__righthandside)  
1460    
1461     def solve(self,**options):     # =============================================================================
1462        """     # functions giving access to coefficients of a particular PDE implementation:
1463        @brief solve the PDE     # =============================================================================
1464       def getCoefficient(self,name):
1465         """
1466         returns the value of the coefficient name
1467    
1468        @param options       @param name: name of the coefficient requested.
1469        """       @type name: C{string}
1470        mat,f=self.getSystem()       @return: the value of the coefficient name
1471        if self.isUsingLumping():       @rtype: L{Data<escript.Data>}
1472           out=f/mat       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1473           self.__copyConstraint(out)       """
1474        else:       if self.hasCoefficient(name):
1475           options[util.TOLERANCE_KEY]=self.getTolerance()           return self.COEFFICIENTS[name].getValue()
1476           options[util.METHOD_KEY]=self.getSolverMethod()       else:
1477           options[util.SYMMETRY_KEY]=self.isSymmetric()          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1478    
1479     def getSolution(self,**options):     def hasCoefficient(self,name):
1480         """       """
1481         @brief returns the solution of the PDE       return True if name is the name of a coefficient
1482    
1483         @param options       @param name: name of the coefficient enquired.
1484         """       @type name: C{string}
1485         if not self.__solution_isValid:       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1486             if self.debug() : print "PDE Debug: PDE is resolved."       @rtype: C{bool}
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
    #============ some serivice functions  =====================================================  
    def getDomain(self):  
1487       """       """
1488       @brief returns the domain of the PDE       return self.COEFFICIENTS.has_key(name)
1489    
1490       def createCoefficient(self, name):
1491       """       """
1492       return self.__domain       create a L{Data<escript.Data>} object corresponding to coefficient name
1493    
1494     def getDim(self):       @return: a coefficient name initialized to 0.
1495         @rtype: L{Data<escript.Data>}
1496         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1497       """       """
1498       @brief returns the spatial dimension of the PDE       if self.hasCoefficient(name):
1499            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1500         else:
1501            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1502    
1503       def getFunctionSpaceForCoefficient(self,name):
1504       """       """
1505       return self.getDomain().getDim()       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1506    
1507     def getNumEquations(self):       @param name: name of the coefficient enquired.
1508         @type name: C{string}
1509         @return: the function space to be used for coefficient name
1510         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1511         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1512       """       """
1513       @brief returns the number of equations       if self.hasCoefficient(name):
1514            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1515         else:
1516            raise ValueError,"unknown coefficient %s requested"%name
1517       def getShapeOfCoefficient(self,name):
1518       """       """
1519       if self.__numEquations>0:       return the shape of the coefficient name
1520           return self.__numEquations  
1521         @param name: name of the coefficient enquired.
1522         @type name: C{string}
1523         @return: the shape of the coefficient name
1524         @rtype: C{tuple} of C{int}
1525         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1526         """
1527         if self.hasCoefficient(name):
1528            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1529       else:       else:
1530           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1531    
1532     def getNumSolutions(self):     def resetCoefficients(self):
1533       """       """
1534       @brief returns the number of unknowns       resets all coefficients to there default values.
1535       """       """
1536       if self.__numSolutions>0:       for i in self.COEFFICIENTS.iterkeys():
1537          return self.__numSolutions           self.COEFFICIENTS[i].resetValue()
1538    
1539       def alteredCoefficient(self,name):
1540         """
1541         announce that coefficient name has been changed
1542    
1543         @param name: name of the coefficient enquired.
1544         @type name: C{string}
1545         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1546         @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.
1547         """
1548         if self.hasCoefficient(name):
1549            self.trace("Coefficient %s has been altered."%name)
1550            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1551               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1552               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1553       else:       else:
1554          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1555    
1556       def copyConstraint(self,u):
1557          """
1558          copies the constraint into u and returns u.
1559    
1560     def checkSymmetry(self):        @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1561          @type u: L{Data<escript.Data>}
1562          @return: the input u modified by the constraints.
1563          @rtype: L{Data<escript.Data>}
1564          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1565        """        """
1566        @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.        q=self.getCoefficientOfGeneralPDE("q")
1567          r=self.getCoefficientOfGeneralPDE("r")
1568          if not q.isEmpty():
1569             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1570             if r.isEmpty():
1571                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1572             else:
1573                 r=escript.Data(r,u.getFunctionSpace())
1574             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1575          return u
1576    
1577       def setValue(self,**coefficients):
1578        """        """
1579        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1580    
1581        return None        @param coefficients: new values assigned to coefficients
1582          @keyword A: value for coefficient A.
1583          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584          @keyword A_reduced: value for coefficient A_reduced.
1585          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1586          @keyword B: value for coefficient B
1587          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1588          @keyword B_reduced: value for coefficient B_reduced
1589          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1590          @keyword C: value for coefficient C
1591          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1592          @keyword C_reduced: value for coefficient C_reduced
1593          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594          @keyword D: value for coefficient D
1595          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1596          @keyword D_reduced: value for coefficient D_reduced
1597          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598          @keyword X: value for coefficient X
1599          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1600          @keyword X_reduced: value for coefficient X_reduced
1601          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602          @keyword Y: value for coefficient Y
1603          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1604          @keyword Y_reduced: value for coefficient Y_reduced
1605          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1606          @keyword d: value for coefficient d
1607          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1608          @keyword d_reduced: value for coefficient d_reduced
1609          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1610          @keyword y: value for coefficient y
1611          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1612          @keyword d_contact: value for coefficient d_contact
1613          @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>}.
1614          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1615          @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>}.
1616          @keyword y_contact: value for coefficient y_contact
1617          @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>}.
1618          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1619          @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>}.
1620          @keyword r: values prescribed to the solution at the locations of constraints
1621          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1622                   depending of reduced order is used for the solution.
1623          @keyword q: mask for location of constraints
1624          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1625                   depending of reduced order is used for the representation of the equation.
1626          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1627          """
1628          # check if the coefficients are  legal:
1629          for i in coefficients.iterkeys():
1630             if not self.hasCoefficient(i):
1631                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1632          # if the number of unknowns or equations is still unknown we try to estimate them:
1633          if self.__numEquations==None or self.__numSolutions==None:
1634             for i,d in coefficients.iteritems():
1635                if hasattr(d,"shape"):
1636                    s=d.shape
1637                elif hasattr(d,"getShape"):
1638                    s=d.getShape()
1639                else:
1640                    s=numarray.array(d).shape
1641                if s!=None:
1642                    # get number of equations and number of unknowns:
1643                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1644                    if res==None:
1645                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1646                    else:
1647                        if self.__numEquations==None: self.__numEquations=res[0]
1648                        if self.__numSolutions==None: self.__numSolutions=res[1]
1649          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1650          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1651          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1652          for i,d in coefficients.iteritems():
1653            try:
1654               self.COEFFICIENTS[i].setValue(self.getDomain(),
1655                                             self.getNumEquations(),self.getNumSolutions(),
1656                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1657               self.alteredCoefficient(i)
1658            except IllegalCoefficientFunctionSpace,m:
1659                # if the function space is wrong then we try the reduced version:
1660                i_red=i+"_reduced"
1661                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1662                    try:
1663                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1664                                                          self.getNumEquations(),self.getNumSolutions(),
1665                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1666                        self.alteredCoefficient(i_red)
1667                    except IllegalCoefficientValue,m:
1668                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1669                    except IllegalCoefficientFunctionSpace,m:
1670                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1671                else:
1672                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673            except IllegalCoefficientValue,m:
1674               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1675          self.__altered_coefficients=True
1676          # check if the systrem is inhomogeneous:
1677          if len(coefficients)>0 and not self.isUsingLumping():
1678             q=self.getCoefficientOfGeneralPDE("q")
1679             r=self.getCoefficientOfGeneralPDE("r")
1680             homogeneous_constraint=True
1681             if not q.isEmpty() and not r.isEmpty():
1682                 if util.Lsup(q*r)>0.:
1683                   self.trace("Inhomogeneous constraint detected.")
1684                   self.__invalidateSystem()
1685    
1686     def getFlux(self,u):     def getSystem(self):
1687         """         """
1688         @brief returns the flux J_ij for a given u         return the operator and right hand side of the PDE
1689    
1690              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}         @return: the discrete version of the PDE
1691           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1692           """
1693           if not self.__operator_is_Valid or not self.__righthandside_isValid:
1694              if self.isUsingLumping():
1695                  if not self.__operator_is_Valid:
1696                     if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1697                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1698                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1699                          raise ValueError,"coefficient A in lumped matrix may not be present."
1700                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1701                          raise ValueError,"coefficient B in lumped matrix may not be present."
1702                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1703                          raise ValueError,"coefficient C in lumped matrix may not be present."
1704                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1705                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1706                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1707                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1708                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1709                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1710                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1711                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1713                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1714                     D=self.getCoefficientOfGeneralPDE("D")
1715                     d=self.getCoefficientOfGeneralPDE("d")
1716                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1717                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1718                     if not D.isEmpty():
1719                         if self.getNumSolutions()>1:
1720                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1721                         else:
1722                            D_times_e=D
1723                     else:
1724                        D_times_e=escript.Data()
1725                     if not d.isEmpty():
1726                         if self.getNumSolutions()>1:
1727                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1728                         else:
1729                            d_times_e=d
1730                     else:
1731                        d_times_e=escript.Data()
1732          
1733                     if not D_reduced.isEmpty():
1734                         if self.getNumSolutions()>1:
1735                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1736                         else:
1737                            D_reduced_times_e=D_reduced
1738                     else:
1739                        D_reduced_times_e=escript.Data()
1740                     if not d_reduced.isEmpty():
1741                         if self.getNumSolutions()>1:
1742                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1743                         else:
1744                            d_reduced_times_e=d_reduced
1745                     else:
1746                        d_reduced_times_e=escript.Data()
1747    
1748                     self.__operator=self.__getNewRightHandSide()
1749                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1750                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1751                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1752                     else:
1753                        self.getDomain().addPDEToRHS(self.__operator, \
1754                                                     escript.Data(), \
1755                                                     D_times_e, \
1756                                                     d_times_e,\
1757                                                     escript.Data())
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_reduced_times_e, \
1761                                                     d_reduced_times_e,\
1762                                                     escript.Data())
1763                     self.__operator=1./self.__operator
1764                     self.trace("New lumped operator has been built.")
1765                     self.__operator_is_Valid=True
1766                  if not self.__righthandside_isValid:
1767                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1768                                   self.getCoefficientOfGeneralPDE("X"), \
1769                                   self.getCoefficientOfGeneralPDE("Y"),\
1770                                   self.getCoefficientOfGeneralPDE("y"),\
1771                                   self.getCoefficientOfGeneralPDE("y_contact"))
1772                     self.getDomain().addPDEToRHS(self.__righthandside, \
1773                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1774                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1775                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1777                     self.trace("New right hand side as been built.")
1778                     self.__righthandside_isValid=True
1779              else:
1780                 if not self.__operator_is_Valid and not self.__righthandside_isValid:
1781                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1782                                   self.getCoefficientOfGeneralPDE("A"), \
1783                                   self.getCoefficientOfGeneralPDE("B"), \
1784                                   self.getCoefficientOfGeneralPDE("C"), \
1785                                   self.getCoefficientOfGeneralPDE("D"), \
1786                                   self.getCoefficientOfGeneralPDE("X"), \
1787                                   self.getCoefficientOfGeneralPDE("Y"), \
1788                                   self.getCoefficientOfGeneralPDE("d"), \
1789                                   self.getCoefficientOfGeneralPDE("y"), \
1790                                   self.getCoefficientOfGeneralPDE("d_contact"), \
1791                                   self.getCoefficientOfGeneralPDE("y_contact"))
1792                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1793                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1803                     self.__applyConstraint()
1804                     self.__righthandside=self.copyConstraint(self.__righthandside)
1805                     self.trace("New system has been built.")
1806                     self.__operator_is_Valid=True
1807                     self.__righthandside_isValid=True
1808                 elif not self.__righthandside_isValid:
1809                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1810                                   self.getCoefficientOfGeneralPDE("X"), \
1811                                   self.getCoefficientOfGeneralPDE("Y"),\
1812                                   self.getCoefficientOfGeneralPDE("y"),\
1813                                   self.getCoefficientOfGeneralPDE("y_contact"))
1814                     self.getDomain().addPDEToRHS(self.__righthandside, \
1815                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1816                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1817                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1819                     self.__righthandside=self.copyConstraint(self.__righthandside)
1820                     self.trace("New right hand side has been built.")
1821                     self.__righthandside_isValid=True
1822                 elif not self.__operator_is_Valid:
1823                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1824                                self.getCoefficientOfGeneralPDE("A"), \
1825                                self.getCoefficientOfGeneralPDE("B"), \
1826                                self.getCoefficientOfGeneralPDE("C"), \
1827                                self.getCoefficientOfGeneralPDE("D"), \
1828                                escript.Data(), \
1829                                escript.Data(), \
1830                                self.getCoefficientOfGeneralPDE("d"), \
1831                                escript.Data(),\
1832                                self.getCoefficientOfGeneralPDE("d_contact"), \
1833                                escript.Data())
1834                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1836                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1839                                escript.Data(), \
1840                                escript.Data(), \
1841                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1842                                escript.Data(),\
1843                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1844                                escript.Data())
1845                     self.__applyConstraint()
1846                     self.trace("New operator has been built.")
1847                     self.__operator_is_Valid=True
1848           return (self.__operator,self.__righthandside)
1849    
        @param u argument of the operator  
1850    
1851         """  class Poisson(LinearPDE):
1852         raise SystemError,"getFlux is not implemented yet"     """
1853         return None     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1854    
1855     def applyOperator(self,u):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
1856    
1857         @param u argument of the operator     with natural boundary conditons
1858    
1859         """     M{n[j]*grad(u)[j] = 0 }
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
1860    
1861         @param u     and constraints:
1862         """  
1863         return self.applyOperator(u)-self.getRightHandSide()     M{u=0} where M{q>0}
1864    
 class Poisson(LinearPDE):  
1865     """     """
1866     @brief Class to define a Poisson equstion problem:  
1867                                                                                                                                                                   def __init__(self,domain,debug=False):
1868     class to define a linear PDE of the form       """
1869                                                                                                                                                                     initializes a new Poisson equation
1870          -u_{,jj} = f  
1871                                                                                                                                                                     @param domain: domain of the PDE
1872       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
1873                                                                                                                                                                     @param debug: if True debug informations are printed.
1874          n_j*u_{,j} = 0  
1875                                                                                                                                                                     """
1876      and constraints:       super(Poisson, self).__init__(domain,1,1,debug)
1877                                                                                                                                                                     self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1878           u=0 where q>0                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                                                                                                                                                                                        "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1880     """       self.setSymmetryOn()
1881    
1882     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
1883         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))       """
1884         self._setValue(A=numarray.identity(self.getDomain().getDim()))       sets new values to coefficients
1885         self.setSymmetryOn()  
1886         self.setValue(f,q)       @param coefficients: new values assigned to coefficients
1887         @keyword f: value for right hand side M{f}
1888     def setValue(self,f=escript.Data(),q=escript.Data()):       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1889         self._setValue(Y=f,q=q)       @keyword q: mask for location of constraints
1890         @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>}
1891                                                                                                                                                                             depending of reduced order is used for the representation of the equation.
1892  # $Log$       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1893  # Revision 1.3  2004/12/17 07:43:10  jgs       """
1894  # *** empty log message ***       super(Poisson, self).setValue(**coefficients)
1895  #  
1896  # Revision 1.1.2.3  2004/12/16 00:12:34  gross     def getCoefficientOfGeneralPDE(self,name):
1897  # __init__ of LinearPDE does not accept any coefficients anymore       """
1898  #       return the value of the coefficient name of the general PDE
1899  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs       @param name: name of the coefficient requested.
1900  # *** empty log message ***       @type name: C{string}
1901  #       @return: the value of the coefficient  name
1902  # Revision 1.1.2.1  2004/12/12 22:53:47  gross       @rtype: L{Data<escript.Data>}
1903  # linearPDE has been renamed LinearPDE       @raise IllegalCoefficient: if name is not one of coefficients
1904  #                    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}.
1905  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1906  # GMRES added       """
1907  #       if name == "A" :
1908  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1909  # options for GMRES and PRES20 added       elif name == "B" :
1910  #           return escript.Data()
1911  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross       elif name == "C" :
1912  # some small changes           return escript.Data()
1913  #       elif name == "D" :
1914  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross           return escript.Data()
1915  # Finley solves 4M unknowns now       elif name == "X" :
1916  #           return escript.Data()
1917  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross       elif name == "Y" :
1918  # poisson solver added           return self.getCoefficient("f")
1919  #       elif name == "d" :
1920  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross           return escript.Data()
1921  # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry       elif name == "y" :
1922  #           return escript.Data()
1923  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross       elif name == "d_contact" :
1924  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed           return escript.Data()
1925  #       elif name == "y_contact" :
1926  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs           return escript.Data()
1927  # initial import of project esys2       elif name == "A_reduced" :
1928  #           return escript.Data()
1929  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs       elif name == "B_reduced" :
1930  # committing Lutz's and Paul's changes to brach jgs           return escript.Data()
1931  #       elif name == "C_reduced" :
1932  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane           return escript.Data()
1933  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       elif name == "D_reduced" :
1934  #           return escript.Data()
1935  # Revision 1.3  2004/09/23 00:53:23  jgs       elif name == "X_reduced" :
1936  # minor fixes           return escript.Data()
1937  #       elif name == "Y_reduced" :
1938  # Revision 1.1  2004/08/28 12:58:06  gross           return self.getCoefficient("f_reduced")
1939  # SimpleSolve is not running yet: problem with == of functionsspace       elif name == "d_reduced" :
1940  #           return escript.Data()
1941  #       elif name == "y_reduced" :
1942             return escript.Data()
1943         elif name == "d_contact_reduced" :
1944             return escript.Data()
1945         elif name == "y_contact_reduced" :
1946             return escript.Data()
1947         elif name == "r" :
1948             return escript.Data()
1949         elif name == "q" :
1950             return self.getCoefficient("q")
1951         else:
1952            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1953    
1954    class Helmholtz(LinearPDE):
1955       """
1956       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1957    
1958       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1959    
1960       with natural boundary conditons
1961    
1962       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1963    
1964       and constraints:
1965    
1966       M{u=r} where M{q>0}
1967    
1968       """
1969    
1970       def __init__(self,domain,debug=False):
1971         """
1972         initializes a new Poisson equation
1973    
1974         @param domain: domain of the PDE
1975         @type domain: L{Domain<escript.Domain>}
1976         @param debug: if True debug informations are printed.
1977    
1978         """
1979         super(Helmholtz, self).__init__(domain,1,1,debug)
1980         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1981                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1983                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1988                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1989         self.setSymmetryOn()
1990    
1991       def setValue(self,**coefficients):
1992         """
1993         sets new values to coefficients
1994    
1995         @param coefficients: new values assigned to coefficients
1996         @keyword omega: value for coefficient M{S{omega}}
1997         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1998         @keyword k: value for coefficeint M{k}
1999         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000         @keyword f: value for right hand side M{f}
2001         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002         @keyword alpha: value for right hand side M{S{alpha}}
2003         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2004         @keyword g: value for right hand side M{g}
2005         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006         @keyword r: prescribed values M{r} for the solution in constraints.
2007         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2008                   depending of reduced order is used for the representation of the equation.
2009         @keyword q: mask for location of constraints
2010         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2011                   depending of reduced order is used for the representation of the equation.
2012         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2013         """
2014         super(Helmholtz, self).setValue(**coefficients)
2015    
2016       def getCoefficientOfGeneralPDE(self,name):
2017         """
2018         return the value of the coefficient name of the general PDE
2019    
2020         @param name: name of the coefficient requested.
2021         @type name: C{string}
2022         @return: the value of the coefficient  name
2023         @rtype: L{Data<escript.Data>}
2024         @raise IllegalCoefficient: if name is not one of coefficients
2025                      "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}.
2026         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2027         """
2028         if name == "A" :
2029             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2030         elif name == "B" :
2031             return escript.Data()
2032         elif name == "C" :
2033             return escript.Data()
2034         elif name == "D" :
2035             return self.getCoefficient("omega")
2036         elif name == "X" :
2037             return escript.Data()
2038         elif name == "Y" :
2039             return self.getCoefficient("f")
2040         elif name == "d" :
2041             return self.getCoefficient("alpha")
2042         elif name == "y" :
2043             return self.getCoefficient("g")
2044         elif name == "d_contact" :
2045             return escript.Data()
2046         elif name == "y_contact" :
2047             return escript.Data()
2048         elif name == "A_reduced" :
2049             return escript.Data()
2050         elif name == "B_reduced" :
2051             return escript.Data()
2052         elif name == "C_reduced" :
2053             return escript.Data()
2054         elif name == "D_reduced" :
2055             return escript.Data()
2056         elif name == "X_reduced" :
2057             return escript.Data()
2058         elif name == "Y_reduced" :
2059             return self.getCoefficient("f_reduced")
2060         elif name == "d_reduced" :
2061             return escript.Data()
2062         elif name == "y_reduced" :
2063            return self.getCoefficient("g_reduced")
2064         elif name == "d_contact_reduced" :
2065             return escript.Data()
2066         elif name == "y_contact_reduced" :
2067             return escript.Data()
2068         elif name == "r" :
2069             return self.getCoefficient("r")
2070         elif name == "q" :
2071             return self.getCoefficient("q")
2072         else:
2073            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2074    
2075    class LameEquation(LinearPDE):
2076       """
2077       Class to define a Lame equation problem:
2078    
2079       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] }
2080    
2081       with natural boundary conditons:
2082    
2083       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] }
2084    
2085       and constraints:
2086    
2087       M{u[i]=r[i]} where M{q[i]>0}
2088    
2089       """
2090    
2091       def __init__(self,domain,debug=False):
2092          super(LameEquation, self).__init__(domain,\
2093                                             domain.getDim(),domain.getDim(),debug)
2094          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2095                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2096                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2097                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2098                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2100                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2101          self.setSymmetryOn()
2102    
2103       def setValues(self,**coefficients):
2104         """
2105         sets new values to coefficients
2106    
2107         @param coefficients: new values assigned to coefficients
2108         @keyword lame_mu: value for coefficient M{S{mu}}
2109         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2110         @keyword lame_lambda: value for coefficient M{S{lambda}}
2111         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112         @keyword F: value for internal force M{F}
2113         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2114         @keyword sigma: value for initial stress M{S{sigma}}
2115         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2116         @keyword f: value for extrenal force M{f}
2117         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2118         @keyword r: prescribed values M{r} for the solution in constraints.
2119         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2120                   depending of reduced order is used for the representation of the equation.
2121         @keyword q: mask for location of constraints
2122         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2123                   depending of reduced order is used for the representation of the equation.
2124         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2125         """
2126         super(LameEquation, self).setValues(**coefficients)
2127    
2128       def getCoefficientOfGeneralPDE(self,name):
2129         """
2130         return the value of the coefficient name of the general PDE
2131    
2132         @param name: name of the coefficient requested.
2133         @type name: C{string}
2134         @return: the value of the coefficient  name
2135         @rtype: L{Data<escript.Data>}
2136         @raise IllegalCoefficient: if name is not one of coefficients
2137                      "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}.
2138         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2139         """
2140         if name == "A" :
2141             out =self.createCoefficientOfGeneralPDE("A")
2142             for i in range(self.getDim()):
2143               for j in range(self.getDim()):
2144                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2145                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2146                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2147             return out
2148         elif name == "B" :
2149             return escript.Data()
2150         elif name == "C" :
2151             return escript.Data()
2152         elif name == "D" :
2153             return escript.Data()
2154         elif name == "X" :
2155             return self.getCoefficient("sigma")
2156         elif name == "Y" :
2157             return self.getCoefficient("F")
2158         elif name == "d" :
2159             return escript.Data()
2160         elif name == "y" :
2161             return self.getCoefficient("f")
2162         elif name == "d_contact" :
2163             return escript.Data()
2164         elif name == "y_contact" :
2165             return escript.Data()
2166         elif name == "A_reduced" :
2167             return escript.Data()
2168         elif name == "B_reduced" :
2169             return escript.Data()
2170         elif name == "C_reduced" :
2171             return escript.Data()
2172         elif name == "D_reduced" :
2173             return escript.Data()
2174         elif name == "X_reduced" :
2175             return escript.Data()
2176         elif name == "Y_reduced" :
2177             return escript.Data()
2178         elif name == "d_reduced" :
2179             return escript.Data()
2180         elif name == "y_reduced" :
2181             return escript.Data()
2182         elif name == "d_contact_reduced" :
2183             return escript.Data()
2184         elif name == "y_contact_reduced" :
2185             return escript.Data()
2186         elif name == "r" :
2187             return self.getCoefficient("r")
2188         elif name == "q" :
2189             return self.getCoefficient("q")
2190         else:
2191            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2192    

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