/[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 1072 by gross, Thu Mar 29 06:44:30 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           super(PDECoefficient, self).__init__()
116         self.what=where         self.what=where
117         self.pattern=pattern         self.pattern=pattern
118         self.altering=altering         self.altering=altering
119           self.resetValue()
120    
121      def getFunctionSpace(self,domain):      def resetValue(self):
122         """         """
123         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
124         """         """
125         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
126         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
127         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
128         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
129           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
130    
131           @param domain: domain on which the PDE uses the coefficient
132           @type domain: L{Domain<escript.Domain>}
133           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
134           @type reducedEquationOrder: C{bool}
135           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
136           @type reducedSolutionOrder: C{bool}
137           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
138           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
139           """
140           if self.what==self.INTERIOR:
141                return escript.Function(domain)
142           elif self.what==self.INTERIOR_REDUCED:
143                return escript.ReducedFunction(domain)
144           elif self.what==self.BOUNDARY:
145                return escript.FunctionOnBoundary(domain)
146           elif self.what==self.BOUNDARY_REDUCED:
147                return escript.ReducedFunctionOnBoundary(domain)
148           elif self.what==self.CONTACT:
149                return escript.FunctionOnContactZero(domain)
150           elif self.what==self.CONTACT_REDUCED:
151                return escript.ReducedFunctionOnContactZero(domain)
152           elif self.what==self.SOLUTION:
153                if reducedEquationOrder and reducedSolutionOrder:
154                    return escript.ReducedSolution(domain)
155                else:
156                    return escript.Solution(domain)
157           elif self.what==self.REDUCED:
158                return escript.ReducedSolution(domain)
159    
160        def getValue(self):
161           """
162           returns the value of the coefficient
163    
164           @return:  value of the coefficient
165           @rtype:  L{Data<escript.Data>}
166           """
167           return self.value
168    
169        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
170           """
171           set the value of the coefficient to a new value
172    
173           @param domain: domain on which the PDE uses the coefficient
174           @type domain: L{Domain<escript.Domain>}
175           @param numEquations: number of equations of the PDE
176           @type numEquations: C{int}
177           @param numSolutions: number of components of the PDE solution
178           @type numSolutions: C{int}
179           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
180           @type reducedEquationOrder: C{bool}
181           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
182           @type reducedSolutionOrder: C{bool}
183           @param newValue: number of components of the PDE solution
184           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
185           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
186           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
187           """
188           if newValue==None:
189               newValue=escript.Data()
190           elif isinstance(newValue,escript.Data):
191               if not newValue.isEmpty():
192                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
193                    try:
194                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
195                    except:
196                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
197           else:
198               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
199           if not newValue.isEmpty():
200               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
201                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
202           self.value=newValue
203    
204      def isAlteringOperator(self):      def isAlteringOperator(self):
205          """          """
206      @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
207    
208            @return:  True if the operator of the PDE is changed when the coefficient is changed
209            @rtype:  C{bool}
210      """      """
211          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
212              return not None              return not None
# Line 119  class PDECoefficientType: Line 215  class PDECoefficientType:
215    
216      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
217          """          """
218      @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
219    
220        @rtype:  C{bool}
221            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
222      """      """
223          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
224              return not None              return not None
225          else:          else:
226              return None              return None
227    
228      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
229         """         """
230         @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
231    
232         @param shape         @param domain: domain on which the PDE uses the coefficient
233         @param dim         @type domain: L{Domain<escript.Domain>}
234           @param shape: suggested shape of the coefficient
235           @type shape: C{tuple} of C{int} values
236           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
237                     If no appropriate numbers could be identified, C{None} is returned
238           @rtype: C{tuple} of two C{int} values or C{None}
239         """         """
240           dim=domain.getDim()
241         if len(shape)>0:         if len(shape)>0:
242             num=max(shape)+1             num=max(shape)+1
243         else:         else:
244             num=1             num=1
245         search=[]         search=[]
246         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
247            for e in range(num):            for u in range(num):
248               search.append((e,u))               for e in range(num):
249         search.sort(_CompTuple2)                  search.append((e,u))
250         for item in search:            search.sort(self.__CompTuple2)
251               s=self.buildShape(item[0],item[1],dim)            for item in search:
252                 s=self.getShape(domain,item[0],item[1])
253               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
254                   return (1,1)                   return (1,1)
255               else:               else:
256                   if s==shape: return item                   if s==shape: return item
257           elif self.definesNumEquation():
258              for e in range(num,0,-1):
259                 s=self.getShape(domain,e,0)
260                 if len(s)==0 and len(shape)==0:
261                     return (1,None)
262                 else:
263                     if s==shape: return (e,None)
264    
265           elif self.definesNumSolutions():
266              for u in range(num,0,-1):
267                 s=self.getShape(domain,0,u)
268                 if len(s)==0 and len(shape)==0:
269                     return (None,1)
270                 else:
271                     if s==shape: return (None,u)
272         return None         return None
273        def definesNumSolutions(self):
274           """
275           checks if the coefficient allows to estimate the number of solution components
276    
277      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
278          """         @rtype: C{bool}
279      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
280           for i in self.pattern:
281                 if i==self.BY_SOLUTION: return True
282           return False
283    
284      @param e      def definesNumEquation(self):
285      @param u         """
286      @param dim         checks if the coefficient allows to estimate the number of equations
287      """  
288          s=()         @return: True if the coefficient allows an estimate of the number of equations
289          for i in self.pattern:         @rtype: C{bool}
290               if i==self.EQUATION:         """
291                  if e>1: s=s+(e,)         for i in self.pattern:
292               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
293                  if u>1: s=s+(u,)         return False
294    
295        def __CompTuple2(self,t1,t2):
296          """
297          Compare two tuples of possible number of equations and number of solutions
298    
299          @param t1: The first tuple
300          @param t2: The second tuple
301    
302          """
303    
304          dif=t1[0]+t1[1]-(t2[0]+t2[1])
305          if dif<0: return 1
306          elif dif>0: return -1
307          else: return 0
308    
309        def getShape(self,domain,numEquations=1,numSolutions=1):
310           """
311           builds the required shape of the coefficient
312    
313           @param domain: domain on which the PDE uses the coefficient
314           @type domain: L{Domain<escript.Domain>}
315           @param numEquations: number of equations of the PDE
316           @type numEquations: C{int}
317           @param numSolutions: number of components of the PDE solution
318           @type numSolutions: C{int}
319           @return: shape of the coefficient
320           @rtype: C{tuple} of C{int} values
321           """
322           dim=domain.getDim()
323           s=()
324           for i in self.pattern:
325                 if i==self.BY_EQUATION:
326                    if numEquations>1: s=s+(numEquations,)
327                 elif i==self.BY_SOLUTION:
328                    if numSolutions>1: s=s+(numSolutions,)
329               else:               else:
330                  s=s+(dim,)                  s=s+(dim,)
331          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),  
 }  
332    
333  class LinearPDE:  class LinearPDE(object):
334     """     """
335     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
336         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  
337    
338       -(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:
339    
340       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)}
341    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
342    
343      and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
344       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
345       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
346       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
347       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
348       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
349       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.
350    
351          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:
352    
353      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}
354    
355           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>}.
356    
    """  
    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  
357    
358     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.  
359    
360       @param args     M{u=r}  where M{q>0}
361       """  
362       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
363       The constraints override any other condition set by the PDE or the boundary condition.
364    
365       The PDE is symmetrical if
366    
367       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]
368    
369       For a system of PDEs and a solution with several components the PDE has the form
370    
371       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] }
372    
373       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.
374       The natural boundary conditions take the form:
375    
376       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]}
377    
378    
379       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>}.
380    
381       Constraints take the form
382    
383       M{u[i]=r[i]}  where  M{q[i]>0}
384    
385       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
386    
387       The system of PDEs is symmetrical if
388    
389            - M{A[i,j,k,l]=A[k,l,i,j]}
390            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
391            - M{B[i,j,k]=C[k,i,j]}
392            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
393            - M{D[i,k]=D[i,k]}
394            - M{D_reduced[i,k]=D_reduced[i,k]}
395            - M{d[i,k]=d[k,i]}
396            - M{d_reduced[i,k]=d_reduced[k,i]}
397    
398       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
399       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
400       defined as
401    
402       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]}
403    
404       For the case of single solution component and single PDE M{J} is defined
405    
406       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
407    
408       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
409       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
410       the contact condition takes the form
411    
412       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]}
413    
414       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
415       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
416       L{jump<util.jump>}.
417       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>}.
418        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>}.
419       In case of a single PDE and a single component solution the contact condition takes the form
420    
421       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
422    
423       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>}
424    
425       @cvar DEFAULT: The default method used to solve the system of linear equations
426       @cvar DIRECT: The direct solver based on LDU factorization
427       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
428       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
429       @cvar CR: The conjugate residual method
430       @cvar CGS: The conjugate gardient square method
431       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
432       @cvar SSOR: The symmetric overrealaxtion method
433       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
434       @cvar ILUT: The incomplete LU factorization preconditioner with will in
435       @cvar JACOBI: The Jacobi preconditioner
436       @cvar GMRES: The Gram-Schmidt minimum residual method
437       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
438       @cvar LUMPING: Matrix lumping.
439       @cvar NO_REORDERING: No matrix reordering allowed
440       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
441       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
442       @cvar PASO: PASO solver package
443       @cvar SCSL: SGI SCSL solver library
444       @cvar MKL: Intel's MKL solver library
445       @cvar UMFPACK: the UMFPACK library
446       @cvar ITERATIVE: The default iterative solver
447       @cvar AMG: algebraic multi grid
448       @cvar RILU: recursive ILU
449    
450       """
451       DEFAULT= 0
452       DIRECT= 1
453       CHOLEVSKY= 2
454       PCG= 3
455       CR= 4
456       CGS= 5
457       BICGSTAB= 6
458       SSOR= 7
459       ILU0= 8
460       ILUT= 9
461       JACOBI= 10
462       GMRES= 11
463       PRES20= 12
464       LUMPING= 13
465       NO_REORDERING= 17
466       MINIMUM_FILL_IN= 18
467       NESTED_DISSECTION= 19
468       SCSL= 14
469       MKL= 15
470       UMFPACK= 16
471       ITERATIVE= 20
472       PASO= 21
473       AMG= 22
474       RILU = 23
475    
476       SMALL_TOLERANCE=1.e-13
477       __PACKAGE_KEY="package"
478       __METHOD_KEY="method"
479       __SYMMETRY_KEY="symmetric"
480       __TOLERANCE_KEY="tolerance"
481       __PRECONDITIONER_KEY="preconditioner"
482    
483    
484       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
485         """
486         initializes a new linear PDE
487    
488         @param domain: domain of the PDE
489         @type domain: L{Domain<escript.Domain>}
490         @param numEquations: number of equations. If numEquations==None the number of equations
491                              is exracted from the PDE coefficients.
492         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
493                              is exracted from the PDE coefficients.
494         @param debug: if True debug informations are printed.
495    
496         """
497         super(LinearPDE, self).__init__()
498         #
499         #   the coefficients of the general PDE:
500         #
501         self.__COEFFICIENTS_OF_GENEARL_PDE={
502           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
503           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
504           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
505           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
506           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
507           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
508           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
509           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
510           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
511           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
512           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
513           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
514           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
515           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
516           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
517           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
518           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
519           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
520           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
522           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
523           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
524    
525         # COEFFICIENTS can be overwritten by subclasses:
526         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
527         self.__altered_coefficients=False
528       # initialize attributes       # initialize attributes
529       self.__debug=None       self.__debug=debug
530       self.__domain=domain       self.__domain=domain
531       self.__numEquations=numEquations       self.__numEquations=numEquations
532       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
533       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  
534    
535       # set some default values:       # set some default values:
536       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
537       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
538       self.__tolerance=1.e-8       self.__tolerance=1.e-8
539       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
540       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
541         self.__preconditioner=self.DEFAULT
542         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
543       self.__sym=False       self.__sym=False
      self.__lumping=False  
544    
545     def getCoefficient(self,name):       self.resetCoefficients()
546         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
547       # =============================================================================
548       #    general stuff:
549       # =============================================================================
550       def __str__(self):
551         """
552         returns string representation of the PDE
553    
554         @return: a simple representation of the PDE
555         @rtype: C{str}
556         """
557         return "<LinearPDE %d>"%id(self)
558       # =============================================================================
559       #    debug :
560       # =============================================================================
561       def setDebugOn(self):
562         """
563         switches on debugging
564       """       """
565       @brief return the value of the coefficient name       self.__debug=not None
566    
567       @param name     def setDebugOff(self):
568         """
569         switches off debugging
570       """       """
571       return self.__coefficient[name]       self.__debug=None
572    
573     def setValue(self,**coefficients):     def trace(self,text):
574        """       """
575        @brief sets new values to coefficients       print the text message if debugging is swiched on.
576         @param text: message
577         @type text: C{string}
578         """
579         if self.__debug: print "%s: %s"%(str(self),text)
580    
581        @param coefficients     # =============================================================================
582        """     # some service functions:
583        self._setValue(**coefficients)     # =============================================================================
584             def getDomain(self):
585         """
586         returns the domain of the PDE
587    
588     def _setValue(self,**coefficients):       @return: the domain of the PDE
589        """       @rtype: L{Domain<escript.Domain>}
590        @brief sets new values to coefficients       """
591         return self.__domain
592    
593        @param coefficients     def getDim(self):
594        """       """
595               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  
596    
597        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
598        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
599           for i in self.__coefficient.iterkeys():       """
600               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()  
601    
602     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
603       """       """
604       @brief return the shape of the coefficient name       returns the number of equations
605    
606       @param name       @return: the number of equations
607         @rtype: C{int}
608         @raise UndefinedPDEError: if the number of equations is not be specified yet.
609       """       """
610       if self.hasCoefficient(name):       if self.__numEquations==None:
611          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
612       else:       else:
613          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
614    
615     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
616       """       """
617       @brief return the atoms of the coefficient name       returns the number of unknowns
618    
619       @param name       @return: the number of unknowns
620         @rtype: C{int}
621         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
622       """       """
623       if self.hasCoefficient(name):       if self.__numSolutions==None:
624          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
625       else:       else:
626          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
627    
628     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
629       """       """
630       @brief annonced that coefficient name has been changed       return status for order reduction for equation
631    
632       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
633         @rtype: L{bool}
634       """       """
635       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  
636    
637     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
638        """       """
639        @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  
640    
641        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
642        """       @rtype: L{bool}
643        return self.__coefficient.has_key(name)       """
644         return self.__reduce_solution_order
645    
646     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
647       """       """
648       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
649    
650         @return: representation space of equation
651         @rtype: L{FunctionSpace<escript.FunctionSpace>}
652       """       """
653       return self.__row_function_space       if self.reduceEquationOrder():
654             return escript.ReducedSolution(self.getDomain())
655         else:
656             return escript.Solution(self.getDomain())
657    
658     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
659       """       """
660       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
661    
662         @return: representation space of solution
663         @rtype: L{FunctionSpace<escript.FunctionSpace>}
664       """       """
665       return self.__column_function_space       if self.reduceSolutionOrder():
666             return escript.ReducedSolution(self.getDomain())
667         else:
668             return escript.Solution(self.getDomain())
669    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
670    
671     def setDebugOff(self):     def getOperator(self):
672         """       """
673         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
674    
675     def debug(self):       @return: the operator of the PDE
676         """       @rtype: L{Operator<escript.Operator>}
677         @brief returns true if the PDE is in the debug mode       """
678         """       m=self.getSystem()[0]
679         return self.__debug       if self.isUsingLumping():
680             return self.copyConstraint(1./m)
681         else:
682             return m
683    
684     #===== Lumping ===========================     def getRightHandSide(self):
685     def setLumpingOn(self):       """
686        """       provides access to the right hand side of the PDE
687        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
688        """       @rtype: L{Data<escript.Data>}
689        if not self.isUsingLumping():       """
690           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
691           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
692           self.__rebuildOperator()           return self.copyConstraint(r)
693           self.__lumping=True       else:
694             return r
695    
696     def setLumpingOff(self):     def applyOperator(self,u=None):
697        """       """
698        @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  
699    
700     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}
701        """                 the current solution is used.
702        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
703        """       @return: image of u
704        if flag:       @rtype: L{Data<escript.Data>}
705           self.setLumpingOn()       """
706        else:       if u==None:
707           self.setLumpingOff()          return self.getOperator()*self.getSolution()
708         else:
709            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
710    
711     def isUsingLumping(self):     def getResidual(self,u=None):
712         """
713         return the residual of u or the current solution if u is not present.
714    
715         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
716                   the current solution is used.
717         @type u: L{Data<escript.Data>} or None
718         @return: residual of u
719         @rtype: L{Data<escript.Data>}
720         """
721         return self.applyOperator(u)-self.getRightHandSide()
722    
723       def checkSymmetry(self,verbose=True):
724        """        """
725        @brief        test the PDE for symmetry.
726    
727          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
728          @type verbose: C{bool}
729          @return:  True if the PDE is symmetric.
730          @rtype: L{Data<escript.Data>}
731          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
732        """        """
733        return self.__lumping        verbose=verbose or self.__debug
734          out=True
735          if self.getNumSolutions()!=self.getNumEquations():
736             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
737             out=False
738          else:
739             A=self.getCoefficientOfGeneralPDE("A")
740             if not A.isEmpty():
741                tol=util.Lsup(A)*self.SMALL_TOLERANCE
742                if self.getNumSolutions()>1:
743                   for i in range(self.getNumEquations()):
744                      for j in range(self.getDim()):
745                         for k in range(self.getNumSolutions()):
746                            for l in range(self.getDim()):
747                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
748                                   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)
749                                   out=False
750                else:
751                   for j in range(self.getDim()):
752                      for l in range(self.getDim()):
753                         if util.Lsup(A[j,l]-A[l,j])>tol:
754                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
755                            out=False
756             B=self.getCoefficientOfGeneralPDE("B")
757             C=self.getCoefficientOfGeneralPDE("C")
758             if B.isEmpty() and not C.isEmpty():
759                if verbose: print "non-symmetric PDE because B is not present but C is"
760                out=False
761             elif not B.isEmpty() and C.isEmpty():
762                if verbose: print "non-symmetric PDE because C is not present but B is"
763                out=False
764             elif not B.isEmpty() and not C.isEmpty():
765                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
766                if self.getNumSolutions()>1:
767                   for i in range(self.getNumEquations()):
768                       for j in range(self.getDim()):
769                          for k in range(self.getNumSolutions()):
770                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
771                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
772                                  out=False
773                else:
774                   for j in range(self.getDim()):
775                      if util.Lsup(B[j]-C[j])>tol:
776                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
777                         out=False
778             if self.getNumSolutions()>1:
779               D=self.getCoefficientOfGeneralPDE("D")
780               if not D.isEmpty():
781                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
782                 for i in range(self.getNumEquations()):
783                    for k in range(self.getNumSolutions()):
784                      if util.Lsup(D[i,k]-D[k,i])>tol:
785                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
786                          out=False
787               d=self.getCoefficientOfGeneralPDE("d")
788               if not d.isEmpty():
789                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
790                 for i in range(self.getNumEquations()):
791                    for k in range(self.getNumSolutions()):
792                      if util.Lsup(d[i,k]-d[k,i])>tol:
793                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
794                          out=False
795               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
796               if not d_contact.isEmpty():
797                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
798                 for i in range(self.getNumEquations()):
799                    for k in range(self.getNumSolutions()):
800                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
801                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
802                          out=False
803             # and now the reduced coefficients
804             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
805             if not A_reduced.isEmpty():
806                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
807                if self.getNumSolutions()>1:
808                   for i in range(self.getNumEquations()):
809                      for j in range(self.getDim()):
810                         for k in range(self.getNumSolutions()):
811                            for l in range(self.getDim()):
812                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
813                                   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)
814                                   out=False
815                else:
816                   for j in range(self.getDim()):
817                      for l in range(self.getDim()):
818                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
819                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
820                            out=False
821             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
822             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
823             if B_reduced.isEmpty() and not C_reduced.isEmpty():
824                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
825                out=False
826             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
827                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
828                out=False
829             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
830                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
831                if self.getNumSolutions()>1:
832                   for i in range(self.getNumEquations()):
833                       for j in range(self.getDim()):
834                          for k in range(self.getNumSolutions()):
835                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
836                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
837                                  out=False
838                else:
839                   for j in range(self.getDim()):
840                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
841                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
842                         out=False
843             if self.getNumSolutions()>1:
844               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
845               if not D_reduced.isEmpty():
846                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
847                 for i in range(self.getNumEquations()):
848                    for k in range(self.getNumSolutions()):
849                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
850                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
851                          out=False
852               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
853               if not d_reduced.isEmpty():
854                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
855                 for i in range(self.getNumEquations()):
856                    for k in range(self.getNumSolutions()):
857                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
858                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
859                          out=False
860               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
861               if not d_contact_reduced.isEmpty():
862                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
863                 for i in range(self.getNumEquations()):
864                    for k in range(self.getNumSolutions()):
865                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
866                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
867                          out=False
868          return out
869    
870     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
871         """         """
872         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
873    
874           @return: the solution
875           @rtype: L{Data<escript.Data>}
876           @param options: solver options
877           @keyword verbose: True to get some information during PDE solution
878           @type verbose: C{bool}
879           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
880                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
881           @keyword iter_max: maximum number of iteration steps allowed.
882           @keyword drop_tolerance: threshold for drupping in L{ILUT}
883           @keyword drop_storage: maximum of allowed memory in L{ILUT}
884           @keyword truncation: maximum number of residuals in L{GMRES}
885           @keyword restart: restart cycle length in L{GMRES}
886         """         """
887         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
888              mat,f=self.getSystem()
889              if self.isUsingLumping():
890                 self.__solution=self.copyConstraint(f*mat)
891              else:
892                 options[self.__TOLERANCE_KEY]=self.getTolerance()
893                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
894                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
895                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
896                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
897                 self.trace("PDE is resolved.")
898                 self.trace("solver options: %s"%str(options))
899                 self.__solution=mat.solve(f,options)
900              self.__solution_isValid=True
901           return self.__solution
902    
903       def getFlux(self,u=None):
904         """
905         returns the flux M{J} for a given M{u}
906    
907         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]}
908    
909         or
910    
911         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
912    
913         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
914         @type u: L{Data<escript.Data>} or None
915         @return: flux
916         @rtype: L{Data<escript.Data>}
917         """
918         if u==None: u=self.getSolution()
919         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
920               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
921               -util.self.getCoefficientOfGeneralPDE("X") \
922               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
923               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
924               -util.self.getCoefficientOfGeneralPDE("X_reduced")
925       # =============================================================================
926       #   solver settings:
927       # =============================================================================
928       def setSolverMethod(self,solver=None,preconditioner=None):
929           """
930           sets a new solver
931    
932           @param solver: sets a new solver method.
933           @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}
934           @param preconditioner: sets a new solver method.
935           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
936           """
937           if solver==None: solve=self.DEFAULT
938           if preconditioner==None: preconditioner=self.DEFAULT
939           if not (solver,preconditioner)==self.getSolverMethod():
940             self.__solver_method=solver             self.__solver_method=solver
941             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
942             self.__checkMatrixType()             self.__checkMatrixType()
943               self.trace("New solver is %s"%self.getSolverMethodName())
944    
945       def getSolverMethodName(self):
946           """
947           returns the name of the solver currently used
948    
949           @return: the name of the solver currently used.
950           @rtype: C{string}
951           """
952    
953           m=self.getSolverMethod()
954           p=self.getSolverPackage()
955           method=""
956           if m[0]==self.DEFAULT: method="DEFAULT"
957           elif m[0]==self.DIRECT: method= "DIRECT"
958           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
959           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
960           elif m[0]==self.PCG: method= "PCG"
961           elif m[0]==self.CR: method= "CR"
962           elif m[0]==self.CGS: method= "CGS"
963           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
964           elif m[0]==self.SSOR: method= "SSOR"
965           elif m[0]==self.GMRES: method= "GMRES"
966           elif m[0]==self.PRES20: method= "PRES20"
967           elif m[0]==self.LUMPING: method= "LUMPING"
968           elif m[0]==self.AMG: method= "AMG"
969           if m[1]==self.DEFAULT: method+="+DEFAULT"
970           elif m[1]==self.JACOBI: method+= "+JACOBI"
971           elif m[1]==self.ILU0: method+= "+ILU0"
972           elif m[1]==self.ILUT: method+= "+ILUT"
973           elif m[1]==self.SSOR: method+= "+SSOR"
974           elif m[1]==self.AMG: method+= "+AMG"
975           elif m[1]==self.RILU: method+= "+RILU"
976           if p==self.DEFAULT: package="DEFAULT"
977           elif p==self.PASO: package= "PASO"
978           elif p==self.MKL: package= "MKL"
979           elif p==self.SCSL: package= "SCSL"
980           elif p==self.UMFPACK: package= "UMFPACK"
981           else : method="unknown"
982           return "%s solver of %s package"%(method,package)
983    
984    
985     def getSolverMethod(self):     def getSolverMethod(self):
986         """         """
987         @brief returns the solver method         returns the solver method
988    
989           @return: the solver method currently be used.
990           @rtype: C{int}
991           """
992           return self.__solver_method,self.__preconditioner
993    
994       def setSolverPackage(self,package=None):
995         """         """
996         return self.__solver_method         sets a new solver package
997    
998           @param package: sets a new solver method.
999           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1000           """
1001           if package==None: package=self.DEFAULT
1002           if not package==self.getSolverPackage():
1003               self.__solver_package=package
1004               self.__checkMatrixType()
1005               self.trace("New solver is %s"%self.getSolverMethodName())
1006    
1007       def getSolverPackage(self):
1008           """
1009           returns the package of the solver
1010    
1011           @return: the solver package currently being used.
1012           @rtype: C{int}
1013           """
1014           return self.__solver_package
1015    
1016       def isUsingLumping(self):
1017          """
1018          checks if matrix lumping is used a solver method
1019    
1020          @return: True is lumping is currently used a solver method.
1021          @rtype: C{bool}
1022          """
1023          return self.getSolverMethod()[0]==self.LUMPING
1024    
    #============ tolerance business =========================================================  
1025     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1026         """         """
1027         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1028    
1029           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1030    
1031           defines the stopping criterion.
1032    
1033           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1034                       the system will be resolved.
1035           @type tol: positive C{float}
1036           @raise ValueError: if tolerance is not positive.
1037         """         """
1038         if not tol>0:         if not tol>0:
1039             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1040         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1041         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1042         self.__tolerance=tol         self.__tolerance=tol
1043         return         return
1044    
1045     def getTolerance(self):     def getTolerance(self):
1046         """         """
1047         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1048    
1049           @return: tolerance currently used.
1050           @rtype: C{float}
1051         """         """
1052         return self.__tolerance         return self.__tolerance
1053    
1054     #===== symmetry  flag ==========================     # =============================================================================
1055       #    symmetry  flag:
1056       # =============================================================================
1057     def isSymmetric(self):     def isSymmetric(self):
1058        """        """
1059        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1060    
1061          @return: True is a symmetric PDE is indicated, otherwise False is returned
1062          @rtype: C{bool}
1063        """        """
1064        return self.__sym        return self.__sym
1065    
1066     def setSymmetryOn(self):     def setSymmetryOn(self):
1067        """        """
1068        @brief sets the symmetry flag to true        sets the symmetry flag.
1069        """        """
1070        if not self.isSymmetric():        if not self.isSymmetric():
1071           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1072           self.__sym=True           self.__sym=True
1073           self.__checkMatrixType()           self.__checkMatrixType()
1074    
1075     def setSymmetryOff(self):     def setSymmetryOff(self):
1076        """        """
1077        @brief sets the symmetry flag to false        removes the symmetry flag.
1078        """        """
1079        if self.isSymmetric():        if self.isSymmetric():
1080           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1081           self.__sym=False           self.__sym=False
1082           self.__checkMatrixType()           self.__checkMatrixType()
1083    
1084     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1085       """        """
1086       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1087    
1088       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1089       """        @type flag: C{bool}
1090       if flag:        """
1091          self.setSymmetryOn()        if flag:
1092       else:           self.setSymmetryOn()
1093          self.setSymmetryOff()        else:
1094             self.setSymmetryOff()
1095    
1096     #===== order reduction ==========================     # =============================================================================
1097       # function space handling for the equation as well as the solution
1098       # =============================================================================
1099     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1100       """       """
1101       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1102    
1103         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1104       """       """
1105       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1106       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1107    
1108     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1109       """       """
1110       @brief switches to full order       switches off reduced order for solution and equation representation
1111    
1112         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1113       """       """
1114       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1115       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1116    
1117     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1118       """       """
1119       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1120         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1121       @param flag                    if flag is not present order reduction is switched off
1122         @type flag: C{bool}
1123         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1124       """       """
1125       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1126       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1127    
1128     #===== order reduction solution ==========================  
1129     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1130       """       """
1131       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1132    
1133         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1134       """       """
1135       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1136       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1137           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1138           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1139           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1140             self.__resetSystem()
1141    
1142     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1143       """       """
1144       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1145    
1146         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1147       """       """
1148       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1149       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1150           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1151           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1152           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1153             self.__resetSystem()
1154    
1155     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1156       """       """
1157       @brief sets order for test functions according to flag       sets order for test functions according to flag
1158    
1159       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1160                      if flag is not present order reduction is switched off
1161         @type flag: C{bool}
1162         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1163       """       """
1164       if flag:       if flag:
1165          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1166       else:       else:
1167          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1168                                                                                                                                                              
    #===== order reduction equation ==========================  
1169     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1170       """       """
1171       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1172    
1173         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1174       """       """
1175       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1176       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1177           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1178           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1179           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1180             self.__resetSystem()
1181    
1182     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1183       """       """
1184       @brief switches to full order for test functions       switches off reduced order for equation representation
1185    
1186         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1187       """       """
1188       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1189       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1190           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1191           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1192           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1193             self.__resetSystem()
1194    
1195     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1196       """       """
1197       @brief sets order for test functions according to flag       sets order for test functions according to flag
1198    
1199       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1200                      if flag is not present order reduction is switched off
1201         @type flag: C{bool}
1202         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1203       """       """
1204       if flag:       if flag:
1205          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1206       else:       else:
1207          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1208    
1209     # ==== initialization =====================================================================     # =============================================================================
1210     def __makeNewOperator(self):     # private method:
1211       # =============================================================================
1212       def __checkMatrixType(self):
1213         """
1214         reassess the matrix type and, if a new matrix is needed, resets the system.
1215         """
1216         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1217         if not new_matrix_type==self.__matrix_type:
1218             self.trace("Matrix type is now %d."%new_matrix_type)
1219             self.__matrix_type=new_matrix_type
1220             self.__resetSystem()
1221       #
1222       #   rebuild switches :
1223       #
1224       def __invalidateSolution(self):
1225         """         """
1226         @brief         indicates the PDE has to be resolved if the solution is requested
1227         """         """
1228           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1229           self.__solution_isValid=False
1230    
1231       def __invalidateOperator(self):
1232           """
1233           indicates the operator has to be rebuilt next time it is used
1234           """
1235           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1236           self.__invalidateSolution()
1237           self.__operator_is_Valid=False
1238    
1239       def __invalidateRightHandSide(self):
1240           """
1241           indicates the right hand side has to be rebuild next time it is used
1242           """
1243           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1244           self.__invalidateSolution()
1245           self.__righthandside_isValid=False
1246    
1247       def __invalidateSystem(self):
1248           """
1249           annonced that everthing has to be rebuild:
1250           """
1251           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1252           self.__invalidateSolution()
1253           self.__invalidateOperator()
1254           self.__invalidateRightHandSide()
1255    
1256       def __resetSystem(self):
1257           """
1258           annonced that everthing has to be rebuild:
1259           """
1260           self.trace("New System is built from scratch.")
1261           self.__operator=escript.Operator()
1262           self.__operator_is_Valid=False
1263           self.__righthandside=escript.Data()
1264           self.__righthandside_isValid=False
1265           self.__solution=escript.Data()
1266           self.__solution_isValid=False
1267       #
1268       #    system initialization:
1269       #
1270       def __getNewOperator(self):
1271           """
1272           returns an instance of a new operator
1273           """
1274           self.trace("New operator is allocated.")
1275         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1276                             self.getNumEquations(), \                             self.getNumEquations(), \
1277                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1279  class LinearPDE:
1279                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1280                             self.__matrix_type)                             self.__matrix_type)
1281    
1282     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1283         """         """
1284         @brief         returns an instance of a new right hand side
1285         """         """
1286         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1287           if self.getNumEquations()>1:
1288               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1289           else:
1290               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1291    
1292     def __makeNewSolution(self):     def __getNewSolution(self):
1293         """         """
1294         @brief         returns an instance of a new solution
1295         """         """
1296         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1297           if self.getNumSolutions()>1:
1298               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1299           else:
1300               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1301    
1302     def __getFreshOperator(self):     def __makeFreshSolution(self):
1303         """         """
1304         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1305         """         """
1306         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1307             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1308         else:         else:
1309             self.__operator.setValue(0.)             self.__solution*=0
1310             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1311         return self.__operator         return self.__solution
1312    
1313     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1314         """         """
1315         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1316         """         """
1317         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1318             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1319         else:         else:
1320             print "fix self.__righthandside*=0"             self.__righthandside*=0
1321             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1322             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)  
   
1323    
1324     def __rebuildOperator(self,deep=False):     def __makeFreshOperator(self):
1325         """         """
1326         @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
1327         """         """
1328         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if self.__operator.isEmpty():
1329         self.__rebuildSolution(deep)             self.__operator=self.__getNewOperator()
1330         self.__operator_isValid=False         else:
1331         if deep: self.__operator=escript.Operator()             self.__operator.resetValues()
1332               self.trace("Operator reset to zero")
1333           return self.__operator
1334    
1335     def __rebuildRightHandSide(self,deep=False):     def __applyConstraint(self):
1336         """         """
1337         @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
1338         """         """
1339         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."         if not self.isUsingLumping():
1340         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1341         self.__righthandside_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1342         if not self.__homogeneous_constraint: self.__rebuildOperator()            if not q.isEmpty() and not self.__operator.isEmpty():
1343         if deep: self.__righthandside=escript.Data()               # q is the row and column mask to indicate where constraints are set:
1344                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1345                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1346                 u=self.__getNewSolution()
1347                 if r.isEmpty():
1348                    r_s=self.__getNewSolution()
1349                 else:
1350                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1351                 u.copyWithMask(r_s,col_q)
1352                 if not self.__righthandside.isEmpty():
1353                    self.__righthandside-=self.__operator*u
1354                    self.__righthandside=self.copyConstraint(self.__righthandside)
1355                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1356       # =============================================================================
1357       # function giving access to coefficients of the general PDE:
1358       # =============================================================================
1359       def getCoefficientOfGeneralPDE(self,name):
1360         """
1361         return the value of the coefficient name of the general PDE.
1362    
1363         @note: This method is called by the assembling routine it can be overwritten
1364               to map coefficients of a particular PDE to the general PDE.
1365         @param name: name of the coefficient requested.
1366         @type name: C{string}
1367         @return: the value of the coefficient  name
1368         @rtype: L{Data<escript.Data>}
1369         @raise IllegalCoefficient: if name is not one of coefficients
1370                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1371                      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}.
1372         """
1373         if self.hasCoefficientOfGeneralPDE(name):
1374            return self.getCoefficient(name)
1375         else:
1376            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1377    
1378     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):  
1379       """       """
1380       @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.
1381    
1382         @param name: name of the coefficient enquired.
1383         @type name: C{string}
1384         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1385         @rtype: C{bool}
1386    
1387       """       """
1388       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)  
1389    
1390     #============ assembling =======================================================     def createCoefficientOfGeneralPDE(self,name):
1391     def __copyConstraint(self,u):       """
1392        """       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()))  
1393    
1394     def __applyConstraint(self,rhs_update=True):       @param name: name of the coefficient requested.
1395         """       @type name: C{string}
1396         @brief applies the constraints  defined by q and r to the system       @return: a coefficient name initialized to 0.
1397         """       @rtype: L{Data<escript.Data>}
1398         q=self.getCoefficient("q")       @raise IllegalCoefficient: if name is not one of coefficients
1399         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},
1400         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}.
1401            # q is the row and column mask to indicate where constraints are set:       """
1402            row_q=escript.Data(q,self.getFunctionSpaceForEquation())       if self.hasCoefficientOfGeneralPDE(name):
1403            col_q=escript.Data(q,self.getFunctionSpaceForSolution())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1404            u=self.__makeNewSolution()       else:
1405            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.)  
1406    
1407     def getOperator(self):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1408         """       """
1409         @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  
1410    
1411     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1412         """       @type name: C{string}
1413         @brief returns the right hand side of the PDE       @return: the function space to be used for coefficient name
1414         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1415         @raise IllegalCoefficient: if name is not one of coefficients
1416                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1417                      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}.
1418         """
1419         if self.hasCoefficientOfGeneralPDE(name):
1420            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1421         else:
1422            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1423    
1424         @param ignoreConstraint     def getShapeOfCoefficientOfGeneralPDE(self,name):
1425         """       """
1426         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  
1427    
1428     def getSystem(self):       @param name: name of the coefficient enquired.
1429         """       @type name: C{string}
1430         @brief       @return: the shape of the coefficient name
1431         """       @rtype: C{tuple} of C{int}
1432         if not self.__operator_isValid and not self.__righthandside_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1433            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},
1434            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}.
1435                self.getRightHandSide(ignoreConstraint=True)       """
1436                self.getOperator()       if self.hasCoefficientOfGeneralPDE(name):
1437            else:          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1438                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \       else:
1439                              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)  
1440    
1441     def solve(self,**options):     # =============================================================================
1442        """     # functions giving access to coefficients of a particular PDE implementation:
1443        @brief solve the PDE     # =============================================================================
1444       def getCoefficient(self,name):
1445         """
1446         returns the value of the coefficient name
1447    
1448        @param options       @param name: name of the coefficient requested.
1449        """       @type name: C{string}
1450        mat,f=self.getSystem()       @return: the value of the coefficient name
1451        if self.isUsingLumping():       @rtype: L{Data<escript.Data>}
1452           out=f/mat       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1453           self.__copyConstraint(out)       """
1454        else:       if self.hasCoefficient(name):
1455           options[util.TOLERANCE_KEY]=self.getTolerance()           return self.COEFFICIENTS[name].getValue()
1456           options[util.METHOD_KEY]=self.getSolverMethod()       else:
1457           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  
1458    
1459     def getSolution(self,**options):     def hasCoefficient(self,name):
1460         """       """
1461         @brief returns the solution of the PDE       return True if name is the name of a coefficient
1462    
1463         @param options       @param name: name of the coefficient enquired.
1464         """       @type name: C{string}
1465         if not self.__solution_isValid:       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1466             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):  
1467       """       """
1468       @brief returns the domain of the PDE       return self.COEFFICIENTS.has_key(name)
1469    
1470       def createCoefficient(self, name):
1471       """       """
1472       return self.__domain       create a L{Data<escript.Data>} object corresponding to coefficient name
1473    
1474     def getDim(self):       @return: a coefficient name initialized to 0.
1475         @rtype: L{Data<escript.Data>}
1476         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1477       """       """
1478       @brief returns the spatial dimension of the PDE       if self.hasCoefficient(name):
1479            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1480         else:
1481            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1482    
1483       def getFunctionSpaceForCoefficient(self,name):
1484       """       """
1485       return self.getDomain().getDim()       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1486    
1487     def getNumEquations(self):       @param name: name of the coefficient enquired.
1488         @type name: C{string}
1489         @return: the function space to be used for coefficient name
1490         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1491         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1492       """       """
1493       @brief returns the number of equations       if self.hasCoefficient(name):
1494            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1495         else:
1496            raise ValueError,"unknown coefficient %s requested"%name
1497       def getShapeOfCoefficient(self,name):
1498       """       """
1499       if self.__numEquations>0:       return the shape of the coefficient name
1500           return self.__numEquations  
1501         @param name: name of the coefficient enquired.
1502         @type name: C{string}
1503         @return: the shape of the coefficient name
1504         @rtype: C{tuple} of C{int}
1505         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1506         """
1507         if self.hasCoefficient(name):
1508            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1509       else:       else:
1510           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1511    
1512     def getNumSolutions(self):     def resetCoefficients(self):
1513       """       """
1514       @brief returns the number of unknowns       resets all coefficients to there default values.
1515       """       """
1516       if self.__numSolutions>0:       for i in self.COEFFICIENTS.iterkeys():
1517          return self.__numSolutions           self.COEFFICIENTS[i].resetValue()
1518    
1519       def alteredCoefficient(self,name):
1520         """
1521         announce that coefficient name has been changed
1522    
1523         @param name: name of the coefficient enquired.
1524         @type name: C{string}
1525         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1526         @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.
1527         """
1528         if self.hasCoefficient(name):
1529            self.trace("Coefficient %s has been altered."%name)
1530            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1531               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1532               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1533       else:       else:
1534          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1535    
1536       def copyConstraint(self,u):
1537          """
1538          copies the constraint into u and returns u.
1539    
1540     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
1541          @type u: L{Data<escript.Data>}
1542          @return: the input u modified by the constraints.
1543          @rtype: L{Data<escript.Data>}
1544          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1545        """        """
1546        @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.        q=self.getCoefficientOfGeneralPDE("q")
1547          r=self.getCoefficientOfGeneralPDE("r")
1548          if not q.isEmpty():
1549             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1550             if r.isEmpty():
1551                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1552             else:
1553                 r=escript.Data(r,u.getFunctionSpace())
1554             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1555          return u
1556    
1557       def setValue(self,**coefficients):
1558        """        """
1559        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1560    
1561          @param coefficients: new values assigned to coefficients
1562          @keyword A: value for coefficient A.
1563          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1564          @keyword A_reduced: value for coefficient A_reduced.
1565          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1566          @keyword B: value for coefficient B
1567          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1568          @keyword B_reduced: value for coefficient B_reduced
1569          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1570          @keyword C: value for coefficient C
1571          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1572          @keyword C_reduced: value for coefficient C_reduced
1573          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1574          @keyword D: value for coefficient D
1575          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1576          @keyword D_reduced: value for coefficient D_reduced
1577          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1578          @keyword X: value for coefficient X
1579          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1580          @keyword X_reduced: value for coefficient X_reduced
1581          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1582          @keyword Y: value for coefficient Y
1583          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584          @keyword Y_reduced: value for coefficient Y_reduced
1585          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1586          @keyword d: value for coefficient d
1587          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1588          @keyword d_reduced: value for coefficient d_reduced
1589          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1590          @keyword y: value for coefficient y
1591          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1592          @keyword d_contact: value for coefficient d_contact
1593          @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>}.
1594          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1595          @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>}.
1596          @keyword y_contact: value for coefficient y_contact
1597          @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>}.
1598          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1599          @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>}.
1600          @keyword r: values prescribed to the solution at the locations of constraints
1601          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1602                   depending of reduced order is used for the solution.
1603          @keyword q: mask for location of constraints
1604          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1605                   depending of reduced order is used for the representation of the equation.
1606          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1607          """
1608          # check if the coefficients are  legal:
1609          for i in coefficients.iterkeys():
1610             if not self.hasCoefficient(i):
1611                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1612          # if the number of unknowns or equations is still unknown we try to estimate them:
1613          if self.__numEquations==None or self.__numSolutions==None:
1614             for i,d in coefficients.iteritems():
1615                if hasattr(d,"shape"):
1616                    s=d.shape
1617                elif hasattr(d,"getShape"):
1618                    s=d.getShape()
1619                else:
1620                    s=numarray.array(d).shape
1621                if s!=None:
1622                    # get number of equations and number of unknowns:
1623                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1624                    if res==None:
1625                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1626                    else:
1627                        if self.__numEquations==None: self.__numEquations=res[0]
1628                        if self.__numSolutions==None: self.__numSolutions=res[1]
1629          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1630          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1631          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1632          for i,d in coefficients.iteritems():
1633            try:
1634               self.COEFFICIENTS[i].setValue(self.getDomain(),
1635                                             self.getNumEquations(),self.getNumSolutions(),
1636                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1637               self.alteredCoefficient(i)
1638            except IllegalCoefficientFunctionSpace,m:
1639                # if the function space is wrong then we try the reduced version:
1640                i_red=i+"_reduced"
1641                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1642                    try:
1643                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1644                                                          self.getNumEquations(),self.getNumSolutions(),
1645                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1646                        self.alteredCoefficient(i_red)
1647                    except IllegalCoefficientValue,m:
1648                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1649                    except IllegalCoefficientFunctionSpace,m:
1650                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1651                else:
1652                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1653            except IllegalCoefficientValue,m:
1654               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1655          self.__altered_coefficients=True
1656          # check if the systrem is inhomogeneous:
1657          if len(coefficients)>0 and not self.isUsingLumping():
1658             q=self.getCoefficientOfGeneralPDE("q")
1659             r=self.getCoefficientOfGeneralPDE("r")
1660             homogeneous_constraint=True
1661             if not q.isEmpty() and not r.isEmpty():
1662                 if util.Lsup(q*r)>0.:
1663                   self.trace("Inhomogeneous constraint detected.")
1664                   self.__invalidateSystem()
1665    
1666        return None     def getSystem(self):
1667           """
1668           return the operator and right hand side of the PDE
1669    
1670     def getFlux(self,u):         @return: the discrete version of the PDE
1671           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1672         """         """
1673         @brief returns the flux J_ij for a given u         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1674              if self.isUsingLumping():
1675                  if not self.__operator_is_Valid:
1676                     if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1677                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1678                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1679                          raise ValueError,"coefficient A in lumped matrix may not be present."
1680                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1681                          raise ValueError,"coefficient B in lumped matrix may not be present."
1682                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1683                          raise ValueError,"coefficient C in lumped matrix may not be present."
1684                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1685                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1686                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1687                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1688                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1689                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1690                     D=self.getCoefficientOfGeneralPDE("D")
1691                     if not D.isEmpty():
1692                         if self.getNumSolutions()>1:
1693                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1694                         else:
1695                            D_times_e=D
1696                     else:
1697                        D_times_e=escript.Data()
1698                     d=self.getCoefficientOfGeneralPDE("d")
1699                     if not d.isEmpty():
1700                         if self.getNumSolutions()>1:
1701                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1702                         else:
1703                            d_times_e=d
1704                     else:
1705                        d_times_e=escript.Data()
1706                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1707                     if not d_contact.isEmpty():
1708                         if self.getNumSolutions()>1:
1709                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1710                         else:
1711                            d_contact_times_e=d_contact
1712                     else:
1713                        d_contact_times_e=escript.Data()
1714        
1715                     self.__operator=self.__getNewRightHandSide()
1716                     self.getDomain().addPDEToRHS(self.__operator, \
1717                                                  escript.Data(), \
1718                                                  D_times_e, \
1719                                                  d_times_e,\
1720                                                  d_contact_times_e)
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     if not D_reduced.isEmpty():
1723                         if self.getNumSolutions()>1:
1724                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1725                         else:
1726                            D_reduced_times_e=D_reduced
1727                     else:
1728                        D_reduced_times_e=escript.Data()
1729                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1730                     if not d_reduced.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_reduced_times_e=d_reduced
1735                     else:
1736                        d_reduced_times_e=escript.Data()
1737                     d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
1738                     if not d_contact_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            d_contact_reduced_times_e=util.matrixmult(d_contact_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            d_contact_reduced_times_e=d_contact_reduced
1743                     else:
1744                        d_contact_reduced_times_e=escript.Data()
1745        
1746                     self.__operator=self.__getNewRightHandSide()
1747                     self.getDomain().addPDEToRHS(self.__operator, \
1748                                                  escript.Data(), \
1749                                                  D_times_e, \
1750                                                  d_times_e,\
1751                                                  d_contact_times_e)
1752                     self.getDomain().addPDEToRHS(self.__operator, \
1753                                                  escript.Data(), \
1754                                                  D_reduced_times_e, \
1755                                                  d_reduced_times_e,\
1756                                                  d_contact_reduced_times_e)
1757                     self.__operator=1./self.__operator
1758                     self.trace("New lumped operator has been built.")
1759                     self.__operator_is_Valid=True
1760                  if not self.__righthandside_isValid:
1761                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1762                                   self.getCoefficientOfGeneralPDE("X"), \
1763                                   self.getCoefficientOfGeneralPDE("Y"),\
1764                                   self.getCoefficientOfGeneralPDE("y"),\
1765                                   self.getCoefficientOfGeneralPDE("y_contact"))
1766                     self.getDomain().addPDEToRHS(self.__righthandside, \
1767                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1768                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1769                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1770                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1771                     self.trace("New right hand side as been built.")
1772                     self.__righthandside_isValid=True
1773              else:
1774                 if not self.__operator_is_Valid and not self.__righthandside_isValid:
1775                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1776                                   self.getCoefficientOfGeneralPDE("A"), \
1777                                   self.getCoefficientOfGeneralPDE("B"), \
1778                                   self.getCoefficientOfGeneralPDE("C"), \
1779                                   self.getCoefficientOfGeneralPDE("D"), \
1780                                   self.getCoefficientOfGeneralPDE("X"), \
1781                                   self.getCoefficientOfGeneralPDE("Y"), \
1782                                   self.getCoefficientOfGeneralPDE("d"), \
1783                                   self.getCoefficientOfGeneralPDE("y"), \
1784                                   self.getCoefficientOfGeneralPDE("d_contact"), \
1785                                   self.getCoefficientOfGeneralPDE("y_contact"))
1786                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1787                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1788                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1789                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1790                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1791                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1792                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1793                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1797                     self.__applyConstraint()
1798                     self.__righthandside=self.copyConstraint(self.__righthandside)
1799                     self.trace("New system has been built.")
1800                     self.__operator_is_Valid=True
1801                     self.__righthandside_isValid=True
1802                 elif not self.__righthandside_isValid:
1803                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1804                                   self.getCoefficientOfGeneralPDE("X"), \
1805                                   self.getCoefficientOfGeneralPDE("Y"),\
1806                                   self.getCoefficientOfGeneralPDE("y"),\
1807                                   self.getCoefficientOfGeneralPDE("y_contact"))
1808                     self.getDomain().addPDEToRHS(self.__righthandside, \
1809                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1811                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1812                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1813                     self.__righthandside=self.copyConstraint(self.__righthandside)
1814                     self.trace("New right hand side has been built.")
1815                     self.__righthandside_isValid=True
1816                 elif not self.__operator_is_Valid:
1817                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1818                                self.getCoefficientOfGeneralPDE("A"), \
1819                                self.getCoefficientOfGeneralPDE("B"), \
1820                                self.getCoefficientOfGeneralPDE("C"), \
1821                                self.getCoefficientOfGeneralPDE("D"), \
1822                                escript.Data(), \
1823                                escript.Data(), \
1824                                self.getCoefficientOfGeneralPDE("d"), \
1825                                escript.Data(),\
1826                                self.getCoefficientOfGeneralPDE("d_contact"), \
1827                                escript.Data())
1828                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1829                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1830                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1831                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1832                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1833                                escript.Data(), \
1834                                escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1836                                escript.Data(),\
1837                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1838                                escript.Data())
1839                     self.__applyConstraint()
1840                     self.trace("New operator has been built.")
1841                     self.__operator_is_Valid=True
1842           return (self.__operator,self.__righthandside)
1843    
             J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}  
1844    
1845         @param u argument of the operator  class Poisson(LinearPDE):
1846       """
1847       Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1848    
1849         """     M{-grad(grad(u)[j])[j] = f}
        raise SystemError,"getFlux is not implemented yet"  
        return None  
1850    
1851     def applyOperator(self,u):     with natural boundary conditons
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
1852    
1853         @param u argument of the operator     M{n[j]*grad(u)[j] = 0 }
1854    
1855         """     and constraints:
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
1856    
1857         @param u     M{u=0} where M{q>0}
1858         """  
1859         return self.applyOperator(u)-self.getRightHandSide()     """
1860    
1861       def __init__(self,domain,debug=False):
1862         """
1863         initializes a new Poisson equation
1864    
1865         @param domain: domain of the PDE
1866         @type domain: L{Domain<escript.Domain>}
1867         @param debug: if True debug informations are printed.
1868    
1869         """
1870         super(Poisson, self).__init__(domain,1,1,debug)
1871         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1872                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1873                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1874         self.setSymmetryOn()
1875    
1876       def setValue(self,**coefficients):
1877         """
1878         sets new values to coefficients
1879    
1880         @param coefficients: new values assigned to coefficients
1881         @keyword f: value for right hand side M{f}
1882         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1883         @keyword q: mask for location of constraints
1884         @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>}
1885                   depending of reduced order is used for the representation of the equation.
1886         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1887         """
1888         super(Poisson, self).setValue(**coefficients)
1889    
1890       def getCoefficientOfGeneralPDE(self,name):
1891         """
1892         return the value of the coefficient name of the general PDE
1893         @param name: name of the coefficient requested.
1894         @type name: C{string}
1895         @return: the value of the coefficient  name
1896         @rtype: L{Data<escript.Data>}
1897         @raise IllegalCoefficient: if name is not one of coefficients
1898                      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}.
1899         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1900         """
1901         if name == "A" :
1902             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1903         elif name == "B" :
1904             return escript.Data()
1905         elif name == "C" :
1906             return escript.Data()
1907         elif name == "D" :
1908             return escript.Data()
1909         elif name == "X" :
1910             return escript.Data()
1911         elif name == "Y" :
1912             return self.getCoefficient("f")
1913         elif name == "d" :
1914             return escript.Data()
1915         elif name == "y" :
1916             return escript.Data()
1917         elif name == "d_contact" :
1918             return escript.Data()
1919         elif name == "y_contact" :
1920             return escript.Data()
1921         elif name == "A_reduced" :
1922             return escript.Data()
1923         elif name == "B_reduced" :
1924             return escript.Data()
1925         elif name == "C_reduced" :
1926             return escript.Data()
1927         elif name == "D_reduced" :
1928             return escript.Data()
1929         elif name == "X_reduced" :
1930             return escript.Data()
1931         elif name == "Y_reduced" :
1932             return self.getCoefficient("f_reduced")
1933         elif name == "d_reduced" :
1934             return escript.Data()
1935         elif name == "y_reduced" :
1936             return escript.Data()
1937         elif name == "d_contact_reduced" :
1938             return escript.Data()
1939         elif name == "y_contact_reduced" :
1940             return escript.Data()
1941         elif name == "r" :
1942             return escript.Data()
1943         elif name == "q" :
1944             return self.getCoefficient("q")
1945         else:
1946            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1947    
1948    class Helmholtz(LinearPDE):
1949       """
1950       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1951    
1952       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1953    
1954       with natural boundary conditons
1955    
1956       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1957    
1958       and constraints:
1959    
1960       M{u=r} where M{q>0}
1961    
 class Poisson(LinearPDE):  
1962     """     """
1963     @brief Class to define a Poisson equstion problem:  
1964                                                                                                                                                                   def __init__(self,domain,debug=False):
1965     class to define a linear PDE of the form       """
1966                                                                                                                                                                     initializes a new Poisson equation
1967          -u_{,jj} = f  
1968                                                                                                                                                                     @param domain: domain of the PDE
1969       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
1970                                                                                                                                                                     @param debug: if True debug informations are printed.
1971          n_j*u_{,j} = 0  
1972                                                                                                                                                                     """
1973      and constraints:       super(Helmholtz, self).__init__(domain,1,1,debug)
1974                                                                                                                                                                     self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1975           u=0 where q>0                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1976                                                                                                                                                                                        "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1977     """                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1978                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1979     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1980         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1981         self._setValue(A=numarray.identity(self.getDomain().getDim()))                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1982         self.setSymmetryOn()                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1983         self.setValue(f,q)       self.setSymmetryOn()
1984    
1985     def setValue(self,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
1986         self._setValue(Y=f,q=q)       """
1987         sets new values to coefficients
1988                                                                                                                                                              
1989  # $Log$       @param coefficients: new values assigned to coefficients
1990  # Revision 1.3  2004/12/17 07:43:10  jgs       @keyword omega: value for coefficient M{S{omega}}
1991  # *** empty log message ***       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1992  #       @keyword k: value for coefficeint M{k}
1993  # 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>}.
1994  # __init__ of LinearPDE does not accept any coefficients anymore       @keyword f: value for right hand side M{f}
1995  #       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1996  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs       @keyword alpha: value for right hand side M{S{alpha}}
1997  # *** empty log message ***       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1998  #       @keyword g: value for right hand side M{g}
1999  # 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>}.
2000  # linearPDE has been renamed LinearPDE       @keyword r: prescribed values M{r} for the solution in constraints.
2001  #       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2002  # 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.
2003  # GMRES added       @keyword q: mask for location of constraints
2004  #       @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2005  # 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.
2006  # options for GMRES and PRES20 added       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2007  #       """
2008  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross       super(Helmholtz, self).setValue(**coefficients)
2009  # some small changes  
2010  #     def getCoefficientOfGeneralPDE(self,name):
2011  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross       """
2012  # Finley solves 4M unknowns now       return the value of the coefficient name of the general PDE
2013  #  
2014  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross       @param name: name of the coefficient requested.
2015  # poisson solver added       @type name: C{string}
2016  #       @return: the value of the coefficient  name
2017  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross       @rtype: L{Data<escript.Data>}
2018  # 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
2019  #                    "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}.
2020  # 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.
2021  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed       """
2022  #       if name == "A" :
2023  # 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")
2024  # initial import of project esys2       elif name == "B" :
2025  #           return escript.Data()
2026  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs       elif name == "C" :
2027  # committing Lutz's and Paul's changes to brach jgs           return escript.Data()
2028  #       elif name == "D" :
2029  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane           return self.getCoefficient("omega")
2030  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       elif name == "X" :
2031  #           return escript.Data()
2032  # Revision 1.3  2004/09/23 00:53:23  jgs       elif name == "Y" :
2033  # minor fixes           return self.getCoefficient("f")
2034  #       elif name == "d" :
2035  # Revision 1.1  2004/08/28 12:58:06  gross           return self.getCoefficient("alpha")
2036  # SimpleSolve is not running yet: problem with == of functionsspace       elif name == "y" :
2037  #           return self.getCoefficient("g")
2038  #       elif name == "d_contact" :
2039             return escript.Data()
2040         elif name == "y_contact" :
2041             return escript.Data()
2042         elif name == "A_reduced" :
2043             return escript.Data()
2044         elif name == "B_reduced" :
2045             return escript.Data()
2046         elif name == "C_reduced" :
2047             return escript.Data()
2048         elif name == "D_reduced" :
2049             return escript.Data()
2050         elif name == "X_reduced" :
2051             return escript.Data()
2052         elif name == "Y_reduced" :
2053             return self.getCoefficient("f_reduced")
2054         elif name == "d_reduced" :
2055             return escript.Data()
2056         elif name == "y_reduced" :
2057            return self.getCoefficient("g_reduced")
2058         elif name == "d_contact_reduced" :
2059             return escript.Data()
2060         elif name == "y_contact_reduced" :
2061             return escript.Data()
2062         elif name == "r" :
2063             return self.getCoefficient("r")
2064         elif name == "q" :
2065             return self.getCoefficient("q")
2066         else:
2067            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2068    
2069    class LameEquation(LinearPDE):
2070       """
2071       Class to define a Lame equation problem:
2072    
2073       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] }
2074    
2075       with natural boundary conditons:
2076    
2077       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] }
2078    
2079       and constraints:
2080    
2081       M{u[i]=r[i]} where M{q[i]>0}
2082    
2083       """
2084    
2085       def __init__(self,domain,debug=False):
2086          super(LameEquation, self).__init__(domain,\
2087                                             domain.getDim(),domain.getDim(),debug)
2088          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2089                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2090                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2091                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2092                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2093                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2094                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2095          self.setSymmetryOn()
2096    
2097       def setValues(self,**coefficients):
2098         """
2099         sets new values to coefficients
2100    
2101         @param coefficients: new values assigned to coefficients
2102         @keyword lame_mu: value for coefficient M{S{mu}}
2103         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2104         @keyword lame_lambda: value for coefficient M{S{lambda}}
2105         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2106         @keyword F: value for internal force M{F}
2107         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2108         @keyword sigma: value for initial stress M{S{sigma}}
2109         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2110         @keyword f: value for extrenal force M{f}
2111         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2112         @keyword r: prescribed values M{r} for the solution in constraints.
2113         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2114                   depending of reduced order is used for the representation of the equation.
2115         @keyword q: mask for location of constraints
2116         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2117                   depending of reduced order is used for the representation of the equation.
2118         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2119         """
2120         super(LameEquation, self).setValues(**coefficients)
2121    
2122       def getCoefficientOfGeneralPDE(self,name):
2123         """
2124         return the value of the coefficient name of the general PDE
2125    
2126         @param name: name of the coefficient requested.
2127         @type name: C{string}
2128         @return: the value of the coefficient  name
2129         @rtype: L{Data<escript.Data>}
2130         @raise IllegalCoefficient: if name is not one of coefficients
2131                      "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}.
2132         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2133         """
2134         if name == "A" :
2135             out =self.createCoefficientOfGeneralPDE("A")
2136             for i in range(self.getDim()):
2137               for j in range(self.getDim()):
2138                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2139                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2140                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2141             return out
2142         elif name == "B" :
2143             return escript.Data()
2144         elif name == "C" :
2145             return escript.Data()
2146         elif name == "D" :
2147             return escript.Data()
2148         elif name == "X" :
2149             return self.getCoefficient("sigma")
2150         elif name == "Y" :
2151             return self.getCoefficient("F")
2152         elif name == "d" :
2153             return escript.Data()
2154         elif name == "y" :
2155             return self.getCoefficient("f")
2156         elif name == "d_contact" :
2157             return escript.Data()
2158         elif name == "y_contact" :
2159             return escript.Data()
2160         elif name == "A_reduced" :
2161             return escript.Data()
2162         elif name == "B_reduced" :
2163             return escript.Data()
2164         elif name == "C_reduced" :
2165             return escript.Data()
2166         elif name == "D_reduced" :
2167             return escript.Data()
2168         elif name == "X_reduced" :
2169             return escript.Data()
2170         elif name == "Y_reduced" :
2171             return escript.Data()
2172         elif name == "d_reduced" :
2173             return escript.Data()
2174         elif name == "y_reduced" :
2175             return escript.Data()
2176         elif name == "d_contact_reduced" :
2177             return escript.Data()
2178         elif name == "y_contact_reduced" :
2179             return escript.Data()
2180         elif name == "r" :
2181             return self.getCoefficient("r")
2182         elif name == "q" :
2183             return self.getCoefficient("q")
2184         else:
2185            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2186    

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