/[escript]/trunk/escript/py_src/linearPDEs.py
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trunk/esys2/escript/py_src/linearPDEs.py revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC trunk/escript/py_src/linearPDEs.py revision 1137 by gross, Thu May 10 08:11:31 2007 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 ## @file linearPDEs.py  
   
2  """  """
3  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
4    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
5    solver capabilities in itself but hands the PDE over to
6    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
7    The general interface is provided through the L{LinearPDE} class. The
8    L{AdvectivePDE} which is derived from the L{LinearPDE} class
9    provides an interface to PDE dominated by its advective terms. The L{Poisson},
10    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11    classs which are also derived form the L{LinearPDE} class should be used
12    to define of solve these sepecial PDEs.
13    
14    @var __author__: name of author
15    @var __copyright__: copyrights
16    @var __license__: licence agreement
17    @var __url__: url entry point on documentation
18    @var __version__: version
19    @var __date__: date of the version
20  """  """
21    
22  import escript  import escript
23  import util  import util
24  import numarray  import numarray
25    
26  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
27       """  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28       @brief Return the Domain which is equal to the input domain (if not None)                      http://www.access.edu.au
29       and is the domain of all Data objects in the dictionary data.                  Primary Business: Queensland, Australia"""
30       An exception is raised if this is not possible  __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32       @param domain  __url__="http://www.iservo.edu.au/esys"
33       @param data  __version__="$Revision$"
34       """  __date__="$Date$"
35       # get the domain used by any Data object in the list data:  
36       data_domain=None  
37       for d in data.itervalues():  class IllegalCoefficient(ValueError):
38            if isinstance(d,escript.Data):     """
39               if not d.isEmpty(): data_domain=d.getDomain()     raised if an illegal coefficient of the general ar particular PDE is requested.
40       # check if domain and data_domain are identical?     """
41       if domain == None:     pass
42           if data_domain == None:  
43                raise ValueError,"Undefined PDE domain. Specify a domain or use a Data class object as coefficient"  class IllegalCoefficientValue(ValueError):
44       else:     """
45           if data_domain == None:     raised if an incorrect value for a coefficient is used.
46                data_domain=domain     """
47           else:     pass
48             if not data_domain == domain:  
49                   raise ValueError,"Domain of coefficients doesnot match specified domain"  class IllegalCoefficientFunctionSpace(ValueError):
50       # now we check if all Data class object coefficients are defined on data_domain:     """
51       for i,d in data.iteritems():     raised if an incorrect function space for a coefficient is used.
52           if isinstance(d,escript.Data):     """
             if not d.isEmpty():  
                if not data_domain==d.getDomain():  
                  raise ValueError,"Illegal domain for coefficient %s."%i  
      # done:  
      return data_domain  
   
 def identifyNumEquationsAndSolutions(dim,coef={}):  
      # get number of equations and number of unknowns:  
      numEquations=0  
      numSolutions=0  
      for i in coef.iterkeys():  
         if not coef[i].isEmpty():  
            res=_PDECoefficientTypes[i].estimateNumEquationsAndNumSolutions(coef[i].getShape(),dim)  
            if res==None:  
                raise ValueError,"Illegal shape %s of coefficient %s"%(coef[i].getShape().__str__(),i)  
            else:  
                numEquations=max(numEquations,res[0])  
                numSolutions=max(numSolutions,res[1])  
      return numEquations,numSolutions  
   
   
 def _CompTuple2(t1,t2):  
    """  
    @brief  
   
    @param t1  
    @param t2  
    """  
    dif=t1[0]+t1[1]-(t2[0]+t2[1])  
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
53    
54  class PDECoefficientType:  class UndefinedPDEError(ValueError):
55       """
56       raised if a PDE is not fully defined yet.
57       """
58       pass
59    
60    class PDECoefficient(object):
61      """      """
62      @brief      A class for describing a PDE coefficient
63    
64        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
65        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
66        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
67        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
68        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
69        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
70        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
71        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
72        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
73        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
74        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
75        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
76        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
77        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
78    
79      """      """
     # identifier for location of Data objects defining coefficients  
80      INTERIOR=0      INTERIOR=0
81      BOUNDARY=1      BOUNDARY=1
82      CONTACT=2      CONTACT=2
83      CONTINUOUS=3      SOLUTION=3
84      # identifier in the pattern of coefficients:      REDUCED=4
85      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
86      # number of unknowns.      BY_SOLUTION=6
87      EQUATION=3      BY_DIM=7
88      SOLUTION=4      OPERATOR=10
89      DIM=5      RIGHTHANDSIDE=11
90      # indicator for what is altered if the coefficient is altered:      BOTH=12
91      OPERATOR=5      INTERIOR_REDUCED=13
92      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
93      BOTH=7      CONTACT_REDUCED=15
94      def __init__(self,where,pattern,altering):  
95         """      def __init__(self, where, pattern, altering):
96         @brief Initialise a PDE Coefficient type         """
97           Initialise a PDE Coefficient type
98    
99           @param where: describes where the coefficient lives
100           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
101                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
102           @param pattern: describes the shape of the coefficient and how the shape is build for a given
103                  spatial dimension and numbers of equation and solution in then PDE. For instance,
104                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
105                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
106                  on a 2-dimensional domain. In the case of single equation and a single solution component
107                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
108                  the example would be read as (2,).
109           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
110           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
111           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
112           @param reduced: indicates if reduced
113           @type reduced: C{bool}
114         """         """
115          
116           super(PDECoefficient, self).__init__()
117         self.what=where         self.what=where
118         self.pattern=pattern         self.pattern=pattern
119         self.altering=altering         self.altering=altering
120           self.resetValue()
121    
122      def getFunctionSpace(self,domain):      def resetValue(self):
123         """         """
124         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
125         """         """
126         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
127         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
128         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
129         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
130           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
131    
132           @param domain: domain on which the PDE uses the coefficient
133           @type domain: L{Domain<escript.Domain>}
134           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
135           @type reducedEquationOrder: C{bool}
136           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
137           @type reducedSolutionOrder: C{bool}
138           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
139           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
140           """
141           if self.what==self.INTERIOR:
142                return escript.Function(domain)
143           elif self.what==self.INTERIOR_REDUCED:
144                return escript.ReducedFunction(domain)
145           elif self.what==self.BOUNDARY:
146                return escript.FunctionOnBoundary(domain)
147           elif self.what==self.BOUNDARY_REDUCED:
148                return escript.ReducedFunctionOnBoundary(domain)
149           elif self.what==self.CONTACT:
150                return escript.FunctionOnContactZero(domain)
151           elif self.what==self.CONTACT_REDUCED:
152                return escript.ReducedFunctionOnContactZero(domain)
153           elif self.what==self.SOLUTION:
154                if reducedEquationOrder and reducedSolutionOrder:
155                    return escript.ReducedSolution(domain)
156                else:
157                    return escript.Solution(domain)
158           elif self.what==self.REDUCED:
159                return escript.ReducedSolution(domain)
160    
161        def getValue(self):
162           """
163           returns the value of the coefficient
164    
165           @return:  value of the coefficient
166           @rtype:  L{Data<escript.Data>}
167           """
168           return self.value
169    
170        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
171           """
172           set the value of the coefficient to a new value
173    
174           @param domain: domain on which the PDE uses the coefficient
175           @type domain: L{Domain<escript.Domain>}
176           @param numEquations: number of equations of the PDE
177           @type numEquations: C{int}
178           @param numSolutions: number of components of the PDE solution
179           @type numSolutions: C{int}
180           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
181           @type reducedEquationOrder: C{bool}
182           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
183           @type reducedSolutionOrder: C{bool}
184           @param newValue: number of components of the PDE solution
185           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
186           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
187           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
188           """
189           if newValue==None:
190               newValue=escript.Data()
191           elif isinstance(newValue,escript.Data):
192               if not newValue.isEmpty():
193                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
194                    try:
195                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
196                    except:
197                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
198           else:
199               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
200           if not newValue.isEmpty():
201               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
202                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
203           self.value=newValue
204    
205      def isAlteringOperator(self):      def isAlteringOperator(self):
206          """          """
207      @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
208    
209            @return:  True if the operator of the PDE is changed when the coefficient is changed
210            @rtype:  C{bool}
211      """      """
212          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
213              return not None              return not None
# Line 119  class PDECoefficientType: Line 216  class PDECoefficientType:
216    
217      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
218          """          """
219      @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
220    
221        @rtype:  C{bool}
222            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
223      """      """
224          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
225              return not None              return not None
226          else:          else:
227              return None              return None
228    
229      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
230         """         """
231         @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
232    
233         @param shape         @param domain: domain on which the PDE uses the coefficient
234         @param dim         @type domain: L{Domain<escript.Domain>}
235           @param shape: suggested shape of the coefficient
236           @type shape: C{tuple} of C{int} values
237           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
238                     If no appropriate numbers could be identified, C{None} is returned
239           @rtype: C{tuple} of two C{int} values or C{None}
240         """         """
241           dim=domain.getDim()
242         if len(shape)>0:         if len(shape)>0:
243             num=max(shape)+1             num=max(shape)+1
244         else:         else:
245             num=1             num=1
246         search=[]         search=[]
247         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
248            for e in range(num):            for u in range(num):
249               search.append((e,u))               for e in range(num):
250         search.sort(_CompTuple2)                  search.append((e,u))
251         for item in search:            search.sort(self.__CompTuple2)
252               s=self.buildShape(item[0],item[1],dim)            for item in search:
253                 s=self.getShape(domain,item[0],item[1])
254               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
255                   return (1,1)                   return (1,1)
256               else:               else:
257                   if s==shape: return item                   if s==shape: return item
258           elif self.definesNumEquation():
259              for e in range(num,0,-1):
260                 s=self.getShape(domain,e,0)
261                 if len(s)==0 and len(shape)==0:
262                     return (1,None)
263                 else:
264                     if s==shape: return (e,None)
265    
266           elif self.definesNumSolutions():
267              for u in range(num,0,-1):
268                 s=self.getShape(domain,0,u)
269                 if len(s)==0 and len(shape)==0:
270                     return (None,1)
271                 else:
272                     if s==shape: return (None,u)
273         return None         return None
274        def definesNumSolutions(self):
275           """
276           checks if the coefficient allows to estimate the number of solution components
277    
278      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
279          """         @rtype: C{bool}
280      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
281           for i in self.pattern:
282                 if i==self.BY_SOLUTION: return True
283           return False
284    
285      @param e      def definesNumEquation(self):
286      @param u         """
287      @param dim         checks if the coefficient allows to estimate the number of equations
288      """  
289          s=()         @return: True if the coefficient allows an estimate of the number of equations
290          for i in self.pattern:         @rtype: C{bool}
291               if i==self.EQUATION:         """
292                  if e>1: s=s+(e,)         for i in self.pattern:
293               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
294                  if u>1: s=s+(u,)         return False
295    
296        def __CompTuple2(self,t1,t2):
297          """
298          Compare two tuples of possible number of equations and number of solutions
299    
300          @param t1: The first tuple
301          @param t2: The second tuple
302    
303          """
304    
305          dif=t1[0]+t1[1]-(t2[0]+t2[1])
306          if dif<0: return 1
307          elif dif>0: return -1
308          else: return 0
309    
310        def getShape(self,domain,numEquations=1,numSolutions=1):
311           """
312           builds the required shape of the coefficient
313    
314           @param domain: domain on which the PDE uses the coefficient
315           @type domain: L{Domain<escript.Domain>}
316           @param numEquations: number of equations of the PDE
317           @type numEquations: C{int}
318           @param numSolutions: number of components of the PDE solution
319           @type numSolutions: C{int}
320           @return: shape of the coefficient
321           @rtype: C{tuple} of C{int} values
322           """
323           dim=domain.getDim()
324           s=()
325           for i in self.pattern:
326                 if i==self.BY_EQUATION:
327                    if numEquations>1: s=s+(numEquations,)
328                 elif i==self.BY_SOLUTION:
329                    if numSolutions>1: s=s+(numSolutions,)
330               else:               else:
331                  s=s+(dim,)                  s=s+(dim,)
332          return s         return s
   
 _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),  
 }  
333    
334  class LinearPDE:  class LinearPDE(object):
335     """     """
336     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
337         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
338    
339       -(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:
340    
341       with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
342    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
343    
344      and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
345       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
346       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
347       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
348       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
349       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
350       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
351    
352          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:
353    
354      and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
355    
356           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>}.
357    
    """  
    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  
358    
359     def __init__(self,domain,numEquations=0,numSolutions=0):     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
      """  
      @brief initializes a new linear PDE.  
360    
361       @param args     M{u=r}  where M{q>0}
362       """  
363       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
364       The constraints override any other condition set by the PDE or the boundary condition.
365    
366       The PDE is symmetrical if
367    
368       M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]
369    
370       For a system of PDEs and a solution with several components the PDE has the form
371    
372       M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
373    
374       M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
375       The natural boundary conditions take the form:
376    
377       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
378    
379    
380       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
381    
382       Constraints take the form
383    
384       M{u[i]=r[i]}  where  M{q[i]>0}
385    
386       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
387    
388       The system of PDEs is symmetrical if
389    
390            - M{A[i,j,k,l]=A[k,l,i,j]}
391            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
392            - M{B[i,j,k]=C[k,i,j]}
393            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
394            - M{D[i,k]=D[i,k]}
395            - M{D_reduced[i,k]=D_reduced[i,k]}
396            - M{d[i,k]=d[k,i]}
397            - M{d_reduced[i,k]=d_reduced[k,i]}
398    
399       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
400       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
401       defined as
402    
403       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
404    
405       For the case of single solution component and single PDE M{J} is defined
406    
407       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
408    
409       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
410       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
411       the contact condition takes the form
412    
413       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
414    
415       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
416       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
417       L{jump<util.jump>}.
418       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
419        The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
420       In case of a single PDE and a single component solution the contact condition takes the form
421    
422       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
423    
424       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
425    
426       @cvar DEFAULT: The default method used to solve the system of linear equations
427       @cvar DIRECT: The direct solver based on LDU factorization
428       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
429       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
430       @cvar CR: The conjugate residual method
431       @cvar CGS: The conjugate gardient square method
432       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
433       @cvar SSOR: The symmetric overrealaxtion method
434       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
435       @cvar ILUT: The incomplete LU factorization preconditioner with will in
436       @cvar JACOBI: The Jacobi preconditioner
437       @cvar GMRES: The Gram-Schmidt minimum residual method
438       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
439       @cvar LUMPING: Matrix lumping.
440       @cvar NO_REORDERING: No matrix reordering allowed
441       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
442       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
443       @cvar PASO: PASO solver package
444       @cvar SCSL: SGI SCSL solver library
445       @cvar MKL: Intel's MKL solver library
446       @cvar UMFPACK: the UMFPACK library
447       @cvar ITERATIVE: The default iterative solver
448       @cvar AMG: algebraic multi grid
449       @cvar RILU: recursive ILU
450    
451       """
452       DEFAULT= 0
453       DIRECT= 1
454       CHOLEVSKY= 2
455       PCG= 3
456       CR= 4
457       CGS= 5
458       BICGSTAB= 6
459       SSOR= 7
460       ILU0= 8
461       ILUT= 9
462       JACOBI= 10
463       GMRES= 11
464       PRES20= 12
465       LUMPING= 13
466       NO_REORDERING= 17
467       MINIMUM_FILL_IN= 18
468       NESTED_DISSECTION= 19
469       SCSL= 14
470       MKL= 15
471       UMFPACK= 16
472       ITERATIVE= 20
473       PASO= 21
474       AMG= 22
475       RILU = 23
476    
477       SMALL_TOLERANCE=1.e-13
478       __PACKAGE_KEY="package"
479       __METHOD_KEY="method"
480       __SYMMETRY_KEY="symmetric"
481       __TOLERANCE_KEY="tolerance"
482       __PRECONDITIONER_KEY="preconditioner"
483    
484    
485       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
486         """
487         initializes a new linear PDE
488    
489         @param domain: domain of the PDE
490         @type domain: L{Domain<escript.Domain>}
491         @param numEquations: number of equations. If numEquations==None the number of equations
492                              is exracted from the PDE coefficients.
493         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
494                              is exracted from the PDE coefficients.
495         @param debug: if True debug informations are printed.
496    
497         """
498         super(LinearPDE, self).__init__()
499         #
500         #   the coefficients of the general PDE:
501         #
502         self.__COEFFICIENTS_OF_GENEARL_PDE={
503           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
504           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
505           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
506           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
507           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
508           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
509           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
510           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
511           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
512           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
513           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
514           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
515           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
516           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
517           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
518           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
519           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
520           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
521           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
522           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
523           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
524           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
525    
526         # COEFFICIENTS can be overwritten by subclasses:
527         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
528         self.__altered_coefficients=False
529       # initialize attributes       # initialize attributes
530       self.__debug=None       self.__debug=debug
531       self.__domain=domain       self.__domain=domain
532       self.__numEquations=numEquations       self.__numEquations=numEquations
533       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
534       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
535    
536       # set some default values:       # set some default values:
537       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
538       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
539       self.__tolerance=1.e-8       self.__tolerance=1.e-8
540       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
541       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
542         self.__preconditioner=self.DEFAULT
543         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
544       self.__sym=False       self.__sym=False
      self.__lumping=False  
545    
546     def getCoefficient(self,name):       self.resetCoefficients()
547         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
548       # =============================================================================
549       #    general stuff:
550       # =============================================================================
551       def __str__(self):
552         """
553         returns string representation of the PDE
554    
555         @return: a simple representation of the PDE
556         @rtype: C{str}
557         """
558         return "<LinearPDE %d>"%id(self)
559       # =============================================================================
560       #    debug :
561       # =============================================================================
562       def setDebugOn(self):
563         """
564         switches on debugging
565       """       """
566       @brief return the value of the coefficient name       self.__debug=not None
567    
568       @param name     def setDebugOff(self):
569         """
570         switches off debugging
571       """       """
572       return self.__coefficient[name]       self.__debug=None
573    
574     def setValue(self,**coefficients):     def trace(self,text):
575        """       """
576        @brief sets new values to coefficients       print the text message if debugging is swiched on.
577         @param text: message
578         @type text: C{string}
579         """
580         if self.__debug: print "%s: %s"%(str(self),text)
581    
582        @param coefficients     # =============================================================================
583        """     # some service functions:
584        self._setValue(**coefficients)     # =============================================================================
585             def getDomain(self):
586         """
587         returns the domain of the PDE
588    
589     def _setValue(self,**coefficients):       @return: the domain of the PDE
590        """       @rtype: L{Domain<escript.Domain>}
591        @brief sets new values to coefficients       """
592         return self.__domain
593    
594        @param coefficients     def getDim(self):
595        """       """
596               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
597    
598        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
599        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
600           for i in self.__coefficient.iterkeys():       """
601               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()  
602    
603     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
604       """       """
605       @brief return the shape of the coefficient name       returns the number of equations
606    
607       @param name       @return: the number of equations
608         @rtype: C{int}
609         @raise UndefinedPDEError: if the number of equations is not be specified yet.
610       """       """
611       if self.hasCoefficient(name):       if self.__numEquations==None:
612          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
613       else:       else:
614          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
615    
616     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
617       """       """
618       @brief return the atoms of the coefficient name       returns the number of unknowns
619    
620       @param name       @return: the number of unknowns
621         @rtype: C{int}
622         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
623       """       """
624       if self.hasCoefficient(name):       if self.__numSolutions==None:
625          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
626       else:       else:
627          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
628    
629     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
630       """       """
631       @brief annonced that coefficient name has been changed       return status for order reduction for equation
632    
633       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
634         @rtype: L{bool}
635       """       """
636       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  
637    
638     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
639        """       """
640        @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  
641    
642        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
643        """       @rtype: L{bool}
644        return self.__coefficient.has_key(name)       """
645         return self.__reduce_solution_order
646    
647     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
648       """       """
649       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
650    
651         @return: representation space of equation
652         @rtype: L{FunctionSpace<escript.FunctionSpace>}
653       """       """
654       return self.__row_function_space       if self.reduceEquationOrder():
655             return escript.ReducedSolution(self.getDomain())
656         else:
657             return escript.Solution(self.getDomain())
658    
659     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
660       """       """
661       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
662    
663         @return: representation space of solution
664         @rtype: L{FunctionSpace<escript.FunctionSpace>}
665       """       """
666       return self.__column_function_space       if self.reduceSolutionOrder():
667             return escript.ReducedSolution(self.getDomain())
668         else:
669             return escript.Solution(self.getDomain())
670    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
671    
672     def setDebugOff(self):     def getOperator(self):
673         """       """
674         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
675    
676     def debug(self):       @return: the operator of the PDE
677         """       @rtype: L{Operator<escript.Operator>}
678         @brief returns true if the PDE is in the debug mode       """
679         """       m=self.getSystem()[0]
680         return self.__debug       if self.isUsingLumping():
681             return self.copyConstraint(1./m)
682         else:
683             return m
684    
685     #===== Lumping ===========================     def getRightHandSide(self):
686     def setLumpingOn(self):       """
687        """       provides access to the right hand side of the PDE
688        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
689        """       @rtype: L{Data<escript.Data>}
690        if not self.isUsingLumping():       """
691           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
692           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
693           self.__rebuildOperator()           return self.copyConstraint(r)
694           self.__lumping=True       else:
695             return r
696    
697     def setLumpingOff(self):     def applyOperator(self,u=None):
698        """       """
699        @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  
700    
701     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}
702        """                 the current solution is used.
703        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
704        """       @return: image of u
705        if flag:       @rtype: L{Data<escript.Data>}
706           self.setLumpingOn()       """
707        else:       if u==None:
708           self.setLumpingOff()          return self.getOperator()*self.getSolution()
709         else:
710            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
711    
712     def isUsingLumping(self):     def getResidual(self,u=None):
713         """
714         return the residual of u or the current solution if u is not present.
715    
716         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
717                   the current solution is used.
718         @type u: L{Data<escript.Data>} or None
719         @return: residual of u
720         @rtype: L{Data<escript.Data>}
721         """
722         return self.applyOperator(u)-self.getRightHandSide()
723    
724       def checkSymmetry(self,verbose=True):
725        """        """
726        @brief        test the PDE for symmetry.
727    
728          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
729          @type verbose: C{bool}
730          @return:  True if the PDE is symmetric.
731          @rtype: L{Data<escript.Data>}
732          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
733        """        """
734        return self.__lumping        verbose=verbose or self.__debug
735          out=True
736          if self.getNumSolutions()!=self.getNumEquations():
737             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
738             out=False
739          else:
740             A=self.getCoefficientOfGeneralPDE("A")
741             if not A.isEmpty():
742                tol=util.Lsup(A)*self.SMALL_TOLERANCE
743                if self.getNumSolutions()>1:
744                   for i in range(self.getNumEquations()):
745                      for j in range(self.getDim()):
746                         for k in range(self.getNumSolutions()):
747                            for l in range(self.getDim()):
748                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
749                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
750                                   out=False
751                else:
752                   for j in range(self.getDim()):
753                      for l in range(self.getDim()):
754                         if util.Lsup(A[j,l]-A[l,j])>tol:
755                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
756                            out=False
757             B=self.getCoefficientOfGeneralPDE("B")
758             C=self.getCoefficientOfGeneralPDE("C")
759             if B.isEmpty() and not C.isEmpty():
760                if verbose: print "non-symmetric PDE because B is not present but C is"
761                out=False
762             elif not B.isEmpty() and C.isEmpty():
763                if verbose: print "non-symmetric PDE because C is not present but B is"
764                out=False
765             elif not B.isEmpty() and not C.isEmpty():
766                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
767                if self.getNumSolutions()>1:
768                   for i in range(self.getNumEquations()):
769                       for j in range(self.getDim()):
770                          for k in range(self.getNumSolutions()):
771                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
772                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
773                                  out=False
774                else:
775                   for j in range(self.getDim()):
776                      if util.Lsup(B[j]-C[j])>tol:
777                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
778                         out=False
779             if self.getNumSolutions()>1:
780               D=self.getCoefficientOfGeneralPDE("D")
781               if not D.isEmpty():
782                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
783                 for i in range(self.getNumEquations()):
784                    for k in range(self.getNumSolutions()):
785                      if util.Lsup(D[i,k]-D[k,i])>tol:
786                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
787                          out=False
788               d=self.getCoefficientOfGeneralPDE("d")
789               if not d.isEmpty():
790                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
791                 for i in range(self.getNumEquations()):
792                    for k in range(self.getNumSolutions()):
793                      if util.Lsup(d[i,k]-d[k,i])>tol:
794                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
795                          out=False
796               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
797               if not d_contact.isEmpty():
798                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
799                 for i in range(self.getNumEquations()):
800                    for k in range(self.getNumSolutions()):
801                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
802                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
803                          out=False
804             # and now the reduced coefficients
805             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
806             if not A_reduced.isEmpty():
807                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
808                if self.getNumSolutions()>1:
809                   for i in range(self.getNumEquations()):
810                      for j in range(self.getDim()):
811                         for k in range(self.getNumSolutions()):
812                            for l in range(self.getDim()):
813                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
814                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
815                                   out=False
816                else:
817                   for j in range(self.getDim()):
818                      for l in range(self.getDim()):
819                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
820                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
821                            out=False
822             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
823             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
824             if B_reduced.isEmpty() and not C_reduced.isEmpty():
825                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
826                out=False
827             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
828                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
829                out=False
830             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
831                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
832                if self.getNumSolutions()>1:
833                   for i in range(self.getNumEquations()):
834                       for j in range(self.getDim()):
835                          for k in range(self.getNumSolutions()):
836                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
837                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
838                                  out=False
839                else:
840                   for j in range(self.getDim()):
841                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
842                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
843                         out=False
844             if self.getNumSolutions()>1:
845               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
846               if not D_reduced.isEmpty():
847                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
848                 for i in range(self.getNumEquations()):
849                    for k in range(self.getNumSolutions()):
850                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
851                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
852                          out=False
853               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
854               if not d_reduced.isEmpty():
855                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
856                 for i in range(self.getNumEquations()):
857                    for k in range(self.getNumSolutions()):
858                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
859                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
860                          out=False
861               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
862               if not d_contact_reduced.isEmpty():
863                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869          return out
870    
871     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
872         """         """
873         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
874    
875           @return: the solution
876           @rtype: L{Data<escript.Data>}
877           @param options: solver options
878           @keyword verbose: True to get some information during PDE solution
879           @type verbose: C{bool}
880           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
881                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
882           @keyword iter_max: maximum number of iteration steps allowed.
883           @keyword drop_tolerance: threshold for drupping in L{ILUT}
884           @keyword drop_storage: maximum of allowed memory in L{ILUT}
885           @keyword truncation: maximum number of residuals in L{GMRES}
886           @keyword restart: restart cycle length in L{GMRES}
887         """         """
888         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
889              mat,f=self.getSystem()
890              if self.isUsingLumping():
891                 self.__solution=self.copyConstraint(f*mat)
892              else:
893                 options[self.__TOLERANCE_KEY]=self.getTolerance()
894                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
895                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
896                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
897                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
898                 self.trace("PDE is resolved.")
899                 self.trace("solver options: %s"%str(options))
900                 self.__solution=mat.solve(f,options)
901              self.__solution_isValid=True
902           return self.__solution
903    
904       def getFlux(self,u=None):
905         """
906         returns the flux M{J} for a given M{u}
907    
908         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
909    
910         or
911    
912         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
913    
914         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
915         @type u: L{Data<escript.Data>} or None
916         @return: flux
917         @rtype: L{Data<escript.Data>}
918         """
919         if u==None: u=self.getSolution()
920         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
921               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
922               -util.self.getCoefficientOfGeneralPDE("X") \
923               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
924               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
925               -util.self.getCoefficientOfGeneralPDE("X_reduced")
926       # =============================================================================
927       #   solver settings:
928       # =============================================================================
929       def setSolverMethod(self,solver=None,preconditioner=None):
930           """
931           sets a new solver
932    
933           @param solver: sets a new solver method.
934           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
935           @param preconditioner: sets a new solver method.
936           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
937           """
938           if solver==None: solve=self.DEFAULT
939           if preconditioner==None: preconditioner=self.DEFAULT
940           if not (solver,preconditioner)==self.getSolverMethod():
941             self.__solver_method=solver             self.__solver_method=solver
942             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
943             self.__checkMatrixType()             self.__checkMatrixType()
944               self.trace("New solver is %s"%self.getSolverMethodName())
945    
946       def getSolverMethodName(self):
947           """
948           returns the name of the solver currently used
949    
950           @return: the name of the solver currently used.
951           @rtype: C{string}
952           """
953    
954           m=self.getSolverMethod()
955           p=self.getSolverPackage()
956           method=""
957           if m[0]==self.DEFAULT: method="DEFAULT"
958           elif m[0]==self.DIRECT: method= "DIRECT"
959           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
960           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
961           elif m[0]==self.PCG: method= "PCG"
962           elif m[0]==self.CR: method= "CR"
963           elif m[0]==self.CGS: method= "CGS"
964           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
965           elif m[0]==self.SSOR: method= "SSOR"
966           elif m[0]==self.GMRES: method= "GMRES"
967           elif m[0]==self.PRES20: method= "PRES20"
968           elif m[0]==self.LUMPING: method= "LUMPING"
969           elif m[0]==self.AMG: method= "AMG"
970           if m[1]==self.DEFAULT: method+="+DEFAULT"
971           elif m[1]==self.JACOBI: method+= "+JACOBI"
972           elif m[1]==self.ILU0: method+= "+ILU0"
973           elif m[1]==self.ILUT: method+= "+ILUT"
974           elif m[1]==self.SSOR: method+= "+SSOR"
975           elif m[1]==self.AMG: method+= "+AMG"
976           elif m[1]==self.RILU: method+= "+RILU"
977           if p==self.DEFAULT: package="DEFAULT"
978           elif p==self.PASO: package= "PASO"
979           elif p==self.MKL: package= "MKL"
980           elif p==self.SCSL: package= "SCSL"
981           elif p==self.UMFPACK: package= "UMFPACK"
982           else : method="unknown"
983           return "%s solver of %s package"%(method,package)
984    
985    
986     def getSolverMethod(self):     def getSolverMethod(self):
987         """         """
988         @brief returns the solver method         returns the solver method
989    
990           @return: the solver method currently be used.
991           @rtype: C{int}
992           """
993           return self.__solver_method,self.__preconditioner
994    
995       def setSolverPackage(self,package=None):
996         """         """
997         return self.__solver_method         sets a new solver package
998    
999           @param package: sets a new solver method.
1000           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1001           """
1002           if package==None: package=self.DEFAULT
1003           if not package==self.getSolverPackage():
1004               self.__solver_package=package
1005               self.__checkMatrixType()
1006               self.trace("New solver is %s"%self.getSolverMethodName())
1007    
1008       def getSolverPackage(self):
1009           """
1010           returns the package of the solver
1011    
1012           @return: the solver package currently being used.
1013           @rtype: C{int}
1014           """
1015           return self.__solver_package
1016    
1017       def isUsingLumping(self):
1018          """
1019          checks if matrix lumping is used a solver method
1020    
1021          @return: True is lumping is currently used a solver method.
1022          @rtype: C{bool}
1023          """
1024          return self.getSolverMethod()[0]==self.LUMPING
1025    
    #============ tolerance business =========================================================  
1026     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1027         """         """
1028         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1029    
1030           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1031    
1032           defines the stopping criterion.
1033    
1034           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1035                       the system will be resolved.
1036           @type tol: positive C{float}
1037           @raise ValueError: if tolerance is not positive.
1038         """         """
1039         if not tol>0:         if not tol>0:
1040             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1041         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1042         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1043         self.__tolerance=tol         self.__tolerance=tol
1044         return         return
1045    
1046     def getTolerance(self):     def getTolerance(self):
1047         """         """
1048         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1049    
1050           @return: tolerance currently used.
1051           @rtype: C{float}
1052         """         """
1053         return self.__tolerance         return self.__tolerance
1054    
1055     #===== symmetry  flag ==========================     # =============================================================================
1056       #    symmetry  flag:
1057       # =============================================================================
1058     def isSymmetric(self):     def isSymmetric(self):
1059        """        """
1060        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1061    
1062          @return: True is a symmetric PDE is indicated, otherwise False is returned
1063          @rtype: C{bool}
1064        """        """
1065        return self.__sym        return self.__sym
1066    
1067     def setSymmetryOn(self):     def setSymmetryOn(self):
1068        """        """
1069        @brief sets the symmetry flag to true        sets the symmetry flag.
1070        """        """
1071        if not self.isSymmetric():        if not self.isSymmetric():
1072           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1073           self.__sym=True           self.__sym=True
1074           self.__checkMatrixType()           self.__checkMatrixType()
1075    
1076     def setSymmetryOff(self):     def setSymmetryOff(self):
1077        """        """
1078        @brief sets the symmetry flag to false        removes the symmetry flag.
1079        """        """
1080        if self.isSymmetric():        if self.isSymmetric():
1081           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1082           self.__sym=False           self.__sym=False
1083           self.__checkMatrixType()           self.__checkMatrixType()
1084    
1085     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1086       """        """
1087       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1088    
1089       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1090       """        @type flag: C{bool}
1091       if flag:        """
1092          self.setSymmetryOn()        if flag:
1093       else:           self.setSymmetryOn()
1094          self.setSymmetryOff()        else:
1095             self.setSymmetryOff()
1096    
1097     #===== order reduction ==========================     # =============================================================================
1098       # function space handling for the equation as well as the solution
1099       # =============================================================================
1100     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1101       """       """
1102       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1103    
1104         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1105       """       """
1106       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1107       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1108    
1109     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1110       """       """
1111       @brief switches to full order       switches off reduced order for solution and equation representation
1112    
1113         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1114       """       """
1115       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1116       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1117    
1118     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1119       """       """
1120       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1121         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1122       @param flag                    if flag is not present order reduction is switched off
1123         @type flag: C{bool}
1124         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1125       """       """
1126       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1127       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1128    
1129     #===== order reduction solution ==========================  
1130     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1131       """       """
1132       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1133    
1134         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1135       """       """
1136       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1137       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1138           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1139           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1140           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1141             self.__resetSystem()
1142    
1143     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1144       """       """
1145       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1146    
1147         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1148       """       """
1149       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1150       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1151           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1152           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1153           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1154             self.__resetSystem()
1155    
1156     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1157       """       """
1158       @brief sets order for test functions according to flag       sets order for test functions according to flag
1159    
1160       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1161                      if flag is not present order reduction is switched off
1162         @type flag: C{bool}
1163         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1164       """       """
1165       if flag:       if flag:
1166          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1167       else:       else:
1168          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1169                                                                                                                                                              
    #===== order reduction equation ==========================  
1170     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1171       """       """
1172       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1173    
1174         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1175       """       """
1176       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1177       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1178           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1179           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1180           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1181             self.__resetSystem()
1182    
1183     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1184       """       """
1185       @brief switches to full order for test functions       switches off reduced order for equation representation
1186    
1187         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1188       """       """
1189       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1190       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1191           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1192           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1193           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1194             self.__resetSystem()
1195    
1196     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1197       """       """
1198       @brief sets order for test functions according to flag       sets order for test functions according to flag
1199    
1200       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1201                      if flag is not present order reduction is switched off
1202         @type flag: C{bool}
1203         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1204       """       """
1205       if flag:       if flag:
1206          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1207       else:       else:
1208          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1209    
1210     # ==== initialization =====================================================================     # =============================================================================
1211     def __makeNewOperator(self):     # private method:
1212       # =============================================================================
1213       def __checkMatrixType(self):
1214         """
1215         reassess the matrix type and, if a new matrix is needed, resets the system.
1216         """
1217         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1218         if not new_matrix_type==self.__matrix_type:
1219             self.trace("Matrix type is now %d."%new_matrix_type)
1220             self.__matrix_type=new_matrix_type
1221             self.__resetSystem()
1222       #
1223       #   rebuild switches :
1224       #
1225       def __invalidateSolution(self):
1226         """         """
1227         @brief         indicates the PDE has to be resolved if the solution is requested
1228         """         """
1229           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1230           self.__solution_isValid=False
1231    
1232       def __invalidateOperator(self):
1233           """
1234           indicates the operator has to be rebuilt next time it is used
1235           """
1236           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1237           self.__invalidateSolution()
1238           self.__operator_is_Valid=False
1239    
1240       def __invalidateRightHandSide(self):
1241           """
1242           indicates the right hand side has to be rebuild next time it is used
1243           """
1244           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1245           self.__invalidateSolution()
1246           self.__righthandside_isValid=False
1247    
1248       def __invalidateSystem(self):
1249           """
1250           annonced that everthing has to be rebuild:
1251           """
1252           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1253           self.__invalidateSolution()
1254           self.__invalidateOperator()
1255           self.__invalidateRightHandSide()
1256    
1257       def __resetSystem(self):
1258           """
1259           annonced that everthing has to be rebuild:
1260           """
1261           self.trace("New System is built from scratch.")
1262           self.__operator=escript.Operator()
1263           self.__operator_is_Valid=False
1264           self.__righthandside=escript.Data()
1265           self.__righthandside_isValid=False
1266           self.__solution=escript.Data()
1267           self.__solution_isValid=False
1268       #
1269       #    system initialization:
1270       #
1271       def __getNewOperator(self):
1272           """
1273           returns an instance of a new operator
1274           """
1275           self.trace("New operator is allocated.")
1276         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1277                             self.getNumEquations(), \                             self.getNumEquations(), \
1278                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1280  class LinearPDE:
1280                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1281                             self.__matrix_type)                             self.__matrix_type)
1282    
1283     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1284         """         """
1285         @brief         returns an instance of a new right hand side
1286         """         """
1287         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1288           if self.getNumEquations()>1:
1289               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1290           else:
1291               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1292    
1293     def __makeNewSolution(self):     def __getNewSolution(self):
1294         """         """
1295         @brief         returns an instance of a new solution
1296         """         """
1297         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1298           if self.getNumSolutions()>1:
1299               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1300           else:
1301               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1302    
1303     def __getFreshOperator(self):     def __makeFreshSolution(self):
1304         """         """
1305         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1306         """         """
1307         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1308             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1309         else:         else:
1310             self.__operator.setValue(0.)             self.__solution*=0
1311             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1312         return self.__operator         return self.__solution
1313    
1314     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1315         """         """
1316         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1317         """         """
1318         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1319             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1320         else:         else:
1321             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1322             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1323             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
   
    # ==== rebuild switches =====================================================================  
    def __rebuildSolution(self,deep=False):  
        """  
        @brief indicates the PDE has to be reolved if the solution is requested  
        """  
        if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."  
        self.__solution_isValid=False  
        if deep: self.__solution=escript.Data(deep)  
   
1324    
1325     def __rebuildOperator(self,deep=False):     def __makeFreshOperator(self):
1326         """         """
1327         @brief indicates the operator has to be rebuilt next time it is used         makes sure that the operator is instantiated and returns it initialized by zeros
1328         """         """
1329         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if self.__operator.isEmpty():
1330         self.__rebuildSolution(deep)             self.__operator=self.__getNewOperator()
1331         self.__operator_isValid=False         else:
1332         if deep: self.__operator=escript.Operator()             self.__operator.resetValues()
1333               self.trace("Operator reset to zero")
1334           return self.__operator
1335    
1336     def __rebuildRightHandSide(self,deep=False):     def __applyConstraint(self):
1337         """         """
1338         @brief indicates the right hand side has to be rebuild next time it is used         applies the constraints defined by q and r to the system
1339         """         """
1340         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."         if not self.isUsingLumping():
1341         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1342         self.__righthandside_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1343         if not self.__homogeneous_constraint: self.__rebuildOperator()            if not q.isEmpty() and not self.__operator.isEmpty():
1344         if deep: self.__righthandside=escript.Data()               # q is the row and column mask to indicate where constraints are set:
1345                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1346                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1347                 u=self.__getNewSolution()
1348                 if r.isEmpty():
1349                    r_s=self.__getNewSolution()
1350                 else:
1351                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1352                 u.copyWithMask(r_s,col_q)
1353                 if not self.__righthandside.isEmpty():
1354                    self.__righthandside-=self.__operator*u
1355                    self.__righthandside=self.copyConstraint(self.__righthandside)
1356                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1357       # =============================================================================
1358       # function giving access to coefficients of the general PDE:
1359       # =============================================================================
1360       def getCoefficientOfGeneralPDE(self,name):
1361         """
1362         return the value of the coefficient name of the general PDE.
1363    
1364         @note: This method is called by the assembling routine it can be overwritten
1365               to map coefficients of a particular PDE to the general PDE.
1366         @param name: name of the coefficient requested.
1367         @type name: C{string}
1368         @return: the value of the coefficient  name
1369         @rtype: L{Data<escript.Data>}
1370         @raise IllegalCoefficient: if name is not one of coefficients
1371                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1372                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1373         """
1374         if self.hasCoefficientOfGeneralPDE(name):
1375            return self.getCoefficient(name)
1376         else:
1377            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1378    
1379     def __rebuildSystem(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
1380       """       """
1381       @brief reassess the matrix type and, if needed, initiates an operator rebuild       checks if name is a the name of a coefficient of the general PDE.
1382    
1383         @param name: name of the coefficient enquired.
1384         @type name: C{string}
1385         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1386         @rtype: C{bool}
1387    
1388       """       """
1389       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
      if not new_matrix_type==self.__matrix_type:  
          if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type  
          self.__matrix_type=new_matrix_type  
          self.__rebuildOperator(deep=True)  
1390    
1391     #============ assembling =======================================================     def createCoefficientOfGeneralPDE(self,name):
1392     def __copyConstraint(self,u):       """
1393        """       returns a new instance of a coefficient for coefficient name of the general PDE
       @brief copies the constrint condition into u  
       """  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty():  
           if r.isEmpty():  
              r2=escript.Data(0,u.getShape(),u.getFunctionSpace())  
           else:  
              r2=escript.Data(r,u.getFunctionSpace())  
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1394    
1395     def __applyConstraint(self,rhs_update=True):       @param name: name of the coefficient requested.
1396         """       @type name: C{string}
1397         @brief applies the constraints  defined by q and r to the system       @return: a coefficient name initialized to 0.
1398         """       @rtype: L{Data<escript.Data>}
1399         q=self.getCoefficient("q")       @raise IllegalCoefficient: if name is not one of coefficients
1400         r=self.getCoefficient("r")                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1401         if not q.isEmpty() and not self.__operator.isEmpty():                    M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1402            # q is the row and column mask to indicate where constraints are set:       """
1403            row_q=escript.Data(q,self.getFunctionSpaceForEquation())       if self.hasCoefficientOfGeneralPDE(name):
1404            col_q=escript.Data(q,self.getFunctionSpaceForSolution())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1405            u=self.__makeNewSolution()       else:
1406            if r.isEmpty():          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if not self.__righthandside.isEmpty() and rhs_update: self.__righthandside-=self.__operator*u  
           self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1407    
1408     def getOperator(self):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1409         """       """
1410         @brief returns the operator of the PDE       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
        """  
        if not self.__operator_isValid:  
            # some Constraints are applying for a lumpled stifness matrix:  
            if self.isUsingLumping():  
               if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():  
                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"  
               if not self.getCoefficient("A").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient A"  
               if not self.getCoefficient("B").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient B"  
               if not self.getCoefficient("C").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient C"  
               if not self.getCoefficient("D").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient D"  
               if self.debug() : print "PDE Debug: New lumped operator is built."  
               mat=self.__makeNewOperator(self)  
            else:  
               if self.debug() : print "PDE Debug: New operator is built."  
               mat=self.__getFreshOperator()  
   
            self.getDomain().addPDEToSystem(mat,escript.Data(), \  
                         self.getCoefficient("A"), \  
                         self.getCoefficient("B"), \  
                         self.getCoefficient("C"), \  
                         self.getCoefficient("D"), \  
                         escript.Data(), \  
                         escript.Data(), \  
                         self.getCoefficient("d"), \  
                         escript.Data(),\  
                         self.getCoefficient("d_contact"), \  
                         escript.Data())  
            if self.isUsingLumping():  
               self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceOfSolution(),True)  
            else:  
               self.__applyConstraint(rhs_update=False)  
            self.__operator_isValid=True  
        return self.__operator  
1411    
1412     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1413         """       @type name: C{string}
1414         @brief returns the right hand side of the PDE       @return: the function space to be used for coefficient name
1415         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1416         @raise IllegalCoefficient: if name is not one of coefficients
1417                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1418                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1419         """
1420         if self.hasCoefficientOfGeneralPDE(name):
1421            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1422         else:
1423            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1424    
1425         @param ignoreConstraint     def getShapeOfCoefficientOfGeneralPDE(self,name):
1426         """       """
1427         if not self.__righthandside_isValid:       return the shape of the coefficient name of the general PDE
            if self.debug() : print "PDE Debug: New right hand side is built."  
            self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \  
                          self.getCoefficient("X"), \  
                          self.getCoefficient("Y"),\  
                          self.getCoefficient("y"),\  
                          self.getCoefficient("y_contact"))  
            self.__righthandside_isValid=True  
            if ignoreConstraint: self.__copyConstraint(self.__righthandside)  
        return self.__righthandside  
1428    
1429     def getSystem(self):       @param name: name of the coefficient enquired.
1430         """       @type name: C{string}
1431         @brief       @return: the shape of the coefficient name
1432         """       @rtype: C{tuple} of C{int}
1433         if not self.__operator_isValid and not self.__righthandside_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1434            if self.debug() : print "PDE Debug: New PDE is built."                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1435            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}.
1436                self.getRightHandSide(ignoreConstraint=True)       """
1437                self.getOperator()       if self.hasCoefficientOfGeneralPDE(name):
1438            else:          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1439                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \       else:
1440                              self.getCoefficient("A"), \          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
                             self.getCoefficient("B"), \  
                             self.getCoefficient("C"), \  
                             self.getCoefficient("D"), \  
                             self.getCoefficient("X"), \  
                             self.getCoefficient("Y"), \  
                             self.getCoefficient("d"), \  
                             self.getCoefficient("y"), \  
                             self.getCoefficient("d_contact"), \  
                             self.getCoefficient("y_contact"))  
           self.__operator_isValid=True  
           self.__righthandside_isValid=True  
           self.__applyConstraint()  
           self.__copyConstraint(self.__righthandside)  
        elif not self.__operator_isValid:  
           self.getOperator()  
        elif not self.__righthandside_isValid:  
           self.getRightHandSide()  
        return (self.__operator,self.__righthandside)  
1441    
1442     def solve(self,**options):     # =============================================================================
1443        """     # functions giving access to coefficients of a particular PDE implementation:
1444        @brief solve the PDE     # =============================================================================
1445       def getCoefficient(self,name):
1446         """
1447         returns the value of the coefficient name
1448    
1449        @param options       @param name: name of the coefficient requested.
1450        """       @type name: C{string}
1451        mat,f=self.getSystem()       @return: the value of the coefficient name
1452        if self.isUsingLumping():       @rtype: L{Data<escript.Data>}
1453           out=f/mat       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1454           self.__copyConstraint(out)       """
1455        else:       if self.hasCoefficient(name):
1456           options[util.TOLERANCE_KEY]=self.getTolerance()           return self.COEFFICIENTS[name].getValue()
1457           options[util.METHOD_KEY]=self.getSolverMethod()       else:
1458           options[util.SYMMETRY_KEY]=self.isSymmetric()          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1459    
1460     def getSolution(self,**options):     def hasCoefficient(self,name):
1461         """       """
1462         @brief returns the solution of the PDE       return True if name is the name of a coefficient
1463    
1464         @param options       @param name: name of the coefficient enquired.
1465         """       @type name: C{string}
1466         if not self.__solution_isValid:       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1467             if self.debug() : print "PDE Debug: PDE is resolved."       @rtype: C{bool}
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
    #============ some serivice functions  =====================================================  
    def getDomain(self):  
1468       """       """
1469       @brief returns the domain of the PDE       return self.COEFFICIENTS.has_key(name)
1470    
1471       def createCoefficient(self, name):
1472       """       """
1473       return self.__domain       create a L{Data<escript.Data>} object corresponding to coefficient name
1474    
1475     def getDim(self):       @return: a coefficient name initialized to 0.
1476         @rtype: L{Data<escript.Data>}
1477         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1478       """       """
1479       @brief returns the spatial dimension of the PDE       if self.hasCoefficient(name):
1480            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1481         else:
1482            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1483    
1484       def getFunctionSpaceForCoefficient(self,name):
1485       """       """
1486       return self.getDomain().getDim()       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1487    
1488     def getNumEquations(self):       @param name: name of the coefficient enquired.
1489         @type name: C{string}
1490         @return: the function space to be used for coefficient name
1491         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1492         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1493       """       """
1494       @brief returns the number of equations       if self.hasCoefficient(name):
1495            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1496         else:
1497            raise ValueError,"unknown coefficient %s requested"%name
1498       def getShapeOfCoefficient(self,name):
1499       """       """
1500       if self.__numEquations>0:       return the shape of the coefficient name
1501           return self.__numEquations  
1502         @param name: name of the coefficient enquired.
1503         @type name: C{string}
1504         @return: the shape of the coefficient name
1505         @rtype: C{tuple} of C{int}
1506         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1507         """
1508         if self.hasCoefficient(name):
1509            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1510       else:       else:
1511           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1512    
1513     def getNumSolutions(self):     def resetCoefficients(self):
1514       """       """
1515       @brief returns the number of unknowns       resets all coefficients to there default values.
1516       """       """
1517       if self.__numSolutions>0:       for i in self.COEFFICIENTS.iterkeys():
1518          return self.__numSolutions           self.COEFFICIENTS[i].resetValue()
1519    
1520       def alteredCoefficient(self,name):
1521         """
1522         announce that coefficient name has been changed
1523    
1524         @param name: name of the coefficient enquired.
1525         @type name: C{string}
1526         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1527         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1528         """
1529         if self.hasCoefficient(name):
1530            self.trace("Coefficient %s has been altered."%name)
1531            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1532               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1533               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1534       else:       else:
1535          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1536    
1537       def copyConstraint(self,u):
1538          """
1539          copies the constraint into u and returns u.
1540    
1541     def checkSymmetry(self):        @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1542          @type u: L{Data<escript.Data>}
1543          @return: the input u modified by the constraints.
1544          @rtype: L{Data<escript.Data>}
1545          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1546        """        """
1547        @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.        q=self.getCoefficientOfGeneralPDE("q")
1548          r=self.getCoefficientOfGeneralPDE("r")
1549          if not q.isEmpty():
1550             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1551             if r.isEmpty():
1552                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1553             else:
1554                 r=escript.Data(r,u.getFunctionSpace())
1555             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1556          return u
1557    
1558       def setValue(self,**coefficients):
1559        """        """
1560        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1561    
1562          @param coefficients: new values assigned to coefficients
1563          @keyword A: value for coefficient A.
1564          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1565          @keyword A_reduced: value for coefficient A_reduced.
1566          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1567          @keyword B: value for coefficient B
1568          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1569          @keyword B_reduced: value for coefficient B_reduced
1570          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1571          @keyword C: value for coefficient C
1572          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1573          @keyword C_reduced: value for coefficient C_reduced
1574          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1575          @keyword D: value for coefficient D
1576          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1577          @keyword D_reduced: value for coefficient D_reduced
1578          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1579          @keyword X: value for coefficient X
1580          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1581          @keyword X_reduced: value for coefficient X_reduced
1582          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1583          @keyword Y: value for coefficient Y
1584          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1585          @keyword Y_reduced: value for coefficient Y_reduced
1586          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1587          @keyword d: value for coefficient d
1588          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1589          @keyword d_reduced: value for coefficient d_reduced
1590          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1591          @keyword y: value for coefficient y
1592          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1593          @keyword d_contact: value for coefficient d_contact
1594          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1595          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1596          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1597          @keyword y_contact: value for coefficient y_contact
1598          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1599          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1600          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1601          @keyword r: values prescribed to the solution at the locations of constraints
1602          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1603                   depending of reduced order is used for the solution.
1604          @keyword q: mask for location of constraints
1605          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1606                   depending of reduced order is used for the representation of the equation.
1607          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1608          """
1609          # check if the coefficients are  legal:
1610          for i in coefficients.iterkeys():
1611             if not self.hasCoefficient(i):
1612                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1613          # if the number of unknowns or equations is still unknown we try to estimate them:
1614          if self.__numEquations==None or self.__numSolutions==None:
1615             for i,d in coefficients.iteritems():
1616                if hasattr(d,"shape"):
1617                    s=d.shape
1618                elif hasattr(d,"getShape"):
1619                    s=d.getShape()
1620                else:
1621                    s=numarray.array(d).shape
1622                if s!=None:
1623                    # get number of equations and number of unknowns:
1624                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1625                    if res==None:
1626                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1627                    else:
1628                        if self.__numEquations==None: self.__numEquations=res[0]
1629                        if self.__numSolutions==None: self.__numSolutions=res[1]
1630          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1631          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1632          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1633          for i,d in coefficients.iteritems():
1634            try:
1635               self.COEFFICIENTS[i].setValue(self.getDomain(),
1636                                             self.getNumEquations(),self.getNumSolutions(),
1637                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1638               self.alteredCoefficient(i)
1639            except IllegalCoefficientFunctionSpace,m:
1640                # if the function space is wrong then we try the reduced version:
1641                i_red=i+"_reduced"
1642                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1643                    try:
1644                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1645                                                          self.getNumEquations(),self.getNumSolutions(),
1646                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1647                        self.alteredCoefficient(i_red)
1648                    except IllegalCoefficientValue,m:
1649                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1650                    except IllegalCoefficientFunctionSpace,m:
1651                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1652                else:
1653                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1654            except IllegalCoefficientValue,m:
1655               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1656          self.__altered_coefficients=True
1657          # check if the systrem is inhomogeneous:
1658          if len(coefficients)>0 and not self.isUsingLumping():
1659             q=self.getCoefficientOfGeneralPDE("q")
1660             r=self.getCoefficientOfGeneralPDE("r")
1661             homogeneous_constraint=True
1662             if not q.isEmpty() and not r.isEmpty():
1663                 if util.Lsup(q*r)>0.:
1664                   self.trace("Inhomogeneous constraint detected.")
1665                   self.__invalidateSystem()
1666    
1667        return None     def getSystem(self):
1668           """
1669           return the operator and right hand side of the PDE
1670    
1671     def getFlux(self,u):         @return: the discrete version of the PDE
1672           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1673         """         """
1674         @brief returns the flux J_ij for a given u         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1675              if self.isUsingLumping():
1676                  if not self.__operator_is_Valid:
1677                     if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1678                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1679                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1680                          raise ValueError,"coefficient A in lumped matrix may not be present."
1681                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1682                          raise ValueError,"coefficient B in lumped matrix may not be present."
1683                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1684                          raise ValueError,"coefficient C in lumped matrix may not be present."
1685                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1686                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1687                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1688                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1689                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1690                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1691                     D=self.getCoefficientOfGeneralPDE("D")
1692                     if not D.isEmpty():
1693                         if self.getNumSolutions()>1:
1694                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1695                         else:
1696                            D_times_e=D
1697                     else:
1698                        D_times_e=escript.Data()
1699                     d=self.getCoefficientOfGeneralPDE("d")
1700                     if not d.isEmpty():
1701                         if self.getNumSolutions()>1:
1702                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1703                         else:
1704                            d_times_e=d
1705                     else:
1706                        d_times_e=escript.Data()
1707                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1708                     if not d_contact.isEmpty():
1709                         if self.getNumSolutions()>1:
1710                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1711                         else:
1712                            d_contact_times_e=d_contact
1713                     else:
1714                        d_contact_times_e=escript.Data()
1715        
1716                     self.__operator=self.__getNewRightHandSide()
1717                     self.getDomain().addPDEToRHS(self.__operator, \
1718                                                  escript.Data(), \
1719                                                  D_times_e, \
1720                                                  d_times_e,\
1721                                                  d_contact_times_e)
1722                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1723                     if not D_reduced.isEmpty():
1724                         if self.getNumSolutions()>1:
1725                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1726                         else:
1727                            D_reduced_times_e=D_reduced
1728                     else:
1729                        D_reduced_times_e=escript.Data()
1730                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1731                     if not d_reduced.isEmpty():
1732                         if self.getNumSolutions()>1:
1733                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1734                         else:
1735                            d_reduced_times_e=d_reduced
1736                     else:
1737                        d_reduced_times_e=escript.Data()
1738                     d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
1739                     if not d_contact_reduced.isEmpty():
1740                         if self.getNumSolutions()>1:
1741                            d_contact_reduced_times_e=util.matrixmult(d_contact_reduced,numarray.ones((self.getNumSolutions(),)))
1742                         else:
1743                            d_contact_reduced_times_e=d_contact_reduced
1744                     else:
1745                        d_contact_reduced_times_e=escript.Data()
1746        
1747                     self.__operator=self.__getNewRightHandSide()
1748                     self.getDomain().addPDEToRHS(self.__operator, \
1749                                                  escript.Data(), \
1750                                                  D_times_e, \
1751                                                  d_times_e,\
1752                                                  d_contact_times_e)
1753                     self.getDomain().addPDEToRHS(self.__operator, \
1754                                                  escript.Data(), \
1755                                                  D_reduced_times_e, \
1756                                                  d_reduced_times_e,\
1757                                                  d_contact_reduced_times_e)
1758                     self.__operator=1./self.__operator
1759                     self.trace("New lumped operator has been built.")
1760                     self.__operator_is_Valid=True
1761                  if not self.__righthandside_isValid:
1762                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1763                                   self.getCoefficientOfGeneralPDE("X"), \
1764                                   self.getCoefficientOfGeneralPDE("Y"),\
1765                                   self.getCoefficientOfGeneralPDE("y"),\
1766                                   self.getCoefficientOfGeneralPDE("y_contact"))
1767                     self.getDomain().addPDEToRHS(self.__righthandside, \
1768                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1769                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1770                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1771                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1772                     self.trace("New right hand side as been built.")
1773                     self.__righthandside_isValid=True
1774              else:
1775                 if not self.__operator_is_Valid and not self.__righthandside_isValid:
1776                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1777                                   self.getCoefficientOfGeneralPDE("A"), \
1778                                   self.getCoefficientOfGeneralPDE("B"), \
1779                                   self.getCoefficientOfGeneralPDE("C"), \
1780                                   self.getCoefficientOfGeneralPDE("D"), \
1781                                   self.getCoefficientOfGeneralPDE("X"), \
1782                                   self.getCoefficientOfGeneralPDE("Y"), \
1783                                   self.getCoefficientOfGeneralPDE("d"), \
1784                                   self.getCoefficientOfGeneralPDE("y"), \
1785                                   self.getCoefficientOfGeneralPDE("d_contact"), \
1786                                   self.getCoefficientOfGeneralPDE("y_contact"))
1787                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1788                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1789                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1790                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1791                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1792                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1793                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1798                     self.__applyConstraint()
1799                     self.__righthandside=self.copyConstraint(self.__righthandside)
1800                     self.trace("New system has been built.")
1801                     self.__operator_is_Valid=True
1802                     self.__righthandside_isValid=True
1803                 elif not self.__righthandside_isValid:
1804                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1805                                   self.getCoefficientOfGeneralPDE("X"), \
1806                                   self.getCoefficientOfGeneralPDE("Y"),\
1807                                   self.getCoefficientOfGeneralPDE("y"),\
1808                                   self.getCoefficientOfGeneralPDE("y_contact"))
1809                     self.getDomain().addPDEToRHS(self.__righthandside, \
1810                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1811                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1812                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1813                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1814                     self.__righthandside=self.copyConstraint(self.__righthandside)
1815                     self.trace("New right hand side has been built.")
1816                     self.__righthandside_isValid=True
1817                 elif not self.__operator_is_Valid:
1818                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1819                                self.getCoefficientOfGeneralPDE("A"), \
1820                                self.getCoefficientOfGeneralPDE("B"), \
1821                                self.getCoefficientOfGeneralPDE("C"), \
1822                                self.getCoefficientOfGeneralPDE("D"), \
1823                                escript.Data(), \
1824                                escript.Data(), \
1825                                self.getCoefficientOfGeneralPDE("d"), \
1826                                escript.Data(),\
1827                                self.getCoefficientOfGeneralPDE("d_contact"), \
1828                                escript.Data())
1829                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1830                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1831                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1832                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1833                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1834                                escript.Data(), \
1835                                escript.Data(), \
1836                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1837                                escript.Data(),\
1838                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1839                                escript.Data())
1840                     self.__applyConstraint()
1841                     self.trace("New operator has been built.")
1842                     self.__operator_is_Valid=True
1843           return (self.__operator,self.__righthandside)
1844    
             J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}  
1845    
1846         @param u argument of the operator  class Poisson(LinearPDE):
1847       """
1848       Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1849    
1850         """     M{-grad(grad(u)[j])[j] = f}
        raise SystemError,"getFlux is not implemented yet"  
        return None  
1851    
1852     def applyOperator(self,u):     with natural boundary conditons
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
1853    
1854         @param u argument of the operator     M{n[j]*grad(u)[j] = 0 }
1855    
1856         """     and constraints:
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
1857    
1858         @param u     M{u=0} where M{q>0}
1859         """  
1860         return self.applyOperator(u)-self.getRightHandSide()     """
1861    
1862       def __init__(self,domain,debug=False):
1863         """
1864         initializes a new Poisson equation
1865    
1866         @param domain: domain of the PDE
1867         @type domain: L{Domain<escript.Domain>}
1868         @param debug: if True debug informations are printed.
1869    
1870         """
1871         super(Poisson, self).__init__(domain,1,1,debug)
1872         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1873                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1874                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1875         self.setSymmetryOn()
1876    
1877       def setValue(self,**coefficients):
1878         """
1879         sets new values to coefficients
1880    
1881         @param coefficients: new values assigned to coefficients
1882         @keyword f: value for right hand side M{f}
1883         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1884         @keyword q: mask for location of constraints
1885         @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>}
1886                   depending of reduced order is used for the representation of the equation.
1887         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1888         """
1889         super(Poisson, self).setValue(**coefficients)
1890    
1891       def getCoefficientOfGeneralPDE(self,name):
1892         """
1893         return the value of the coefficient name of the general PDE
1894         @param name: name of the coefficient requested.
1895         @type name: C{string}
1896         @return: the value of the coefficient  name
1897         @rtype: L{Data<escript.Data>}
1898         @raise IllegalCoefficient: if name is not one of coefficients
1899                      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}.
1900         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1901         """
1902         if name == "A" :
1903             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1904         elif name == "B" :
1905             return escript.Data()
1906         elif name == "C" :
1907             return escript.Data()
1908         elif name == "D" :
1909             return escript.Data()
1910         elif name == "X" :
1911             return escript.Data()
1912         elif name == "Y" :
1913             return self.getCoefficient("f")
1914         elif name == "d" :
1915             return escript.Data()
1916         elif name == "y" :
1917             return escript.Data()
1918         elif name == "d_contact" :
1919             return escript.Data()
1920         elif name == "y_contact" :
1921             return escript.Data()
1922         elif name == "A_reduced" :
1923             return escript.Data()
1924         elif name == "B_reduced" :
1925             return escript.Data()
1926         elif name == "C_reduced" :
1927             return escript.Data()
1928         elif name == "D_reduced" :
1929             return escript.Data()
1930         elif name == "X_reduced" :
1931             return escript.Data()
1932         elif name == "Y_reduced" :
1933             return self.getCoefficient("f_reduced")
1934         elif name == "d_reduced" :
1935             return escript.Data()
1936         elif name == "y_reduced" :
1937             return escript.Data()
1938         elif name == "d_contact_reduced" :
1939             return escript.Data()
1940         elif name == "y_contact_reduced" :
1941             return escript.Data()
1942         elif name == "r" :
1943             return escript.Data()
1944         elif name == "q" :
1945             return self.getCoefficient("q")
1946         else:
1947            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1948    
1949    class Helmholtz(LinearPDE):
1950       """
1951       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1952    
1953       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1954    
1955       with natural boundary conditons
1956    
1957       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1958    
1959       and constraints:
1960    
1961       M{u=r} where M{q>0}
1962    
 class Poisson(LinearPDE):  
1963     """     """
1964     @brief Class to define a Poisson equstion problem:  
1965                                                                                                                                                                   def __init__(self,domain,debug=False):
1966     class to define a linear PDE of the form       """
1967                                                                                                                                                                     initializes a new Poisson equation
1968          -u_{,jj} = f  
1969                                                                                                                                                                     @param domain: domain of the PDE
1970       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
1971                                                                                                                                                                     @param debug: if True debug informations are printed.
1972          n_j*u_{,j} = 0  
1973                                                                                                                                                                     """
1974      and constraints:       super(Helmholtz, self).__init__(domain,1,1,debug)
1975                                                                                                                                                                     self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1976           u=0 where q>0                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1977                                                                                                                                                                                        "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1978     """                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1979                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1980     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1981         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1982         self._setValue(A=numarray.identity(self.getDomain().getDim()))                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1983         self.setSymmetryOn()                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1984         self.setValue(f,q)       self.setSymmetryOn()
1985    
1986     def setValue(self,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
1987         self._setValue(Y=f,q=q)       """
1988         sets new values to coefficients
1989                                                                                                                                                              
1990  # $Log$       @param coefficients: new values assigned to coefficients
1991  # Revision 1.3  2004/12/17 07:43:10  jgs       @keyword omega: value for coefficient M{S{omega}}
1992  # *** empty log message ***       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1993  #       @keyword k: value for coefficeint M{k}
1994  # Revision 1.1.2.3  2004/12/16 00:12:34  gross       @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1995  # __init__ of LinearPDE does not accept any coefficients anymore       @keyword f: value for right hand side M{f}
1996  #       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1997  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs       @keyword alpha: value for right hand side M{S{alpha}}
1998  # *** empty log message ***       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1999  #       @keyword g: value for right hand side M{g}
2000  # Revision 1.1.2.1  2004/12/12 22:53:47  gross       @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2001  # linearPDE has been renamed LinearPDE       @keyword r: prescribed values M{r} for the solution in constraints.
2002  #       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2003  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 depending of reduced order is used for the representation of the equation.
2004  # GMRES added       @keyword q: mask for location of constraints
2005  #       @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2006  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                 depending of reduced order is used for the representation of the equation.
2007  # options for GMRES and PRES20 added       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2008  #       """
2009  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross       super(Helmholtz, self).setValue(**coefficients)
2010  # some small changes  
2011  #     def getCoefficientOfGeneralPDE(self,name):
2012  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross       """
2013  # Finley solves 4M unknowns now       return the value of the coefficient name of the general PDE
2014  #  
2015  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross       @param name: name of the coefficient requested.
2016  # poisson solver added       @type name: C{string}
2017  #       @return: the value of the coefficient  name
2018  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross       @rtype: L{Data<escript.Data>}
2019  # 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       @raise IllegalCoefficient: if name is not one of coefficients
2020  #                    "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}.
2021  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2022  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed       """
2023  #       if name == "A" :
2024  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2025  # initial import of project esys2       elif name == "B" :
2026  #           return escript.Data()
2027  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs       elif name == "C" :
2028  # committing Lutz's and Paul's changes to brach jgs           return escript.Data()
2029  #       elif name == "D" :
2030  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane           return self.getCoefficient("omega")
2031  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       elif name == "X" :
2032  #           return escript.Data()
2033  # Revision 1.3  2004/09/23 00:53:23  jgs       elif name == "Y" :
2034  # minor fixes           return self.getCoefficient("f")
2035  #       elif name == "d" :
2036  # Revision 1.1  2004/08/28 12:58:06  gross           return self.getCoefficient("alpha")
2037  # SimpleSolve is not running yet: problem with == of functionsspace       elif name == "y" :
2038  #           return self.getCoefficient("g")
2039  #       elif name == "d_contact" :
2040             return escript.Data()
2041         elif name == "y_contact" :
2042             return escript.Data()
2043         elif name == "A_reduced" :
2044             return escript.Data()
2045         elif name == "B_reduced" :
2046             return escript.Data()
2047         elif name == "C_reduced" :
2048             return escript.Data()
2049         elif name == "D_reduced" :
2050             return escript.Data()
2051         elif name == "X_reduced" :
2052             return escript.Data()
2053         elif name == "Y_reduced" :
2054             return self.getCoefficient("f_reduced")
2055         elif name == "d_reduced" :
2056             return escript.Data()
2057         elif name == "y_reduced" :
2058            return self.getCoefficient("g_reduced")
2059         elif name == "d_contact_reduced" :
2060             return escript.Data()
2061         elif name == "y_contact_reduced" :
2062             return escript.Data()
2063         elif name == "r" :
2064             return self.getCoefficient("r")
2065         elif name == "q" :
2066             return self.getCoefficient("q")
2067         else:
2068            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2069    
2070    class LameEquation(LinearPDE):
2071       """
2072       Class to define a Lame equation problem:
2073    
2074       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] }
2075    
2076       with natural boundary conditons:
2077    
2078       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] }
2079    
2080       and constraints:
2081    
2082       M{u[i]=r[i]} where M{q[i]>0}
2083    
2084       """
2085    
2086       def __init__(self,domain,debug=False):
2087          super(LameEquation, self).__init__(domain,\
2088                                             domain.getDim(),domain.getDim(),debug)
2089          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2090                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2091                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2092                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2093                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2094                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2095                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2096          self.setSymmetryOn()
2097    
2098       def setValues(self,**coefficients):
2099         """
2100         sets new values to coefficients
2101    
2102         @param coefficients: new values assigned to coefficients
2103         @keyword lame_mu: value for coefficient M{S{mu}}
2104         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2105         @keyword lame_lambda: value for coefficient M{S{lambda}}
2106         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2107         @keyword F: value for internal force M{F}
2108         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2109         @keyword sigma: value for initial stress M{S{sigma}}
2110         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2111         @keyword f: value for extrenal force M{f}
2112         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2113         @keyword r: prescribed values M{r} for the solution in constraints.
2114         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2115                   depending of reduced order is used for the representation of the equation.
2116         @keyword q: mask for location of constraints
2117         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2118                   depending of reduced order is used for the representation of the equation.
2119         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2120         """
2121         super(LameEquation, self).setValues(**coefficients)
2122    
2123       def getCoefficientOfGeneralPDE(self,name):
2124         """
2125         return the value of the coefficient name of the general PDE
2126    
2127         @param name: name of the coefficient requested.
2128         @type name: C{string}
2129         @return: the value of the coefficient  name
2130         @rtype: L{Data<escript.Data>}
2131         @raise IllegalCoefficient: if name is not one of coefficients
2132                      "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}.
2133         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2134         """
2135         if name == "A" :
2136             out =self.createCoefficientOfGeneralPDE("A")
2137             for i in range(self.getDim()):
2138               for j in range(self.getDim()):
2139                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2140                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2141                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2142             return out
2143         elif name == "B" :
2144             return escript.Data()
2145         elif name == "C" :
2146             return escript.Data()
2147         elif name == "D" :
2148             return escript.Data()
2149         elif name == "X" :
2150             return self.getCoefficient("sigma")
2151         elif name == "Y" :
2152             return self.getCoefficient("F")
2153         elif name == "d" :
2154             return escript.Data()
2155         elif name == "y" :
2156             return self.getCoefficient("f")
2157         elif name == "d_contact" :
2158             return escript.Data()
2159         elif name == "y_contact" :
2160             return escript.Data()
2161         elif name == "A_reduced" :
2162             return escript.Data()
2163         elif name == "B_reduced" :
2164             return escript.Data()
2165         elif name == "C_reduced" :
2166             return escript.Data()
2167         elif name == "D_reduced" :
2168             return escript.Data()
2169         elif name == "X_reduced" :
2170             return escript.Data()
2171         elif name == "Y_reduced" :
2172             return escript.Data()
2173         elif name == "d_reduced" :
2174             return escript.Data()
2175         elif name == "y_reduced" :
2176             return escript.Data()
2177         elif name == "d_contact_reduced" :
2178             return escript.Data()
2179         elif name == "y_contact_reduced" :
2180             return escript.Data()
2181         elif name == "r" :
2182             return self.getCoefficient("r")
2183         elif name == "q" :
2184             return self.getCoefficient("q")
2185         else:
2186            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2187    

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