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trunk/esys2/escript/py_src/linearPDEs.py revision 102 by jgs, Wed Dec 15 07:08:39 2004 UTC trunk/escript/py_src/linearPDEs.py revision 1809 by ksteube, Thu Sep 25 06:43:44 2008 UTC
# Line 1  Line 1 
 # $Id$  
1    
2  ## @file linearPDEs.py  ########################################################
3    #
4    # Copyright (c) 2003-2008 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7    #
8    # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11    #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
24    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
25    solver capabilities in itself but hands the PDE over to
26    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
27    The general interface is provided through the L{LinearPDE} class. The
28    L{AdvectivePDE} which is derived from the L{LinearPDE} class
29    provides an interface to PDE dominated by its advective terms. The L{Poisson},
30    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
31    classs which are also derived form the L{LinearPDE} class should be used
32    to define of solve these sepecial PDEs.
33    
34    @var __author__: name of author
35    @var __copyright__: copyrights
36    @var __license__: licence agreement
37    @var __url__: url entry point on documentation
38    @var __version__: version
39    @var __date__: date of the version
40  """  """
41    
42    import math
43  import escript  import escript
44  import util  import util
45  import numarray  import numarray
46    
47  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
48       """  
      @brief Return the Domain which is equal to the input domain (if not None)  
      and is the domain of all Data objects in the dictionary data.  
      An exception is raised if this is not possible  
   
      @param domain  
      @param data  
      """  
      # get the domain used by any Data object in the list data:  
      data_domain=None  
      for d in data.itervalues():  
           if isinstance(d,escript.Data):  
              if not d.isEmpty(): data_domain=d.getDomain()  
      # check if domain and data_domain are identical?  
      if domain == None:  
          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  
49    
50    class IllegalCoefficient(ValueError):
51       """
52       raised if an illegal coefficient of the general ar particular PDE is requested.
53       """
54       pass
55    
56    class IllegalCoefficientValue(ValueError):
57       """
58       raised if an incorrect value for a coefficient is used.
59       """
60       pass
61    
62  def _CompTuple2(t1,t2):  class IllegalCoefficientFunctionSpace(ValueError):
63       """
64       raised if an incorrect function space for a coefficient is used.
65     """     """
    @brief  
66    
67     @param t1  class UndefinedPDEError(ValueError):
68     @param t2     """
69       raised if a PDE is not fully defined yet.
70     """     """
71     dif=t1[0]+t1[1]-(t2[0]+t2[1])     pass
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
72    
73  class PDECoefficientType:  class PDECoefficient(object):
74      """      """
75      @brief      A class for describing a PDE coefficient
76    
77        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
78        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
79        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
80        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
81        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
82        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
83        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
84        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
85        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
86        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
87        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
88        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
89        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
90        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
91    
92      """      """
     # identifier for location of Data objects defining coefficients  
93      INTERIOR=0      INTERIOR=0
94      BOUNDARY=1      BOUNDARY=1
95      CONTACT=2      CONTACT=2
96      CONTINUOUS=3      SOLUTION=3
97      # identifier in the pattern of coefficients:      REDUCED=4
98      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
99      # number of unknowns.      BY_SOLUTION=6
100      EQUATION=3      BY_DIM=7
101      SOLUTION=4      OPERATOR=10
102      DIM=5      RIGHTHANDSIDE=11
103      # indicator for what is altered if the coefficient is altered:      BOTH=12
104      OPERATOR=5      INTERIOR_REDUCED=13
105      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
106      BOTH=7      CONTACT_REDUCED=15
107      def __init__(self,where,pattern,altering):  
108         """      def __init__(self, where, pattern, altering):
109         @brief Initialise a PDE Coefficient type         """
110           Initialise a PDE Coefficient type
111    
112           @param where: describes where the coefficient lives
113           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
114                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
115           @param pattern: describes the shape of the coefficient and how the shape is build for a given
116                  spatial dimension and numbers of equation and solution in then PDE. For instance,
117                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
118                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
119                  on a 2-dimensional domain. In the case of single equation and a single solution component
120                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
121                  the example would be read as (2,).
122           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
123           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
124           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
125           @param reduced: indicates if reduced
126           @type reduced: C{bool}
127         """         """
128           super(PDECoefficient, self).__init__()
129         self.what=where         self.what=where
130         self.pattern=pattern         self.pattern=pattern
131         self.altering=altering         self.altering=altering
132           self.resetValue()
133    
134      def getFunctionSpace(self,domain):      def resetValue(self):
135         """         """
136         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
137         """         """
138         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
139         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
140         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
141         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
142           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
143    
144           @param domain: domain on which the PDE uses the coefficient
145           @type domain: L{Domain<escript.Domain>}
146           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
147           @type reducedEquationOrder: C{bool}
148           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
149           @type reducedSolutionOrder: C{bool}
150           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
151           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
152           """
153           if self.what==self.INTERIOR:
154                return escript.Function(domain)
155           elif self.what==self.INTERIOR_REDUCED:
156                return escript.ReducedFunction(domain)
157           elif self.what==self.BOUNDARY:
158                return escript.FunctionOnBoundary(domain)
159           elif self.what==self.BOUNDARY_REDUCED:
160                return escript.ReducedFunctionOnBoundary(domain)
161           elif self.what==self.CONTACT:
162                return escript.FunctionOnContactZero(domain)
163           elif self.what==self.CONTACT_REDUCED:
164                return escript.ReducedFunctionOnContactZero(domain)
165           elif self.what==self.SOLUTION:
166                if reducedEquationOrder and reducedSolutionOrder:
167                    return escript.ReducedSolution(domain)
168                else:
169                    return escript.Solution(domain)
170           elif self.what==self.REDUCED:
171                return escript.ReducedSolution(domain)
172    
173        def getValue(self):
174           """
175           returns the value of the coefficient
176    
177           @return:  value of the coefficient
178           @rtype:  L{Data<escript.Data>}
179           """
180           return self.value
181    
182        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
183           """
184           set the value of the coefficient to a new value
185    
186           @param domain: domain on which the PDE uses the coefficient
187           @type domain: L{Domain<escript.Domain>}
188           @param numEquations: number of equations of the PDE
189           @type numEquations: C{int}
190           @param numSolutions: number of components of the PDE solution
191           @type numSolutions: C{int}
192           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
193           @type reducedEquationOrder: C{bool}
194           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
195           @type reducedSolutionOrder: C{bool}
196           @param newValue: number of components of the PDE solution
197           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
198           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
199           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
200           """
201           if newValue==None:
202               newValue=escript.Data()
203           elif isinstance(newValue,escript.Data):
204               if not newValue.isEmpty():
205                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
206                    try:
207                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
208                    except:
209                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
210           else:
211               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
212           if not newValue.isEmpty():
213               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
214                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
215           self.value=newValue
216    
217      def isAlteringOperator(self):      def isAlteringOperator(self):
218          """          """
219      @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
220    
221            @return:  True if the operator of the PDE is changed when the coefficient is changed
222            @rtype:  C{bool}
223      """      """
224          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
225              return not None              return not None
# Line 119  class PDECoefficientType: Line 228  class PDECoefficientType:
228    
229      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
230          """          """
231      @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
232    
233        @rtype:  C{bool}
234            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
235      """      """
236          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
237              return not None              return not None
238          else:          else:
239              return None              return None
240    
241      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
242         """         """
243         @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
244    
245         @param shape         @param domain: domain on which the PDE uses the coefficient
246         @param dim         @type domain: L{Domain<escript.Domain>}
247           @param shape: suggested shape of the coefficient
248           @type shape: C{tuple} of C{int} values
249           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
250                     If no appropriate numbers could be identified, C{None} is returned
251           @rtype: C{tuple} of two C{int} values or C{None}
252         """         """
253           dim=domain.getDim()
254         if len(shape)>0:         if len(shape)>0:
255             num=max(shape)+1             num=max(shape)+1
256         else:         else:
257             num=1             num=1
258         search=[]         search=[]
259         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
260            for e in range(num):            for u in range(num):
261               search.append((e,u))               for e in range(num):
262         search.sort(_CompTuple2)                  search.append((e,u))
263         for item in search:            search.sort(self.__CompTuple2)
264               s=self.buildShape(item[0],item[1],dim)            for item in search:
265                 s=self.getShape(domain,item[0],item[1])
266               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
267                   return (1,1)                   return (1,1)
268               else:               else:
269                   if s==shape: return item                   if s==shape: return item
270           elif self.definesNumEquation():
271              for e in range(num,0,-1):
272                 s=self.getShape(domain,e,0)
273                 if len(s)==0 and len(shape)==0:
274                     return (1,None)
275                 else:
276                     if s==shape: return (e,None)
277    
278           elif self.definesNumSolutions():
279              for u in range(num,0,-1):
280                 s=self.getShape(domain,0,u)
281                 if len(s)==0 and len(shape)==0:
282                     return (None,1)
283                 else:
284                     if s==shape: return (None,u)
285         return None         return None
286        def definesNumSolutions(self):
287           """
288           checks if the coefficient allows to estimate the number of solution components
289    
290      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
291          """         @rtype: C{bool}
292      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
293           for i in self.pattern:
294                 if i==self.BY_SOLUTION: return True
295           return False
296    
297      @param e      def definesNumEquation(self):
298      @param u         """
299      @param dim         checks if the coefficient allows to estimate the number of equations
300      """  
301          s=()         @return: True if the coefficient allows an estimate of the number of equations
302          for i in self.pattern:         @rtype: C{bool}
303               if i==self.EQUATION:         """
304                  if e>1: s=s+(e,)         for i in self.pattern:
305               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
306                  if u>1: s=s+(u,)         return False
307    
308        def __CompTuple2(self,t1,t2):
309          """
310          Compare two tuples of possible number of equations and number of solutions
311    
312          @param t1: The first tuple
313          @param t2: The second tuple
314    
315          """
316    
317          dif=t1[0]+t1[1]-(t2[0]+t2[1])
318          if dif<0: return 1
319          elif dif>0: return -1
320          else: return 0
321    
322        def getShape(self,domain,numEquations=1,numSolutions=1):
323           """
324           builds the required shape of the coefficient
325    
326           @param domain: domain on which the PDE uses the coefficient
327           @type domain: L{Domain<escript.Domain>}
328           @param numEquations: number of equations of the PDE
329           @type numEquations: C{int}
330           @param numSolutions: number of components of the PDE solution
331           @type numSolutions: C{int}
332           @return: shape of the coefficient
333           @rtype: C{tuple} of C{int} values
334           """
335           dim=domain.getDim()
336           s=()
337           for i in self.pattern:
338                 if i==self.BY_EQUATION:
339                    if numEquations>1: s=s+(numEquations,)
340                 elif i==self.BY_SOLUTION:
341                    if numSolutions>1: s=s+(numSolutions,)
342               else:               else:
343                  s=s+(dim,)                  s=s+(dim,)
344          return s         return s
   
 _PDECoefficientTypes={  
 "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),  
 }  
345    
346  class LinearPDE:  class LinearPDE(object):
347     """     """
348     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
349         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
350    
351       -(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:
352    
353       with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
354    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
355    
356      and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
357       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
358       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
359       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
360       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
361       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
362       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
363    
364          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:
365    
366      and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
367    
368           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>}.
369    
    """  
    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  
370    
371     def __init__(self,**args):     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.  
372    
373       @param args     M{u=r}  where M{q>0}
      """  
374    
375       # initialize attributes     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
376       self.__debug=None     The constraints override any other condition set by the PDE or the boundary condition.
377       self.__domain=None  
378       self.__numEquations=0     The PDE is symmetrical if
      self.__numSolutions=0  
      self.cleanCoefficients()  
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
   
      # check the arguments  
      coef={}  
      for arg in args.iterkeys():  
           if arg=="domain":  
               self.__domain=args[arg]  
           elif arg=="numEquations":  
               self.__numEquations=args[arg]  
           elif arg=="numSolutions":  
               self.__numSolutions=args[arg]  
           elif _PDECoefficientTypes.has_key(arg):  
               coef[arg]=args[arg]  
           else:  
               raise ValueError,"Illegal argument %s"%arg  
379    
380       # get the domain of the PDE     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
381       self.__domain=identifyDomain(self.__domain,coef)  
382       For a system of PDEs and a solution with several components the PDE has the form
383    
384       M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
385    
386       M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
387       The natural boundary conditions take the form:
388    
389       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
390    
391    
392       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
393    
394       Constraints take the form
395    
396       M{u[i]=r[i]}  where  M{q[i]>0}
397    
398       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
399    
400       The system of PDEs is symmetrical if
401    
402            - M{A[i,j,k,l]=A[k,l,i,j]}
403            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
404            - M{B[i,j,k]=C[k,i,j]}
405            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
406            - M{D[i,k]=D[i,k]}
407            - M{D_reduced[i,k]=D_reduced[i,k]}
408            - M{d[i,k]=d[k,i]}
409            - M{d_reduced[i,k]=d_reduced[k,i]}
410    
411       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
412       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
413       defined as
414    
415       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
416    
417       For the case of single solution component and single PDE M{J} is defined
418    
419       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
420    
421       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
422       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
423       the contact condition takes the form
424    
425       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
426    
427       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
428       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
429       L{jump<util.jump>}.
430       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
431       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
432       In case of a single PDE and a single component solution the contact condition takes the form
433    
434       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
435    
436       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
437    
438       @cvar DEFAULT: The default method used to solve the system of linear equations
439       @cvar DIRECT: The direct solver based on LDU factorization
440       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
441       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
442       @cvar CR: The conjugate residual method
443       @cvar CGS: The conjugate gardient square method
444       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
445       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
446       @cvar MINRES: Minimum residual method.
447       @cvar SSOR: The symmetric overrealaxtion method
448       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449       @cvar ILUT: The incomplete LU factorization preconditioner with will in
450       @cvar JACOBI: The Jacobi preconditioner
451       @cvar GMRES: The Gram-Schmidt minimum residual method
452       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
453       @cvar LUMPING: Matrix lumping.
454       @cvar NO_REORDERING: No matrix reordering allowed
455       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
456       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
457       @cvar PASO: PASO solver package
458       @cvar SCSL: SGI SCSL solver library
459       @cvar MKL: Intel's MKL solver library
460       @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462       @cvar ITERATIVE: The default iterative solver
463       @cvar AMG: algebraic multi grid
464       @cvar RILU: recursive ILU
465    
466       """
467       DEFAULT= 0
468       DIRECT= 1
469       CHOLEVSKY= 2
470       PCG= 3
471       CR= 4
472       CGS= 5
473       BICGSTAB= 6
474       SSOR= 7
475       ILU0= 8
476       ILUT= 9
477       JACOBI= 10
478       GMRES= 11
479       PRES20= 12
480       LUMPING= 13
481       NO_REORDERING= 17
482       MINIMUM_FILL_IN= 18
483       NESTED_DISSECTION= 19
484       SCSL= 14
485       MKL= 15
486       UMFPACK= 16
487       ITERATIVE= 20
488       PASO= 21
489       AMG= 22
490       RILU = 23
491       TRILINOS = 24
492       NONLINEAR_GMRES = 25
493       TFQMR = 26
494       MINRES = 27
495    
496       SMALL_TOLERANCE=1.e-13
497       __PACKAGE_KEY="package"
498       __METHOD_KEY="method"
499       __SYMMETRY_KEY="symmetric"
500       __TOLERANCE_KEY="tolerance"
501       __PRECONDITIONER_KEY="preconditioner"
502    
503    
504       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
505         """
506         initializes a new linear PDE
507    
508         @param domain: domain of the PDE
509         @type domain: L{Domain<escript.Domain>}
510         @param numEquations: number of equations. If numEquations==None the number of equations
511                              is exracted from the PDE coefficients.
512         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
513                              is exracted from the PDE coefficients.
514         @param debug: if True debug informations are printed.
515    
516         """
517         super(LinearPDE, self).__init__()
518         #
519         #   the coefficients of the general PDE:
520         #
521         self.__COEFFICIENTS_OF_GENEARL_PDE={
522           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
523           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
524           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
525           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
527           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
537           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
543           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
544    
545         # COEFFICIENTS can be overwritten by subclasses:
546         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
547         self.__altered_coefficients=False
548         # initialize attributes
549         self.__debug=debug
550         self.__domain=domain
551         self.__numEquations=numEquations
552         self.__numSolutions=numSolutions
553         self.__resetSystem()
554    
555       # set some default values:       # set some default values:
556       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
557       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
558       self.__tolerance=1.e-8       self.__tolerance=1.e-8
559       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
560       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
561         self.__preconditioner=self.DEFAULT
562         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
563       self.__sym=False       self.__sym=False
      self.__lumping=False  
      self.__numEquations=0  
      self.__numSolutions=0  
      # now we can set the ceofficients:  
      self._setCoefficient(**coef)  
564    
565     def getCoefficient(self,name):       self.resetCoefficients()
566         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
567       # =============================================================================
568       #    general stuff:
569       # =============================================================================
570       def __str__(self):
571         """
572         returns string representation of the PDE
573    
574         @return: a simple representation of the PDE
575         @rtype: C{str}
576         """
577         return "<LinearPDE %d>"%id(self)
578       # =============================================================================
579       #    debug :
580       # =============================================================================
581       def setDebugOn(self):
582         """
583         switches on debugging
584       """       """
585       @brief return the value of the coefficient name       self.__debug=not None
586    
587       @param name     def setDebugOff(self):
588         """
589         switches off debugging
590       """       """
591       return self.__coefficient[name]       self.__debug=None
592    
593     def setValue(self,**coefficients):     def trace(self,text):
594        """       """
595        @brief sets new values to coefficients       print the text message if debugging is swiched on.
596         @param text: message
597         @type text: C{string}
598         """
599         if self.__debug: print "%s: %s"%(str(self),text)
600    
601        @param coefficients     # =============================================================================
602        """     # some service functions:
603        self._setCoefficient(**coefficients)     # =============================================================================
604             def getDomain(self):
605         """
606         returns the domain of the PDE
607    
608     def _setCoefficient(self,**coefficients):       @return: the domain of the PDE
609        """       @rtype: L{Domain<escript.Domain>}
610        @brief sets new values to coefficients       """
611         return self.__domain
612    
613        @param coefficients     def getDim(self):
614        """       """
615               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:  
                 if self.__numEquations>0 and  self.__numSolutions>0:  
                    alteredCoefficients[i]=escript.Data(d,self.getShapeOfCoefficient(i),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  
616    
617        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
618        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
619           for i in self.__coefficient.iterkeys():       """
620               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()  
621    
622     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
623       """       """
624       @brief return the shape of the coefficient name       returns the number of equations
625    
626       @param name       @return: the number of equations
627         @rtype: C{int}
628         @raise UndefinedPDEError: if the number of equations is not be specified yet.
629       """       """
630       if self.hasCoefficient(name):       if self.__numEquations==None:
631          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
632       else:       else:
633          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
634    
635     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
636       """       """
637       @brief return the atoms of the coefficient name       returns the number of unknowns
638    
639       @param name       @return: the number of unknowns
640         @rtype: C{int}
641         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
642       """       """
643       if self.hasCoefficient(name):       if self.__numSolutions==None:
644          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
645       else:       else:
646          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
647    
648     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
649       """       """
650       @brief annonced that coefficient name has been changed       return status for order reduction for equation
651    
652       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
653         @rtype: L{bool}
654       """       """
655       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  
656    
657     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
658        """       """
659        @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  
660    
661        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
662        """       @rtype: L{bool}
663        return self.__coefficient.has_key(name)       """
664         return self.__reduce_solution_order
665    
666     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
667       """       """
668       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
669    
670         @return: representation space of equation
671         @rtype: L{FunctionSpace<escript.FunctionSpace>}
672       """       """
673       return self.__row_function_space       if self.reduceEquationOrder():
674             return escript.ReducedSolution(self.getDomain())
675         else:
676             return escript.Solution(self.getDomain())
677    
678     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
679       """       """
680       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
681    
682         @return: representation space of solution
683         @rtype: L{FunctionSpace<escript.FunctionSpace>}
684       """       """
685       return self.__column_function_space       if self.reduceSolutionOrder():
686             return escript.ReducedSolution(self.getDomain())
687         else:
688             return escript.Solution(self.getDomain())
689    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
690    
691     def setDebugOff(self):     def getOperator(self):
692         """       """
693         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
694    
695     def debug(self):       @return: the operator of the PDE
696         """       @rtype: L{Operator<escript.Operator>}
697         @brief returns true if the PDE is in the debug mode       """
698         """       m=self.getSystem()[0]
699         return self.__debug       if self.isUsingLumping():
700             return self.copyConstraint(1./m)
701         else:
702             return m
703    
704     #===== Lumping ===========================     def getRightHandSide(self):
705     def setLumpingOn(self):       """
706        """       provides access to the right hand side of the PDE
707        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
708        """       @rtype: L{Data<escript.Data>}
709        if not self.isUsingLumping():       """
710           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
711           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
712           self.__rebuildOperator()           return self.copyConstraint(r)
713           self.__lumping=True       else:
714             return r
715    
716     def setLumpingOff(self):     def applyOperator(self,u=None):
717        """       """
718        @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  
719    
720     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}
721        """                 the current solution is used.
722        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
723        """       @return: image of u
724        if flag:       @rtype: L{Data<escript.Data>}
725           self.setLumpingOn()       """
726        else:       if u==None:
727           self.setLumpingOff()          return self.getOperator()*self.getSolution()
728         else:
729            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
730    
731     def isUsingLumping(self):     def getResidual(self,u=None):
732         """
733         return the residual of u or the current solution if u is not present.
734    
735         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
736                   the current solution is used.
737         @type u: L{Data<escript.Data>} or None
738         @return: residual of u
739         @rtype: L{Data<escript.Data>}
740         """
741         return self.applyOperator(u)-self.getRightHandSide()
742    
743       def checkSymmetry(self,verbose=True):
744        """        """
745        @brief        test the PDE for symmetry.
746    
747          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
748          @type verbose: C{bool}
749          @return:  True if the PDE is symmetric.
750          @rtype: L{Data<escript.Data>}
751          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
752        """        """
753        return self.__lumping        verbose=verbose or self.__debug
754          out=True
755          if self.getNumSolutions()!=self.getNumEquations():
756             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
757             out=False
758          else:
759             A=self.getCoefficientOfGeneralPDE("A")
760             if not A.isEmpty():
761                tol=util.Lsup(A)*self.SMALL_TOLERANCE
762                if self.getNumSolutions()>1:
763                   for i in range(self.getNumEquations()):
764                      for j in range(self.getDim()):
765                         for k in range(self.getNumSolutions()):
766                            for l in range(self.getDim()):
767                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
768                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
769                                   out=False
770                else:
771                   for j in range(self.getDim()):
772                      for l in range(self.getDim()):
773                         if util.Lsup(A[j,l]-A[l,j])>tol:
774                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
775                            out=False
776             B=self.getCoefficientOfGeneralPDE("B")
777             C=self.getCoefficientOfGeneralPDE("C")
778             if B.isEmpty() and not C.isEmpty():
779                if verbose: print "non-symmetric PDE because B is not present but C is"
780                out=False
781             elif not B.isEmpty() and C.isEmpty():
782                if verbose: print "non-symmetric PDE because C is not present but B is"
783                out=False
784             elif not B.isEmpty() and not C.isEmpty():
785                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
786                if self.getNumSolutions()>1:
787                   for i in range(self.getNumEquations()):
788                       for j in range(self.getDim()):
789                          for k in range(self.getNumSolutions()):
790                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
791                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
792                                  out=False
793                else:
794                   for j in range(self.getDim()):
795                      if util.Lsup(B[j]-C[j])>tol:
796                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
797                         out=False
798             if self.getNumSolutions()>1:
799               D=self.getCoefficientOfGeneralPDE("D")
800               if not D.isEmpty():
801                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
802                 for i in range(self.getNumEquations()):
803                    for k in range(self.getNumSolutions()):
804                      if util.Lsup(D[i,k]-D[k,i])>tol:
805                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
806                          out=False
807               d=self.getCoefficientOfGeneralPDE("d")
808               if not d.isEmpty():
809                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
810                 for i in range(self.getNumEquations()):
811                    for k in range(self.getNumSolutions()):
812                      if util.Lsup(d[i,k]-d[k,i])>tol:
813                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
814                          out=False
815               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
816               if not d_contact.isEmpty():
817                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
818                 for i in range(self.getNumEquations()):
819                    for k in range(self.getNumSolutions()):
820                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
821                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
822                          out=False
823             # and now the reduced coefficients
824             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
825             if not A_reduced.isEmpty():
826                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
827                if self.getNumSolutions()>1:
828                   for i in range(self.getNumEquations()):
829                      for j in range(self.getDim()):
830                         for k in range(self.getNumSolutions()):
831                            for l in range(self.getDim()):
832                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
833                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
834                                   out=False
835                else:
836                   for j in range(self.getDim()):
837                      for l in range(self.getDim()):
838                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
839                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
840                            out=False
841             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
842             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
843             if B_reduced.isEmpty() and not C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
850                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
851                if self.getNumSolutions()>1:
852                   for i in range(self.getNumEquations()):
853                       for j in range(self.getDim()):
854                          for k in range(self.getNumSolutions()):
855                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
856                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
857                                  out=False
858                else:
859                   for j in range(self.getDim()):
860                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
861                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
862                         out=False
863             if self.getNumSolutions()>1:
864               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
865               if not D_reduced.isEmpty():
866                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
867                 for i in range(self.getNumEquations()):
868                    for k in range(self.getNumSolutions()):
869                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
870                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
871                          out=False
872               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
873               if not d_reduced.isEmpty():
874                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
875                 for i in range(self.getNumEquations()):
876                    for k in range(self.getNumSolutions()):
877                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
878                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
879                          out=False
880               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
881               if not d_contact_reduced.isEmpty():
882                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
883                 for i in range(self.getNumEquations()):
884                    for k in range(self.getNumSolutions()):
885                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
886                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
887                          out=False
888          return out
889    
890     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
891         """         """
892         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
893    
894           @return: the solution
895           @rtype: L{Data<escript.Data>}
896           @param options: solver options
897           @keyword verbose: True to get some information during PDE solution
898           @type verbose: C{bool}
899           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
900                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
901           @keyword iter_max: maximum number of iteration steps allowed.
902           @keyword drop_tolerance: threshold for drupping in L{ILUT}
903           @keyword drop_storage: maximum of allowed memory in L{ILUT}
904           @keyword truncation: maximum number of residuals in L{GMRES}
905           @keyword restart: restart cycle length in L{GMRES}
906         """         """
907         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
908              mat,f=self.getSystem()
909              if self.isUsingLumping():
910                 self.__solution=self.copyConstraint(f*mat)
911              else:
912                 options[self.__TOLERANCE_KEY]=self.getTolerance()
913                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
914                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
915                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
916                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
917                 self.trace("PDE is resolved.")
918                 self.trace("solver options: %s"%str(options))
919                 self.__solution=mat.solve(f,options)
920              self.__solution_isValid=True
921           return self.__solution
922    
923       def getFlux(self,u=None):
924         """
925         returns the flux M{J} for a given M{u}
926    
927         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
928    
929         or
930    
931         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
932    
933         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
934         @type u: L{Data<escript.Data>} or None
935         @return: flux
936         @rtype: L{Data<escript.Data>}
937         """
938         if u==None: u=self.getSolution()
939         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X") \
942               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X_reduced")
945       # =============================================================================
946       #   solver settings:
947       # =============================================================================
948       def setSolverMethod(self,solver=None,preconditioner=None):
949           """
950           sets a new solver
951    
952           @param solver: sets a new solver method.
953           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
954           @param preconditioner: sets a new solver method.
955           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
956           """
957           if solver==None: solver=self.__solver_method
958           if preconditioner==None: preconditioner=self.__preconditioner
959           if solver==None: solver=self.DEFAULT
960           if preconditioner==None: preconditioner=self.DEFAULT
961           if not (solver,preconditioner)==self.getSolverMethod():
962             self.__solver_method=solver             self.__solver_method=solver
963             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
964             self.__checkMatrixType()             self.__checkMatrixType()
965               self.trace("New solver is %s"%self.getSolverMethodName())
966    
967       def getSolverMethodName(self):
968           """
969           returns the name of the solver currently used
970    
971           @return: the name of the solver currently used.
972           @rtype: C{string}
973           """
974    
975           m=self.getSolverMethod()
976           p=self.getSolverPackage()
977           method=""
978           if m[0]==self.DEFAULT: method="DEFAULT"
979           elif m[0]==self.DIRECT: method= "DIRECT"
980           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
981           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
982           elif m[0]==self.PCG: method= "PCG"
983           elif m[0]==self.TFQMR: method= "TFQMR"
984           elif m[0]==self.MINRES: method= "MINRES"
985           elif m[0]==self.CR: method= "CR"
986           elif m[0]==self.CGS: method= "CGS"
987           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
988           elif m[0]==self.SSOR: method= "SSOR"
989           elif m[0]==self.GMRES: method= "GMRES"
990           elif m[0]==self.PRES20: method= "PRES20"
991           elif m[0]==self.LUMPING: method= "LUMPING"
992           elif m[0]==self.AMG: method= "AMG"
993           if m[1]==self.DEFAULT: method+="+DEFAULT"
994           elif m[1]==self.JACOBI: method+= "+JACOBI"
995           elif m[1]==self.ILU0: method+= "+ILU0"
996           elif m[1]==self.ILUT: method+= "+ILUT"
997           elif m[1]==self.SSOR: method+= "+SSOR"
998           elif m[1]==self.AMG: method+= "+AMG"
999           elif m[1]==self.RILU: method+= "+RILU"
1000           if p==self.DEFAULT: package="DEFAULT"
1001           elif p==self.PASO: package= "PASO"
1002           elif p==self.MKL: package= "MKL"
1003           elif p==self.SCSL: package= "SCSL"
1004           elif p==self.UMFPACK: package= "UMFPACK"
1005           elif p==self.TRILINOS: package= "TRILINOS"
1006           else : method="unknown"
1007           return "%s solver of %s package"%(method,package)
1008    
1009    
1010     def getSolverMethod(self):     def getSolverMethod(self):
1011         """         """
1012         @brief returns the solver method         returns the solver method
1013    
1014           @return: the solver method currently be used.
1015           @rtype: C{int}
1016           """
1017           return self.__solver_method,self.__preconditioner
1018    
1019       def setSolverPackage(self,package=None):
1020           """
1021           sets a new solver package
1022    
1023           @param package: sets a new solver method.
1024           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1025           """
1026           if package==None: package=self.DEFAULT
1027           if not package==self.getSolverPackage():
1028               self.__solver_package=package
1029               self.__checkMatrixType()
1030               self.trace("New solver is %s"%self.getSolverMethodName())
1031    
1032       def getSolverPackage(self):
1033           """
1034           returns the package of the solver
1035    
1036           @return: the solver package currently being used.
1037           @rtype: C{int}
1038         """         """
1039         return self.__solver_method         return self.__solver_package
1040    
1041       def isUsingLumping(self):
1042          """
1043          checks if matrix lumping is used a solver method
1044    
1045          @return: True is lumping is currently used a solver method.
1046          @rtype: C{bool}
1047          """
1048          return self.getSolverMethod()[0]==self.LUMPING
1049    
    #============ tolerance business =========================================================  
1050     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1051         """         """
1052         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1053    
1054           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1055    
1056           defines the stopping criterion.
1057    
1058           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1059                       the system will be resolved.
1060           @type tol: positive C{float}
1061           @raise ValueError: if tolerance is not positive.
1062         """         """
1063         if not tol>0:         if not tol>0:
1064             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1065         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1066         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1067         self.__tolerance=tol         self.__tolerance=tol
1068         return         return
1069    
1070     def getTolerance(self):     def getTolerance(self):
1071         """         """
1072         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1073    
1074           @return: tolerance currently used.
1075           @rtype: C{float}
1076         """         """
1077         return self.__tolerance         return self.__tolerance
1078    
1079     #===== symmetry  flag ==========================     # =============================================================================
1080       #    symmetry  flag:
1081       # =============================================================================
1082     def isSymmetric(self):     def isSymmetric(self):
1083        """        """
1084        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1085    
1086          @return: True is a symmetric PDE is indicated, otherwise False is returned
1087          @rtype: C{bool}
1088        """        """
1089        return self.__sym        return self.__sym
1090    
1091     def setSymmetryOn(self):     def setSymmetryOn(self):
1092        """        """
1093        @brief sets the symmetry flag to true        sets the symmetry flag.
1094        """        """
1095        if not self.isSymmetric():        if not self.isSymmetric():
1096           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1097           self.__sym=True           self.__sym=True
1098           self.__checkMatrixType()           self.__checkMatrixType()
1099    
1100     def setSymmetryOff(self):     def setSymmetryOff(self):
1101        """        """
1102        @brief sets the symmetry flag to false        removes the symmetry flag.
1103        """        """
1104        if self.isSymmetric():        if self.isSymmetric():
1105           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1106           self.__sym=False           self.__sym=False
1107           self.__checkMatrixType()           self.__checkMatrixType()
1108    
1109     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1110       """        """
1111       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1112    
1113       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1114       """        @type flag: C{bool}
1115       if flag:        """
1116          self.setSymmetryOn()        if flag:
1117       else:           self.setSymmetryOn()
1118          self.setSymmetryOff()        else:
1119             self.setSymmetryOff()
1120    
1121     #===== order reduction ==========================     # =============================================================================
1122       # function space handling for the equation as well as the solution
1123       # =============================================================================
1124     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1125       """       """
1126       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1127    
1128         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1129       """       """
1130       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1131       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1132    
1133     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1134       """       """
1135       @brief switches to full order       switches off reduced order for solution and equation representation
1136    
1137         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1138       """       """
1139       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1140       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1141    
1142     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1143       """       """
1144       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1145         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1146       @param flag                    if flag is not present order reduction is switched off
1147         @type flag: C{bool}
1148         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1149       """       """
1150       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1151       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1152    
1153     #===== order reduction solution ==========================  
1154     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1155       """       """
1156       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1157    
1158         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1159       """       """
1160       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1161       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1162           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1163           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1164           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1165             self.__resetSystem()
1166    
1167     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1168       """       """
1169       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1170    
1171         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1172       """       """
1173       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1174       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1175           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1176           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1177           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1178             self.__resetSystem()
1179    
1180     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1181       """       """
1182       @brief sets order for test functions according to flag       sets order for test functions according to flag
1183    
1184       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1185                      if flag is not present order reduction is switched off
1186         @type flag: C{bool}
1187         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1188       """       """
1189       if flag:       if flag:
1190          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1191       else:       else:
1192          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1193                                                                                                                                                              
    #===== order reduction equation ==========================  
1194     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1195       """       """
1196       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1197    
1198         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1199       """       """
1200       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1201       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1202           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1203           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1204           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1205             self.__resetSystem()
1206    
1207     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1208       """       """
1209       @brief switches to full order for test functions       switches off reduced order for equation representation
1210    
1211         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1212       """       """
1213       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1214       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1215           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1216           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1217           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1218             self.__resetSystem()
1219    
1220     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1221       """       """
1222       @brief sets order for test functions according to flag       sets order for test functions according to flag
1223    
1224       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1225                      if flag is not present order reduction is switched off
1226         @type flag: C{bool}
1227         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1228       """       """
1229       if flag:       if flag:
1230          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1231       else:       else:
1232          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1233    
1234     # ==== initialization =====================================================================     # =============================================================================
1235     def __makeNewOperator(self):     # private method:
1236       # =============================================================================
1237       def __checkMatrixType(self):
1238         """
1239         reassess the matrix type and, if a new matrix is needed, resets the system.
1240         """
1241         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1242         if not new_matrix_type==self.__matrix_type:
1243             self.trace("Matrix type is now %d."%new_matrix_type)
1244             self.__matrix_type=new_matrix_type
1245             self.__resetSystem()
1246       #
1247       #   rebuild switches :
1248       #
1249       def __invalidateSolution(self):
1250           """
1251           indicates the PDE has to be resolved if the solution is requested
1252           """
1253           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1254           self.__solution_isValid=False
1255    
1256       def __invalidateOperator(self):
1257           """
1258           indicates the operator has to be rebuilt next time it is used
1259           """
1260           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1261           self.__invalidateSolution()
1262           self.__operator_is_Valid=False
1263    
1264       def __invalidateRightHandSide(self):
1265           """
1266           indicates the right hand side has to be rebuild next time it is used
1267           """
1268           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1269           self.__invalidateSolution()
1270           self.__righthandside_isValid=False
1271    
1272       def __invalidateSystem(self):
1273           """
1274           annonced that everthing has to be rebuild:
1275           """
1276           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1277           self.__invalidateSolution()
1278           self.__invalidateOperator()
1279           self.__invalidateRightHandSide()
1280    
1281       def __resetSystem(self):
1282           """
1283           annonced that everthing has to be rebuild:
1284           """
1285           self.trace("New System is built from scratch.")
1286           self.__operator=escript.Operator()
1287           self.__operator_is_Valid=False
1288           self.__righthandside=escript.Data()
1289           self.__righthandside_isValid=False
1290           self.__solution=escript.Data()
1291           self.__solution_isValid=False
1292       #
1293       #    system initialization:
1294       #
1295       def __getNewOperator(self):
1296         """         """
1297         @brief         returns an instance of a new operator
1298         """         """
1299           self.trace("New operator is allocated.")
1300         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1301                             self.getNumEquations(), \                             self.getNumEquations(), \
1302                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 641  class LinearPDE: Line 1304  class LinearPDE:
1304                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1305                             self.__matrix_type)                             self.__matrix_type)
1306    
1307     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1308         """         """
1309         @brief         returns an instance of a new right hand side
1310         """         """
1311         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1312           if self.getNumEquations()>1:
1313               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1314           else:
1315               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1316    
1317     def __makeNewSolution(self):     def __getNewSolution(self):
1318         """         """
1319         @brief         returns an instance of a new solution
1320         """         """
1321         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1322           if self.getNumSolutions()>1:
1323               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1324           else:
1325               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1326    
1327     def __getFreshOperator(self):     def __makeFreshSolution(self):
1328         """         """
1329         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1330         """         """
1331         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1332             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1333         else:         else:
1334             self.__operator.setValue(0.)             self.__solution*=0
1335             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1336         return self.__operator         return self.__solution
1337    
1338     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1339         """         """
1340         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1341         """         """
1342         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1343             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1344         else:         else:
1345             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1346             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1347             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1348    
1349     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1350         """         """
1351         @brief indicates the PDE has to be reolved if the solution is requested         makes sure that the operator is instantiated and returns it initialized by zeros
1352         """         """
1353         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1354         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1355         if deep: self.__solution=escript.Data(deep)         else:
1356               self.__operator.resetValues()
1357               self.trace("Operator reset to zero")
1358           return self.__operator
1359    
1360     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1361         """         """
1362         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1363         """         """
1364         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1365         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1366         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1367         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1368                 # q is the row and column mask to indicate where constraints are set:
1369                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1370                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1371                 u=self.__getNewSolution()
1372                 if r.isEmpty():
1373                    r_s=self.__getNewSolution()
1374                 else:
1375                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1376                 u.copyWithMask(r_s,col_q)
1377                 if not self.__righthandside.isEmpty():
1378                    self.__righthandside-=self.__operator*u
1379                    self.__righthandside=self.copyConstraint(self.__righthandside)
1380                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1381       # =============================================================================
1382       # function giving access to coefficients of the general PDE:
1383       # =============================================================================
1384       def getCoefficientOfGeneralPDE(self,name):
1385         """
1386         return the value of the coefficient name of the general PDE.
1387    
1388         @note: This method is called by the assembling routine it can be overwritten
1389               to map coefficients of a particular PDE to the general PDE.
1390         @param name: name of the coefficient requested.
1391         @type name: C{string}
1392         @return: the value of the coefficient  name
1393         @rtype: L{Data<escript.Data>}
1394         @raise IllegalCoefficient: if name is not one of coefficients
1395                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1396                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1397         """
1398         if self.hasCoefficientOfGeneralPDE(name):
1399            return self.getCoefficient(name)
1400         else:
1401            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1402    
1403     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1404         """       """
1405         @brief indicates the right hand side has to be rebuild next time it is used       checks if name is a the name of a coefficient of the general PDE.
1406         """  
1407         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."       @param name: name of the coefficient enquired.
1408         self.__rebuildSolution(deep)       @type name: C{string}
1409         self.__righthandside_isValid=False       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1410         if not self.__homogeneous_constraint: self.__rebuildOperator()       @rtype: C{bool}
        if deep: self.__righthandside=escript.Data()  
1411    
    def __rebuildSystem(self,deep=False):  
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
1412       """       """
1413       @brief reassess the matrix type and, if needed, initiates an operator rebuild       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1414    
1415       def createCoefficientOfGeneralPDE(self,name):
1416       """       """
1417       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       returns a new instance of a coefficient for coefficient name of the general PDE
      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)  
1418    
1419     #============ assembling =======================================================       @param name: name of the coefficient requested.
1420     def __copyConstraint(self,u):       @type name: C{string}
1421        """       @return: a coefficient name initialized to 0.
1422        @brief copies the constrint condition into u       @rtype: L{Data<escript.Data>}
1423        """       @raise IllegalCoefficient: if name is not one of coefficients
1424        q=self.getCoefficient("q")                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1425        r=self.getCoefficient("r")                    M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1426        if not q.isEmpty():       """
1427            if r.isEmpty():       if self.hasCoefficientOfGeneralPDE(name):
1428               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1429            else:       else:
1430               r2=escript.Data(r,u.getFunctionSpace())          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1431    
1432     def __applyConstraint(self,rhs_update=True):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1433         """       """
1434         @brief applies the constraints  defined by q and r to the system       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
        """  
        q=self.getCoefficient("q")  
        r=self.getCoefficient("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__makeNewSolution()  
           if r.isEmpty():  
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if not self.__righthandside.isEmpty() and rhs_update: self.__righthandside-=self.__operator*u  
           self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1435    
1436     def getOperator(self):       @param name: name of the coefficient enquired.
1437         """       @type name: C{string}
1438         @brief returns the operator of the PDE       @return: the function space to be used for coefficient name
1439         """       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1440         if not self.__operator_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1441             # some Constraints are applying for a lumpled stifness matrix:                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1442             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}.
1443                if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():       """
1444                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"       if self.hasCoefficientOfGeneralPDE(name):
1445                if not self.getCoefficient("A").isEmpty():          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1446                         raise Warning,"Lumped matrix does not allow coefficient A"       else:
1447                if not self.getCoefficient("B").isEmpty():          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
                        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()  
1448    
1449             self.getDomain().addPDEToSystem(mat,escript.Data(), \     def getShapeOfCoefficientOfGeneralPDE(self,name):
1450                          self.getCoefficient("A"), \       """
1451                          self.getCoefficient("B"), \       return the shape of the coefficient name of the general PDE
                         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  
1452    
1453     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1454         """       @type name: C{string}
1455         @brief returns the right hand side of the PDE       @return: the shape of the coefficient name
1456         @rtype: C{tuple} of C{int}
1457         @raise IllegalCoefficient: if name is not one of coefficients
1458                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1459                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1460         """
1461         if self.hasCoefficientOfGeneralPDE(name):
1462            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1463         else:
1464            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1465    
1466         @param ignoreConstraint     # =============================================================================
1467         """     # functions giving access to coefficients of a particular PDE implementation:
1468         if not self.__righthandside_isValid:     # =============================================================================
1469             if self.debug() : print "PDE Debug: New right hand side is built."     def getCoefficient(self,name):
1470             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \       """
1471                           self.getCoefficient("X"), \       returns the value of the coefficient name
1472                           self.getCoefficient("Y"),\  
1473                           self.getCoefficient("y"),\       @param name: name of the coefficient requested.
1474                           self.getCoefficient("y_contact"))       @type name: C{string}
1475             self.__righthandside_isValid=True       @return: the value of the coefficient name
1476             if ignoreConstraint: self.__copyConstraint(self.__righthandside)       @rtype: L{Data<escript.Data>}
1477         return self.__righthandside       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1478         """
1479         if self.hasCoefficient(name):
1480             return self.COEFFICIENTS[name].getValue()
1481         else:
1482            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1483    
1484       def hasCoefficient(self,name):
1485         """
1486         return True if name is the name of a coefficient
1487    
1488         @param name: name of the coefficient enquired.
1489         @type name: C{string}
1490         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1491         @rtype: C{bool}
1492         """
1493         return self.COEFFICIENTS.has_key(name)
1494    
1495       def createCoefficient(self, name):
1496         """
1497         create a L{Data<escript.Data>} object corresponding to coefficient name
1498    
1499         @return: a coefficient name initialized to 0.
1500         @rtype: L{Data<escript.Data>}
1501         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1502         """
1503         if self.hasCoefficient(name):
1504            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1505         else:
1506            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1507    
1508       def getFunctionSpaceForCoefficient(self,name):
1509         """
1510         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1511    
1512         @param name: name of the coefficient enquired.
1513         @type name: C{string}
1514         @return: the function space to be used for coefficient name
1515         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1516         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1517         """
1518         if self.hasCoefficient(name):
1519            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1520         else:
1521            raise ValueError,"unknown coefficient %s requested"%name
1522       def getShapeOfCoefficient(self,name):
1523         """
1524         return the shape of the coefficient name
1525    
1526         @param name: name of the coefficient enquired.
1527         @type name: C{string}
1528         @return: the shape of the coefficient name
1529         @rtype: C{tuple} of C{int}
1530         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1531         """
1532         if self.hasCoefficient(name):
1533            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1534         else:
1535            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1536    
1537       def resetCoefficients(self):
1538         """
1539         resets all coefficients to there default values.
1540         """
1541         for i in self.COEFFICIENTS.iterkeys():
1542             self.COEFFICIENTS[i].resetValue()
1543    
1544       def alteredCoefficient(self,name):
1545         """
1546         announce that coefficient name has been changed
1547    
1548         @param name: name of the coefficient enquired.
1549         @type name: C{string}
1550         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1551         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1552         """
1553         if self.hasCoefficient(name):
1554            self.trace("Coefficient %s has been altered."%name)
1555            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1556               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1557               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1558         else:
1559            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1560    
1561       def copyConstraint(self,u):
1562          """
1563          copies the constraint into u and returns u.
1564    
1565          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1566          @type u: L{Data<escript.Data>}
1567          @return: the input u modified by the constraints.
1568          @rtype: L{Data<escript.Data>}
1569          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1570          """
1571          q=self.getCoefficientOfGeneralPDE("q")
1572          r=self.getCoefficientOfGeneralPDE("r")
1573          if not q.isEmpty():
1574             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1575             if r.isEmpty():
1576                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1577             else:
1578                 r=escript.Data(r,u.getFunctionSpace())
1579             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1580          return u
1581    
1582       def setValue(self,**coefficients):
1583          """
1584          sets new values to coefficients
1585    
1586          @param coefficients: new values assigned to coefficients
1587          @keyword A: value for coefficient A.
1588          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589          @keyword A_reduced: value for coefficient A_reduced.
1590          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591          @keyword B: value for coefficient B
1592          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword B_reduced: value for coefficient B_reduced
1594          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595          @keyword C: value for coefficient C
1596          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword C_reduced: value for coefficient C_reduced
1598          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599          @keyword D: value for coefficient D
1600          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword D_reduced: value for coefficient D_reduced
1602          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603          @keyword X: value for coefficient X
1604          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword X_reduced: value for coefficient X_reduced
1606          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1607          @keyword Y: value for coefficient Y
1608          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1609          @keyword Y_reduced: value for coefficient Y_reduced
1610          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1611          @keyword d: value for coefficient d
1612          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_reduced: value for coefficient d_reduced
1614          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1615          @keyword y: value for coefficient y
1616          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1617          @keyword d_contact: value for coefficient d_contact
1618          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1619          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1620          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1621          @keyword y_contact: value for coefficient y_contact
1622          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1623          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1624          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1625          @keyword r: values prescribed to the solution at the locations of constraints
1626          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                   depending of reduced order is used for the solution.
1628          @keyword q: mask for location of constraints
1629          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                   depending of reduced order is used for the representation of the equation.
1631          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1632          """
1633          # check if the coefficients are  legal:
1634          for i in coefficients.iterkeys():
1635             if not self.hasCoefficient(i):
1636                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1637          # if the number of unknowns or equations is still unknown we try to estimate them:
1638          if self.__numEquations==None or self.__numSolutions==None:
1639             for i,d in coefficients.iteritems():
1640                if hasattr(d,"shape"):
1641                    s=d.shape
1642                elif hasattr(d,"getShape"):
1643                    s=d.getShape()
1644                else:
1645                    s=numarray.array(d).shape
1646                if s!=None:
1647                    # get number of equations and number of unknowns:
1648                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1649                    if res==None:
1650                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1651                    else:
1652                        if self.__numEquations==None: self.__numEquations=res[0]
1653                        if self.__numSolutions==None: self.__numSolutions=res[1]
1654          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1655          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1656          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1657          for i,d in coefficients.iteritems():
1658            try:
1659               self.COEFFICIENTS[i].setValue(self.getDomain(),
1660                                             self.getNumEquations(),self.getNumSolutions(),
1661                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1662               self.alteredCoefficient(i)
1663            except IllegalCoefficientFunctionSpace,m:
1664                # if the function space is wrong then we try the reduced version:
1665                i_red=i+"_reduced"
1666                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1667                    try:
1668                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1669                                                          self.getNumEquations(),self.getNumSolutions(),
1670                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1671                        self.alteredCoefficient(i_red)
1672                    except IllegalCoefficientValue,m:
1673                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1674                    except IllegalCoefficientFunctionSpace,m:
1675                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1676                else:
1677                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1678            except IllegalCoefficientValue,m:
1679               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1680          self.__altered_coefficients=True
1681          # check if the systrem is inhomogeneous:
1682          if len(coefficients)>0 and not self.isUsingLumping():
1683             q=self.getCoefficientOfGeneralPDE("q")
1684             r=self.getCoefficientOfGeneralPDE("r")
1685             homogeneous_constraint=True
1686             if not q.isEmpty() and not r.isEmpty():
1687                 if util.Lsup(q*r)>0.:
1688                   self.trace("Inhomogeneous constraint detected.")
1689                   self.__invalidateSystem()
1690    
1691     def getSystem(self):     def getSystem(self):
1692         """         """
1693         @brief         return the operator and right hand side of the PDE
1694    
1695           @return: the discrete version of the PDE
1696           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1697         """         """
1698         if not self.__operator_isValid and not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
           if self.debug() : print "PDE Debug: New PDE is built."  
1699            if self.isUsingLumping():            if self.isUsingLumping():
1700                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1701                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1702                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1703                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1704                          raise ValueError,"coefficient A in lumped matrix may not be present."
1705                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1706                          raise ValueError,"coefficient B in lumped matrix may not be present."
1707                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1708                          raise ValueError,"coefficient C in lumped matrix may not be present."
1709                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1710                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1711                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1712                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1713                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1714                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1715                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1716                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1717                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1718                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1719                     D=self.getCoefficientOfGeneralPDE("D")
1720                     d=self.getCoefficientOfGeneralPDE("d")
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1723                     if not D.isEmpty():
1724                         if self.getNumSolutions()>1:
1725                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1726                         else:
1727                            D_times_e=D
1728                     else:
1729                        D_times_e=escript.Data()
1730                     if not d.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_times_e=d
1735                     else:
1736                        d_times_e=escript.Data()
1737          
1738                     if not D_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            D_reduced_times_e=D_reduced
1743                     else:
1744                        D_reduced_times_e=escript.Data()
1745                     if not d_reduced.isEmpty():
1746                         if self.getNumSolutions()>1:
1747                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1748                         else:
1749                            d_reduced_times_e=d_reduced
1750                     else:
1751                        d_reduced_times_e=escript.Data()
1752    
1753                     self.__operator=self.__getNewRightHandSide()
1754                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1755                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1756                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1757                     else:
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_times_e, \
1761                                                     d_times_e,\
1762                                                     escript.Data())
1763                        self.getDomain().addPDEToRHS(self.__operator, \
1764                                                     escript.Data(), \
1765                                                     D_reduced_times_e, \
1766                                                     d_reduced_times_e,\
1767                                                     escript.Data())
1768                     self.__operator=1./self.__operator
1769                     self.trace("New lumped operator has been built.")
1770                     self.__operator_is_Valid=True
1771                  if not self.__righthandside_isValid:
1772                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1773                                   self.getCoefficientOfGeneralPDE("X"), \
1774                                   self.getCoefficientOfGeneralPDE("Y"),\
1775                                   self.getCoefficientOfGeneralPDE("y"),\
1776                                   self.getCoefficientOfGeneralPDE("y_contact"))
1777                     self.getDomain().addPDEToRHS(self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1780                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1781                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1782                     self.trace("New right hand side as been built.")
1783                     self.__righthandside_isValid=True
1784            else:            else:
1785                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1786                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1787                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1788                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1789                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1790                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1791                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1792                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1793                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1794                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1795                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1796            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1797            self.__righthandside_isValid=True                   self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1798            self.__applyConstraint()                                 self.getCoefficientOfGeneralPDE("A_reduced"), \
1799            self.__copyConstraint(self.__righthandside)                                 self.getCoefficientOfGeneralPDE("B_reduced"), \
1800         elif not self.__operator_isValid:                                 self.getCoefficientOfGeneralPDE("C_reduced"), \
1801            self.getOperator()                                 self.getCoefficientOfGeneralPDE("D_reduced"), \
1802         elif not self.__righthandside_isValid:                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1803            self.getRightHandSide()                                 self.getCoefficientOfGeneralPDE("Y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1808                     self.__applyConstraint()
1809                     self.__righthandside=self.copyConstraint(self.__righthandside)
1810                     self.trace("New system has been built.")
1811                     self.__operator_is_Valid=True
1812                     self.__righthandside_isValid=True
1813                 elif not self.__righthandside_isValid:
1814                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1815                                   self.getCoefficientOfGeneralPDE("X"), \
1816                                   self.getCoefficientOfGeneralPDE("Y"),\
1817                                   self.getCoefficientOfGeneralPDE("y"),\
1818                                   self.getCoefficientOfGeneralPDE("y_contact"))
1819                     self.getDomain().addPDEToRHS(self.__righthandside, \
1820                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1821                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1822                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1823                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1824                     self.__righthandside=self.copyConstraint(self.__righthandside)
1825                     self.trace("New right hand side has been built.")
1826                     self.__righthandside_isValid=True
1827                 elif not self.__operator_is_Valid:
1828                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1829                                self.getCoefficientOfGeneralPDE("A"), \
1830                                self.getCoefficientOfGeneralPDE("B"), \
1831                                self.getCoefficientOfGeneralPDE("C"), \
1832                                self.getCoefficientOfGeneralPDE("D"), \
1833                                escript.Data(), \
1834                                escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("d"), \
1836                                escript.Data(),\
1837                                self.getCoefficientOfGeneralPDE("d_contact"), \
1838                                escript.Data())
1839                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1840                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1842                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1843                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1844                                escript.Data(), \
1845                                escript.Data(), \
1846                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1847                                escript.Data(),\
1848                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1849                                escript.Data())
1850                     self.__applyConstraint()
1851                     self.trace("New operator has been built.")
1852                     self.__operator_is_Valid=True
1853         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1854    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1855    
1856        @param options  class Poisson(LinearPDE):
1857        """     """
1858        mat,f=self.getSystem()     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
       if self.isUsingLumping():  
          out=f/mat  
          self.__copyConstraint(out)  
       else:  
          options[util.TOLERANCE_KEY]=self.getTolerance()  
          options[util.METHOD_KEY]=self.getSolverMethod()  
          options[util.SYMMETRY_KEY]=self.isSymmetric()  
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1859    
1860     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1861    
1862         @param options     with natural boundary conditons
1863         """  
1864         if not self.__solution_isValid:     M{n[j]*grad(u)[j] = 0 }
1865             if self.debug() : print "PDE Debug: PDE is resolved."  
1866             self.__solution=self.solve(**options)     and constraints:
1867             self.__solution_isValid=True  
1868         return self.__solution     M{u=0} where M{q>0}
1869     #============ some serivice functions  =====================================================  
1870     def getDomain(self):     """
1871       """  
1872       @brief returns the domain of the PDE     def __init__(self,domain,debug=False):
1873       """       """
1874       return self.__domain       initializes a new Poisson equation
1875    
1876         @param domain: domain of the PDE
1877         @type domain: L{Domain<escript.Domain>}
1878         @param debug: if True debug informations are printed.
1879    
    def getNumEquations(self):  
1880       """       """
1881       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1882         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1883                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1884                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1885         self.setSymmetryOn()
1886    
1887       def setValue(self,**coefficients):
1888       """       """
1889       if self.__numEquations>0:       sets new values to coefficients
1890           return self.__numEquations  
1891         @param coefficients: new values assigned to coefficients
1892         @keyword f: value for right hand side M{f}
1893         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1894         @keyword q: mask for location of constraints
1895         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1896                   depending of reduced order is used for the representation of the equation.
1897         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1898         """
1899         super(Poisson, self).setValue(**coefficients)
1900    
1901       def getCoefficientOfGeneralPDE(self,name):
1902         """
1903         return the value of the coefficient name of the general PDE
1904         @param name: name of the coefficient requested.
1905         @type name: C{string}
1906         @return: the value of the coefficient  name
1907         @rtype: L{Data<escript.Data>}
1908         @raise IllegalCoefficient: if name is not one of coefficients
1909                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1910         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1911         """
1912         if name == "A" :
1913             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1914         elif name == "B" :
1915             return escript.Data()
1916         elif name == "C" :
1917             return escript.Data()
1918         elif name == "D" :
1919             return escript.Data()
1920         elif name == "X" :
1921             return escript.Data()
1922         elif name == "Y" :
1923             return self.getCoefficient("f")
1924         elif name == "d" :
1925             return escript.Data()
1926         elif name == "y" :
1927             return escript.Data()
1928         elif name == "d_contact" :
1929             return escript.Data()
1930         elif name == "y_contact" :
1931             return escript.Data()
1932         elif name == "A_reduced" :
1933             return escript.Data()
1934         elif name == "B_reduced" :
1935             return escript.Data()
1936         elif name == "C_reduced" :
1937             return escript.Data()
1938         elif name == "D_reduced" :
1939             return escript.Data()
1940         elif name == "X_reduced" :
1941             return escript.Data()
1942         elif name == "Y_reduced" :
1943             return self.getCoefficient("f_reduced")
1944         elif name == "d_reduced" :
1945             return escript.Data()
1946         elif name == "y_reduced" :
1947             return escript.Data()
1948         elif name == "d_contact_reduced" :
1949             return escript.Data()
1950         elif name == "y_contact_reduced" :
1951             return escript.Data()
1952         elif name == "r" :
1953             return escript.Data()
1954         elif name == "q" :
1955             return self.getCoefficient("q")
1956       else:       else:
1957           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1958    
1959     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1960       """
1961       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1962    
1963       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1964    
1965       with natural boundary conditons
1966    
1967       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1968    
1969       and constraints:
1970    
1971       M{u=r} where M{q>0}
1972    
1973       """
1974    
1975       def __init__(self,domain,debug=False):
1976       """       """
1977       @brief returns the number of unknowns       initializes a new Poisson equation
1978    
1979         @param domain: domain of the PDE
1980         @type domain: L{Domain<escript.Domain>}
1981         @param debug: if True debug informations are printed.
1982    
1983         """
1984         super(Helmholtz, self).__init__(domain,1,1,debug)
1985         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1993                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1994         self.setSymmetryOn()
1995    
1996       def setValue(self,**coefficients):
1997       """       """
1998       if self.__numSolutions>0:       sets new values to coefficients
1999          return self.__numSolutions  
2000         @param coefficients: new values assigned to coefficients
2001         @keyword omega: value for coefficient M{S{omega}}
2002         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword k: value for coefficeint M{k}
2004         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2005         @keyword f: value for right hand side M{f}
2006         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2007         @keyword alpha: value for right hand side M{S{alpha}}
2008         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2009         @keyword g: value for right hand side M{g}
2010         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2011         @keyword r: prescribed values M{r} for the solution in constraints.
2012         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                   depending of reduced order is used for the representation of the equation.
2014         @keyword q: mask for location of constraints
2015         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2016                   depending of reduced order is used for the representation of the equation.
2017         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2018         """
2019         super(Helmholtz, self).setValue(**coefficients)
2020    
2021       def getCoefficientOfGeneralPDE(self,name):
2022         """
2023         return the value of the coefficient name of the general PDE
2024    
2025         @param name: name of the coefficient requested.
2026         @type name: C{string}
2027         @return: the value of the coefficient  name
2028         @rtype: L{Data<escript.Data>}
2029         @raise IllegalCoefficient: if name is not one of coefficients
2030                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2031         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2032         """
2033         if name == "A" :
2034             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2035         elif name == "B" :
2036             return escript.Data()
2037         elif name == "C" :
2038             return escript.Data()
2039         elif name == "D" :
2040             return self.getCoefficient("omega")
2041         elif name == "X" :
2042             return escript.Data()
2043         elif name == "Y" :
2044             return self.getCoefficient("f")
2045         elif name == "d" :
2046             return self.getCoefficient("alpha")
2047         elif name == "y" :
2048             return self.getCoefficient("g")
2049         elif name == "d_contact" :
2050             return escript.Data()
2051         elif name == "y_contact" :
2052             return escript.Data()
2053         elif name == "A_reduced" :
2054             return escript.Data()
2055         elif name == "B_reduced" :
2056             return escript.Data()
2057         elif name == "C_reduced" :
2058             return escript.Data()
2059         elif name == "D_reduced" :
2060             return escript.Data()
2061         elif name == "X_reduced" :
2062             return escript.Data()
2063         elif name == "Y_reduced" :
2064             return self.getCoefficient("f_reduced")
2065         elif name == "d_reduced" :
2066             return escript.Data()
2067         elif name == "y_reduced" :
2068            return self.getCoefficient("g_reduced")
2069         elif name == "d_contact_reduced" :
2070             return escript.Data()
2071         elif name == "y_contact_reduced" :
2072             return escript.Data()
2073         elif name == "r" :
2074             return self.getCoefficient("r")
2075         elif name == "q" :
2076             return self.getCoefficient("q")
2077       else:       else:
2078          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2079    
2080    class LameEquation(LinearPDE):
2081       """
2082       Class to define a Lame equation problem:
2083    
2084     def checkSymmetry(self):     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] }
       """  
       @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.  
       """  
       raise SystemError,"checkSymmetry is not implemented yet"  
2085    
2086        return None     with natural boundary conditons:
2087    
2088     def getFlux(self,u):     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] }
        """  
        @brief returns the flux J_ij for a given u  
2089    
2090              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     and constraints:
2091    
2092         @param u argument of the operator     M{u[i]=r[i]} where M{q[i]>0}
2093    
2094         """     """
        raise SystemError,"getFlux is not implemented yet"  
        return None  
2095    
2096     def applyOperator(self,u):     def __init__(self,domain,debug=False):
2097         """        super(LameEquation, self).__init__(domain,\
2098         @brief applies the operator of the PDE to a given solution u in weak from                                           domain.getDim(),domain.getDim(),debug)
2099          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2100                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2101                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2102                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2103                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2104                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2105                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2106          self.setSymmetryOn()
2107    
2108       def setValues(self,**coefficients):
2109         """
2110         sets new values to coefficients
2111    
2112         @param coefficients: new values assigned to coefficients
2113         @keyword lame_mu: value for coefficient M{S{mu}}
2114         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2115         @keyword lame_lambda: value for coefficient M{S{lambda}}
2116         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2117         @keyword F: value for internal force M{F}
2118         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2119         @keyword sigma: value for initial stress M{S{sigma}}
2120         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2121         @keyword f: value for extrenal force M{f}
2122         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2123         @keyword r: prescribed values M{r} for the solution in constraints.
2124         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @keyword q: mask for location of constraints
2127         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2128                   depending of reduced order is used for the representation of the equation.
2129         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2130         """
2131         super(LameEquation, self).setValues(**coefficients)
2132    
2133       def getCoefficientOfGeneralPDE(self,name):
2134         """
2135         return the value of the coefficient name of the general PDE
2136    
2137         @param name: name of the coefficient requested.
2138         @type name: C{string}
2139         @return: the value of the coefficient  name
2140         @rtype: L{Data<escript.Data>}
2141         @raise IllegalCoefficient: if name is not one of coefficients
2142                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2143         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2144         """
2145         if name == "A" :
2146             out =self.createCoefficientOfGeneralPDE("A")
2147             for i in range(self.getDim()):
2148               for j in range(self.getDim()):
2149                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2150                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2151                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2152             return out
2153         elif name == "B" :
2154             return escript.Data()
2155         elif name == "C" :
2156             return escript.Data()
2157         elif name == "D" :
2158             return escript.Data()
2159         elif name == "X" :
2160             return self.getCoefficient("sigma")
2161         elif name == "Y" :
2162             return self.getCoefficient("F")
2163         elif name == "d" :
2164             return escript.Data()
2165         elif name == "y" :
2166             return self.getCoefficient("f")
2167         elif name == "d_contact" :
2168             return escript.Data()
2169         elif name == "y_contact" :
2170             return escript.Data()
2171         elif name == "A_reduced" :
2172             return escript.Data()
2173         elif name == "B_reduced" :
2174             return escript.Data()
2175         elif name == "C_reduced" :
2176             return escript.Data()
2177         elif name == "D_reduced" :
2178             return escript.Data()
2179         elif name == "X_reduced" :
2180             return escript.Data()
2181         elif name == "Y_reduced" :
2182             return escript.Data()
2183         elif name == "d_reduced" :
2184             return escript.Data()
2185         elif name == "y_reduced" :
2186             return escript.Data()
2187         elif name == "d_contact_reduced" :
2188             return escript.Data()
2189         elif name == "y_contact_reduced" :
2190             return escript.Data()
2191         elif name == "r" :
2192             return self.getCoefficient("r")
2193         elif name == "q" :
2194             return self.getCoefficient("q")
2195         else:
2196            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2197    
2198         @param u argument of the operator  def LinearSinglePDE(domain,debug=False):
2199       """
2200       defines a single linear PDEs
2201    
2202         """     @param domain: domain of the PDE
2203         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())     @type domain: L{Domain<escript.Domain>}
2204                                                                                                                                                                 @param debug: if True debug informations are printed.
2205     def getResidual(self,u):     @rtype: L{LinearPDE}
2206         """     """
2207         @brief return the residual of u in the weak from     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2208    
2209         @param u  def LinearPDESystem(domain,debug=False):
2210         """     """
2211         return self.applyOperator(u)-self.getRightHandSide()     defines a system of linear PDEs
2212    
2213  class Poisson(LinearPDE):     @param domain: domain of the PDE
2214       @type domain: L{Domain<escript.Domain>}
2215       @param debug: if True debug informations are printed.
2216       @rtype: L{LinearPDE}
2217     """     """
2218     @brief Class to define a Poisson equstion problem:     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2219                                                                                                                                                                
2220     class to define a linear PDE of the form  class TransportPDE(object):
2221                                                                                                                                                                     """
2222          -u_{,jj} = f       Warning: This is still a very experimental. The class is still changing!
2223                                                                                                                                                                
2224       with boundary conditons:       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2225                                                                                                                                                                    
2226          n_j*u_{,j} = 0       u=r where q>0
2227                                                                                                                                                                    
2228      and constraints:       all coefficients are constant over time.
2229                                                                                                                                                                
2230           u=0 where q>0       typical usage:
2231                                                                                                                                                                
2232     """           p=TransportPDE(dom)
2233             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2234     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2235         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))           t=0
2236         self._setCoefficient(A=numarray.identity(self.getDomain().getDim()))           dt=0.1
2237         self.setSymmetryOn()           while (t<1.):
2238         self.setValue(f,q)                u=p.solve(dt)
2239    
2240     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2241         self._setCoefficient(Y=f,q=q)       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2242            self.__domain=domain
2243                                                                                                                                                                      self.__num_equations=num_equations
2244  # $Log$          self.__useSUPG=useSUPG
2245  # Revision 1.2  2004/12/15 07:08:27  jgs          self.__trace=trace
2246  # *** empty log message ***          self.__theta=theta
2247  #          self.__matrix_type=0
2248  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs          self.__reduced=True
2249  # *** empty log message ***          self.__reassemble=True
2250  #          if self.__useSUPG:
2251  # Revision 1.1.2.1  2004/12/12 22:53:47  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2252  # linearPDE has been renamed LinearPDE             self.__pde.setSymmetryOn()
2253  #             self.__pde.setReducedOrderOn()
2254  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross          else:
2255  # GMRES added             self.__transport_problem=self.__getNewTransportProblem()
2256  #          self.setTolerance()
2257  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross          self.__M=escript.Data()
2258  # options for GMRES and PRES20 added          self.__A=escript.Data()
2259  #          self.__B=escript.Data()
2260  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross          self.__C=escript.Data()
2261  # some small changes          self.__D=escript.Data()
2262  #          self.__X=escript.Data()
2263  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross          self.__Y=escript.Data()
2264  # Finley solves 4M unknowns now          self.__d=escript.Data()
2265  #          self.__y=escript.Data()
2266  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross          self.__d_contact=escript.Data()
2267  # poisson solver added          self.__y_contact=escript.Data()
2268  #          self.__r=escript.Data()
2269  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross          self.__q=escript.Data()
2270  # 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  
2271  #       def trace(self,text):
2272  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross               if self.__trace: print text
2273  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed       def getSafeTimeStepSize(self):
2274  #          if self.__useSUPG:
2275  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs              if self.__reassemble:
2276  # initial import of project esys2                 h=self.__domain.getSize()
2277  #                 dt=None
2278  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                 if not self.__A.isEmpty():
2279  # committing Lutz's and Paul's changes to brach jgs                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2280  #                    if dt == None:
2281  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                       dt = dt2
2282  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.                    else:
2283  #                       dt=1./(1./dt+1./dt2)
2284  # Revision 1.3  2004/09/23 00:53:23  jgs                 if not self.__B.isEmpty():
2285  # minor fixes                    dt2=util.inf(h*self.__M/util.length(self.__B))
2286  #                    if dt == None:
2287  # Revision 1.1  2004/08/28 12:58:06  gross                       dt = dt2
2288  # SimpleSolve is not running yet: problem with == of functionsspace                    else:
2289  #                       dt=1./(1./dt+1./dt2)
2290  #                 if not  self.__C.isEmpty():
2291                      dt2=util.inf(h*self.__M/util.length(self.__C))
2292                      if dt == None:
2293                         dt = dt2
2294                      else:
2295                         dt=1./(1./dt+1./dt2)
2296                   if not self.__D.isEmpty():
2297                      dt2=util.inf(self.__M/util.length(self.__D))
2298                      if dt == None:
2299                         dt = dt2
2300                      else:
2301                         dt=1./(1./dt+1./dt2)
2302                   self.__dt = dt/2
2303                return self.__dt
2304            else:
2305                return self.__getTransportProblem().getSafeTimeStepSize()
2306         def getDomain(self):
2307            return self.__domain
2308         def getTheta(self):
2309            return self.__theta
2310         def getNumEquations(self):
2311            return self.__num_equations
2312         def setReducedOn(self):
2313              if not self.reduced():
2314                  if self.__useSUPG:
2315                     self.__pde.setReducedOrderOn()
2316                  else:
2317                     self.__transport_problem=self.__getNewTransportProblem()
2318              self.__reduced=True
2319         def setReducedOff(self):
2320              if self.reduced():
2321                  if self.__useSUPG:
2322                     self.__pde.setReducedOrderOff()
2323                  else:
2324                     self.__transport_problem=self.__getNewTransportProblem()
2325              self.__reduced=False
2326         def reduced(self):
2327             return self.__reduced
2328         def getFunctionSpace(self):
2329            if self.reduced():
2330               return escript.ReducedSolution(self.getDomain())
2331            else:
2332               return escript.Solution(self.getDomain())
2333    
2334         def setTolerance(self,tol=1.e-8):
2335            self.__tolerance=tol
2336            if self.__useSUPG:
2337                  self.__pde.setTolerance(self.__tolerance)
2338    
2339         def __getNewTransportProblem(self):
2340           """
2341           returns an instance of a new operator
2342           """
2343           self.trace("New Transport problem is allocated.")
2344           return self.getDomain().newTransportProblem( \
2345                                   self.getTheta(),
2346                                   self.getNumEquations(), \
2347                                   self.getFunctionSpace(), \
2348                                   self.__matrix_type)
2349              
2350         def __getNewSolutionVector(self):
2351             if self.getNumEquations() ==1 :
2352                    out=escript.Data(0.0,(),self.getFunctionSpace())
2353             else:
2354                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2355             return out
2356    
2357         def __getTransportProblem(self):
2358           if self.__reassemble:
2359                 self.__source=self.__getNewSolutionVector()
2360                 self.__transport_problem.reset()
2361                 self.getDomain().addPDEToTransportProblem(
2362                             self.__transport_problem,
2363                             self.__source,
2364                             self.__M,
2365                             self.__A,
2366                             self.__B,
2367                             self.__C,
2368                             self.__D,
2369                             self.__X,
2370                             self.__Y,
2371                             self.__d,
2372                             self.__y,
2373                             self.__d_contact,
2374                             self.__y_contact)
2375                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2376                 self.__reassemble=False
2377           return self.__transport_problem
2378         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2379                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2380                 if not M==None:
2381                      self.__reassemble=True
2382                      self.__M=M
2383                 if not A==None:
2384                      self.__reassemble=True
2385                      self.__A=A
2386                 if not B==None:
2387                      self.__reassemble=True
2388                      self.__B=B
2389                 if not C==None:
2390                      self.__reassemble=True
2391                      self.__C=C
2392                 if not D==None:
2393                      self.__reassemble=True
2394                      self.__D=D
2395                 if not X==None:
2396                      self.__reassemble=True
2397                      self.__X=X
2398                 if not Y==None:
2399                      self.__reassemble=True
2400                      self.__Y=Y
2401                 if not d==None:
2402                      self.__reassemble=True
2403                      self.__d=d
2404                 if not y==None:
2405                      self.__reassemble=True
2406                      self.__y=y
2407                 if not d_contact==None:
2408                      self.__reassemble=True
2409                      self.__d_contact=d_contact
2410                 if not y_contact==None:
2411                      self.__reassemble=True
2412                      self.__y_contact=y_contact
2413                 if not q==None:
2414                      self.__reassemble=True
2415                      self.__q=q
2416                 if not r==None:
2417                      self.__reassemble=True
2418                      self.__r=r
2419    
2420         def setInitialSolution(self,u):
2421                 if self.__useSUPG:
2422                     self.__u=util.interpolate(u,self.getFunctionSpace())
2423                 else:
2424                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2425    
2426         def solve(self,dt,**kwarg):
2427               if self.__useSUPG:
2428                    if self.__reassemble:
2429                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2430                        self.__reassemble=False
2431                    dt2=self.getSafeTimeStepSize()
2432                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2433                    dt2=dt/nn
2434                    nnn=0
2435                    u=self.__u
2436                    self.trace("number of substeps is %d."%nn)
2437                    while nnn<nn :
2438                        self.__setSUPG(u,u,dt2/2)
2439                        u_half=self.__pde.getSolution(verbose=True)
2440                        self.__setSUPG(u,u_half,dt2)
2441                        u=self.__pde.getSolution(verbose=True)
2442                        nnn+=1
2443                    self.__u=u
2444                    return self.__u
2445               else:
2446                   kwarg["tolerance"]=self.__tolerance
2447                   tp=self.__getTransportProblem()
2448                   return tp.solve(self.__source,dt,kwarg)
2449         def __setSUPG(self,u0,u,dt):
2450                g=util.grad(u)
2451                X=0
2452                Y=self.__M*u0
2453                X=0
2454                self.__pde.setValue(r=u0)
2455                if not self.__A.isEmpty():
2456                   X=X+dt*util.matrixmult(self.__A,g)
2457                if not self.__B.isEmpty():
2458                   X=X+dt*self.__B*u
2459                if not  self.__C.isEmpty():
2460                   Y=Y+dt*util.inner(self.__C,g)
2461                if not self.__D.isEmpty():
2462                   Y=Y+dt*self.__D*u
2463                if not self.__X.isEmpty():
2464                   X=X+dt*self.__X
2465                if not self.__Y.isEmpty():
2466                   Y=Y+dt*self.__Y
2467                self.__pde.setValue(X=X,Y=Y)
2468                if not self.__y.isEmpty():
2469                   self.__pde.setValue(y=dt*self.__y)
2470                if not self.__y_contact.isEmpty():
2471                   self.__pde.setValue(y=dt*self.__y_contact)
2472                self.__pde.setValue(r=u0)

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