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trunk/esys2/escript/py_src/linearPDEs.py revision 148 by jgs, Tue Aug 23 01:24:31 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1661 by gross, Mon Jul 21 22:08:27 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4  ## @file linearPDEs.py  #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
19    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
20    solver capabilities in itself but hands the PDE over to
21    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
22    The general interface is provided through the L{LinearPDE} class. The
23    L{AdvectivePDE} which is derived from the L{LinearPDE} class
24    provides an interface to PDE dominated by its advective terms. The L{Poisson},
25    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26    classs which are also derived form the L{LinearPDE} class should be used
27    to define of solve these sepecial PDEs.
28    
29    @var __author__: name of author
30    @var __copyright__: copyrights
31    @var __license__: licence agreement
32    @var __url__: url entry point on documentation
33    @var __version__: version
34    @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
41    
42    __author__="Lutz Gross, l.gross@uq.edu.au"
43    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
44                        http://www.access.edu.au
45                    Primary Business: Queensland, Australia"""
46    __license__="""Licensed under the Open Software License version 3.0
47                 http://www.opensource.org/licenses/osl-3.0.php"""
48    __url__="http://www.iservo.edu.au/esys"
49    __version__="$Revision$"
50    __date__="$Date$"
51    
52    
53  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
54     """     """
55     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
56     """     """
57       pass
58    
59  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
60     """     """
61     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
62     """     """
63       pass
64    
65    class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68       """
69    
70  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
71     """     """
72     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
73     """     """
74       pass
75    
76  def _CompTuple2(t1,t2):  class PDECoefficient(object):
       """  
       Compare two tuples  
     
       @param t1 The first tuple  
       @param t2 The second tuple  
     
       """  
     
       dif=t1[0]+t1[1]-(t2[0]+t2[1])  
       if dif<0: return 1  
       elif dif>0: return -1  
       else: return 0  
     
 class PDECoefficient:  
77      """      """
78      A class for PDE coefficients      A class for describing a PDE coefficient
79    
80        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
89        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
90        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
91        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
92        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
93        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
94    
95      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
96      INTERIOR=0      INTERIOR=0
97      BOUNDARY=1      BOUNDARY=1
98      CONTACT=2      CONTACT=2
99      CONTINUOUS=3      SOLUTION=3
100      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
101      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
102      # number of unknowns.      BY_SOLUTION=6
103      EQUATION=3      BY_DIM=7
104      SOLUTION=4      OPERATOR=10
105      DIM=5      RIGHTHANDSIDE=11
106      # indicator for what is altered if the coefficient is altered:      BOTH=12
107      OPERATOR=5      INTERIOR_REDUCED=13
108      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
109      BOTH=7      CONTACT_REDUCED=15
110      def __init__(self,where,pattern,altering):  
111        def __init__(self, where, pattern, altering):
112         """         """
113         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
114    
115           @param where: describes where the coefficient lives
116           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118           @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                  spatial dimension and numbers of equation and solution in then PDE. For instance,
120                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
121                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
122                  on a 2-dimensional domain. In the case of single equation and a single solution component
123                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
124                  the example would be read as (2,).
125           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131           super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
133         self.pattern=pattern         self.pattern=pattern
134         self.altering=altering         self.altering=altering
# Line 74  class PDECoefficient: Line 140  class PDECoefficient:
140         """         """
141         self.value=escript.Data()         self.value=escript.Data()
142    
143      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
144         """         """
145         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
146    
147         @param domain:         @param domain: domain on which the PDE uses the coefficient
148         """         @type domain: L{Domain<escript.Domain>}
149         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
150         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
151         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
152         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
153           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
154           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
155           """
156           if self.what==self.INTERIOR:
157                return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160           elif self.what==self.BOUNDARY:
161                return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164           elif self.what==self.CONTACT:
165                return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168           elif self.what==self.SOLUTION:
169                if reducedEquationOrder and reducedSolutionOrder:
170                    return escript.ReducedSolution(domain)
171                else:
172                    return escript.Solution(domain)
173           elif self.what==self.REDUCED:
174                return escript.ReducedSolution(domain)
175    
176      def getValue(self):      def getValue(self):
177         """         """
178         returns the value of the coefficient:         returns the value of the coefficient
179    
180           @return:  value of the coefficient
181           @rtype:  L{Data<escript.Data>}
182         """         """
183         return self.value         return self.value
184    
185      def setValue(self,domain,numEquations=1,numSolutions=1,newValue=None):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
186         """         """
187         set the value of the coefficient to new value         set the value of the coefficient to a new value
188    
189           @param domain: domain on which the PDE uses the coefficient
190           @type domain: L{Domain<escript.Domain>}
191           @param numEquations: number of equations of the PDE
192           @type numEquations: C{int}
193           @param numSolutions: number of components of the PDE solution
194           @type numSolutions: C{int}
195           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
196           @type reducedEquationOrder: C{bool}
197           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
198           @type reducedSolutionOrder: C{bool}
199           @param newValue: number of components of the PDE solution
200           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203         """         """
204         if newValue==None:         if newValue==None:
205             newValue=escript.Data()             newValue=escript.Data()
206         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
207             if not newValue.isEmpty():             if not newValue.isEmpty():
208                newValue=escript.Data(newValue,self.getFunctionSpace(domain))                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                    try:
210                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                    except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213         else:         else:
214             newValue=escript.Data(newValue,self.getFunctionSpace(domain))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215         if not newValue.isEmpty():         if not newValue.isEmpty():
216             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
217                 raise IllegalCoefficientValue,"Expected shape for coefficient %s is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())                 raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
218         self.value=newValue         self.value=newValue
219    
220      def isAlteringOperator(self):      def isAlteringOperator(self):
221          """          """
222      return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
223    
224            @return:  True if the operator of the PDE is changed when the coefficient is changed
225            @rtype:  C{bool}
226      """      """
227          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
228              return not None              return not None
# Line 118  class PDECoefficient: Line 231  class PDECoefficient:
231    
232      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
233          """          """
234      return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
235    
236        @rtype:  C{bool}
237            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
238      """      """
239          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
240              return not None              return not None
# Line 127  class PDECoefficient: Line 243  class PDECoefficient:
243    
244      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
245         """         """
246         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
247    
248         @param shape:         @param domain: domain on which the PDE uses the coefficient
249         @param dim:         @type domain: L{Domain<escript.Domain>}
250           @param shape: suggested shape of the coefficient
251           @type shape: C{tuple} of C{int} values
252           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
253                     If no appropriate numbers could be identified, C{None} is returned
254           @rtype: C{tuple} of two C{int} values or C{None}
255         """         """
256         dim=domain.getDim()         dim=domain.getDim()
257         if len(shape)>0:         if len(shape)>0:
# Line 138  class PDECoefficient: Line 259  class PDECoefficient:
259         else:         else:
260             num=1             num=1
261         search=[]         search=[]
262         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
263            for e in range(num):            for u in range(num):
264               search.append((e,u))               for e in range(num):
265         search.sort(_CompTuple2)                  search.append((e,u))
266         for item in search:            search.sort(self.__CompTuple2)
267              for item in search:
268               s=self.getShape(domain,item[0],item[1])               s=self.getShape(domain,item[0],item[1])
269               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
270                   return (1,1)                   return (1,1)
271               else:               else:
272                   if s==shape: return item                   if s==shape: return item
273           elif self.definesNumEquation():
274              for e in range(num,0,-1):
275                 s=self.getShape(domain,e,0)
276                 if len(s)==0 and len(shape)==0:
277                     return (1,None)
278                 else:
279                     if s==shape: return (e,None)
280    
281           elif self.definesNumSolutions():
282              for u in range(num,0,-1):
283                 s=self.getShape(domain,0,u)
284                 if len(s)==0 and len(shape)==0:
285                     return (None,1)
286                 else:
287                     if s==shape: return (None,u)
288         return None         return None
289        def definesNumSolutions(self):
290           """
291           checks if the coefficient allows to estimate the number of solution components
292    
293           @return: True if the coefficient allows an estimate of the number of solution components
294           @rtype: C{bool}
295           """
296           for i in self.pattern:
297                 if i==self.BY_SOLUTION: return True
298           return False
299    
300        def definesNumEquation(self):
301           """
302           checks if the coefficient allows to estimate the number of equations
303    
304           @return: True if the coefficient allows an estimate of the number of equations
305           @rtype: C{bool}
306           """
307           for i in self.pattern:
308                 if i==self.BY_EQUATION: return True
309           return False
310    
311        def __CompTuple2(self,t1,t2):
312          """
313          Compare two tuples of possible number of equations and number of solutions
314    
315          @param t1: The first tuple
316          @param t2: The second tuple
317    
318          """
319    
320          dif=t1[0]+t1[1]-(t2[0]+t2[1])
321          if dif<0: return 1
322          elif dif>0: return -1
323          else: return 0
324    
325      def getShape(self,domain,numEquations=1,numSolutions=1):      def getShape(self,domain,numEquations=1,numSolutions=1):
326          """         """
327      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         builds the required shape of the coefficient
328    
329      @param e:         @param domain: domain on which the PDE uses the coefficient
330      @param u:         @type domain: L{Domain<escript.Domain>}
331      @param dim:         @param numEquations: number of equations of the PDE
332      """         @type numEquations: C{int}
333          dim=domain.getDim()         @param numSolutions: number of components of the PDE solution
334          s=()         @type numSolutions: C{int}
335          for i in self.pattern:         @return: shape of the coefficient
336               if i==self.EQUATION:         @rtype: C{tuple} of C{int} values
337           """
338           dim=domain.getDim()
339           s=()
340           for i in self.pattern:
341                 if i==self.BY_EQUATION:
342                  if numEquations>1: s=s+(numEquations,)                  if numEquations>1: s=s+(numEquations,)
343               elif i==self.SOLUTION:               elif i==self.BY_SOLUTION:
344                  if numSolutions>1: s=s+(numSolutions,)                  if numSolutions>1: s=s+(numSolutions,)
345               else:               else:
346                  s=s+(dim,)                  s=s+(dim,)
347          return s         return s
348    
349  class LinearPDE:  class LinearPDE(object):
350     """     """
351     Class to define a linear PDE of the form     This class is used to define a general linear, steady, second order PDE
352       for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
353    
354     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(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  
    \f]  
355    
356     with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
357    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
358    
359     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
362       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
363       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
366    
367     \f[     The following natural boundary conditions are considered:
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
368    
369     and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
370    
371       where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
372    
373    
374       Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
375    
376       M{u=r}  where M{q>0}
377    
378       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
379       The constraints override any other condition set by the PDE or the boundary condition.
380    
381       The PDE is symmetrical if
382    
383       M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
384    
385       For a system of PDEs and a solution with several components the PDE has the form
386    
387       M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
388    
389       M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
390       The natural boundary conditions take the form:
391    
392       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399       M{u[i]=r[i]}  where  M{q[i]>0}
400    
401       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
402    
403       The system of PDEs is symmetrical if
404    
405     \f[          - M{A[i,j,k,l]=A[k,l,i,j]}
406     u_i=r_i \quad \mathrm{where} \quad q_i>0          - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407     \f]          - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409            - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411            - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416       defined as
417    
418       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420       For the case of single solution component and single PDE M{J} is defined
421    
422       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426       the contact condition takes the form
427    
428       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432       L{jump<util.jump>}.
433       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435       In case of a single PDE and a single component solution the contact condition takes the form
436    
437       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
440    
441       @cvar DEFAULT: The default method used to solve the system of linear equations
442       @cvar DIRECT: The direct solver based on LDU factorization
443       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
444       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
445       @cvar CR: The conjugate residual method
446       @cvar CGS: The conjugate gardient square method
447       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
448       @cvar SSOR: The symmetric overrealaxtion method
449       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
450       @cvar ILUT: The incomplete LU factorization preconditioner with will in
451       @cvar JACOBI: The Jacobi preconditioner
452       @cvar GMRES: The Gram-Schmidt minimum residual method
453       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
454       @cvar LUMPING: Matrix lumping.
455       @cvar NO_REORDERING: No matrix reordering allowed
456       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
457       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
458       @cvar PASO: PASO solver package
459       @cvar SCSL: SGI SCSL solver library
460       @cvar MKL: Intel's MKL solver library
461       @cvar UMFPACK: the UMFPACK library
462       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
463       @cvar ITERATIVE: The default iterative solver
464       @cvar AMG: algebraic multi grid
465       @cvar RILU: recursive ILU
466    
467     """     """
468     TOL=1.e-13     DEFAULT= 0
469     # solver methods     DIRECT= 1
470     UNKNOWN=-1     CHOLEVSKY= 2
471     DEFAULT_METHOD=0     PCG= 3
472     DIRECT=1     CR= 4
473     CHOLEVSKY=2     CGS= 5
474     PCG=3     BICGSTAB= 6
475     CR=4     SSOR= 7
476     CGS=5     ILU0= 8
477     BICGSTAB=6     ILUT= 9
478     SSOR=7     JACOBI= 10
479     ILU0=8     GMRES= 11
480     ILUT=9     PRES20= 12
481     JACOBI=10     LUMPING= 13
482     GMRES=11     NO_REORDERING= 17
483     PRES20=12     MINIMUM_FILL_IN= 18
484     LUMPING=13     NESTED_DISSECTION= 19
485     # matrix reordering:     SCSL= 14
486     NO_REORDERING=0     MKL= 15
487     MINIMUM_FILL_IN=1     UMFPACK= 16
488     NESTED_DISSECTION=2     ITERATIVE= 20
489     # important keys in the dictonary used to hand over options to the solver library:     PASO= 21
490     METHOD_KEY="method"     AMG= 22
491     SYMMETRY_KEY="symmetric"     RILU = 23
492     TOLERANCE_KEY="tolerance"     TRILINOS = 24
493       NONLINEAR_GMRES = 25
494    
495       SMALL_TOLERANCE=1.e-13
496       __PACKAGE_KEY="package"
497       __METHOD_KEY="method"
498       __SYMMETRY_KEY="symmetric"
499       __TOLERANCE_KEY="tolerance"
500       __PRECONDITIONER_KEY="preconditioner"
501    
502    
503     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
# Line 228  class LinearPDE: Line 505  class LinearPDE:
505       initializes a new linear PDE       initializes a new linear PDE
506    
507       @param domain: domain of the PDE       @param domain: domain of the PDE
508       @type domain: L{Domain}       @type domain: L{Domain<escript.Domain>}
509       @param numEquations: number of equations. If numEquations==None the number of equations       @param numEquations: number of equations. If numEquations==None the number of equations
510                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
511       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
512                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
513       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
514    
   
515       """       """
516         super(LinearPDE, self).__init__()
517       #       #
518       #   the coefficients of the general PDE:       #   the coefficients of the general PDE:
519       #       #
520       self.__COEFFICIENTS_OF_GENEARL_PDE={       self.__COEFFICIENTS_OF_GENEARL_PDE={
521         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
522         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
524         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
525         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
526         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
530         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}         "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
534           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
535           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
536           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
540           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
542           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
543    
544       # COEFFICIENTS can be overwritten by subclasses:       # COEFFICIENTS can be overwritten by subclasses:
545       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
546         self.__altered_coefficients=False
547       # initialize attributes       # initialize attributes
548       self.__debug=debug       self.__debug=debug
549       self.__domain=domain       self.__domain=domain
# Line 264  class LinearPDE: Line 552  class LinearPDE:
552       self.__resetSystem()       self.__resetSystem()
553    
554       # set some default values:       # set some default values:
555       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
556       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
557       self.__tolerance=1.e-8       self.__tolerance=1.e-8
558       self.__solver_method=self.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
559       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
560         self.__preconditioner=self.DEFAULT
561         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
562       self.__sym=False       self.__sym=False
563    
564       self.resetCoefficients()       self.resetCoefficients()
# Line 278  class LinearPDE: Line 567  class LinearPDE:
567     #    general stuff:     #    general stuff:
568     # =============================================================================     # =============================================================================
569     def __str__(self):     def __str__(self):
570         return "<LinearPDE %d>"%id(self)       """
571         returns string representation of the PDE
572    
573         @return: a simple representation of the PDE
574         @rtype: C{str}
575         """
576         return "<LinearPDE %d>"%id(self)
577     # =============================================================================     # =============================================================================
578     #    debug :     #    debug :
579     # =============================================================================     # =============================================================================
580     def setDebugOn(self):     def setDebugOn(self):
581       """       """
582       switches on debugging       switches on debugging
583       """       """
584       self.__debug=not None       self.__debug=not None
# Line 296  class LinearPDE: Line 591  class LinearPDE:
591    
592     def trace(self,text):     def trace(self,text):
593       """       """
594       print the text message if debugging is swiched on.       print the text message if debugging is swiched on.
595         @param text: message
596       @param name: name of the coefficient enquired.       @type text: C{string}
      @type name: C{string}  
597       """       """
598       if self.__debug: print "%s: %s"%(str(self),text)       if self.__debug: print "%s: %s"%(str(self),text)
599    
# Line 309  class LinearPDE: Line 603  class LinearPDE:
603     def getDomain(self):     def getDomain(self):
604       """       """
605       returns the domain of the PDE       returns the domain of the PDE
       
      @return : the domain of the PDE  
      @rtype : C{Domain}  
606    
607         @return: the domain of the PDE
608         @rtype: L{Domain<escript.Domain>}
609       """       """
610       return self.__domain       return self.__domain
611    
# Line 320  class LinearPDE: Line 613  class LinearPDE:
613       """       """
614       returns the spatial dimension of the PDE       returns the spatial dimension of the PDE
615    
616       @return : the spatial dimension of the PDE domain       @return: the spatial dimension of the PDE domain
617       @rtype : C{int}       @rtype: C{int}
618       """       """
619       return self.getDomain().getDim()       return self.getDomain().getDim()
620    
# Line 329  class LinearPDE: Line 622  class LinearPDE:
622       """       """
623       returns the number of equations       returns the number of equations
624    
625       @return : the number of equations       @return: the number of equations
626       @rtype : C{int}       @rtype: C{int}
627       @raise UndefinedPDEError: if the number of equations is not be specified yet.       @raise UndefinedPDEError: if the number of equations is not be specified yet.
628       """       """
629       if self.__numEquations==None:       if self.__numEquations==None:
# Line 342  class LinearPDE: Line 635  class LinearPDE:
635       """       """
636       returns the number of unknowns       returns the number of unknowns
637    
638       @return : the number of unknowns       @return: the number of unknowns
639       @rtype : C{int}       @rtype: C{int}
640       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
641       """       """
642       if self.__numSolutions==None:       if self.__numSolutions==None:
# Line 351  class LinearPDE: Line 644  class LinearPDE:
644       else:       else:
645          return self.__numSolutions          return self.__numSolutions
646    
647       def reduceEquationOrder(self):
648         """
649         return status for order reduction for equation
650    
651         @return: return True is reduced interpolation order is used for the represenation of the equation
652         @rtype: L{bool}
653         """
654         return self.__reduce_equation_order
655    
656       def reduceSolutionOrder(self):
657         """
658         return status for order reduction for the solution
659    
660         @return: return True is reduced interpolation order is used for the represenation of the solution
661         @rtype: L{bool}
662         """
663         return self.__reduce_solution_order
664    
665     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
666       """       """
667       returns the L{escript.FunctionSpace} used to discretize the equation       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
       
      @return : representation space of equation  
      @rtype : L{escript.FunctionSpace}  
668    
669         @return: representation space of equation
670         @rtype: L{FunctionSpace<escript.FunctionSpace>}
671       """       """
672       return self.__row_function_space       if self.reduceEquationOrder():
673             return escript.ReducedSolution(self.getDomain())
674         else:
675             return escript.Solution(self.getDomain())
676    
677     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
678       """       """
679       returns the L{escript.FunctionSpace} used to represent the solution       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
       
      @return : representation space of solution  
      @rtype : L{escript.FunctionSpace}  
680    
681         @return: representation space of solution
682         @rtype: L{FunctionSpace<escript.FunctionSpace>}
683       """       """
684       return self.__column_function_space       if self.reduceSolutionOrder():
685             return escript.ReducedSolution(self.getDomain())
686         else:
687             return escript.Solution(self.getDomain())
688    
689    
690     def getOperator(self):     def getOperator(self):
691       """       """
692       provides access to the operator of the PDE       provides access to the operator of the PDE
693    
694       @return : the operator of the PDE       @return: the operator of the PDE
695       @rtype : L{Operator}       @rtype: L{Operator<escript.Operator>}
696       """       """
697       m=self.getSystem()[0]       m=self.getSystem()[0]
698       if self.isUsingLumping():       if self.isUsingLumping():
# Line 388  class LinearPDE: Line 703  class LinearPDE:
703     def getRightHandSide(self):     def getRightHandSide(self):
704       """       """
705       provides access to the right hand side of the PDE       provides access to the right hand side of the PDE
706         @return: the right hand side of the PDE
707       @return : the right hand side of the PDE       @rtype: L{Data<escript.Data>}
      @rtype : L{escript.Data}  
708       """       """
709       r=self.getSystem()[1]       r=self.getSystem()[1]
710       if self.isUsingLumping():       if self.isUsingLumping():
# Line 404  class LinearPDE: Line 718  class LinearPDE:
718    
719       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
720                 the current solution is used.                 the current solution is used.
721       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
722       @return : image of u       @return: image of u
723       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
724       """       """
725       if u==None:       if u==None:
726            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
727       else:       else:
728          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
729    
730     def getResidual(self,u=None):     def getResidual(self,u=None):
731       """       """
# Line 419  class LinearPDE: Line 733  class LinearPDE:
733    
734       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
735                 the current solution is used.                 the current solution is used.
736       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
737       @return : residual of u       @return: residual of u
738       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
739       """       """
740       return self.applyOperator(u)-self.getRightHandSide()       return self.applyOperator(u)-self.getRightHandSide()
741    
# Line 429  class LinearPDE: Line 743  class LinearPDE:
743        """        """
744        test the PDE for symmetry.        test the PDE for symmetry.
745    
746          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
747       @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.        @type verbose: C{bool}
748       @type verbose: C{bool}        @return:  True if the PDE is symmetric.
749       @return:  True if the PDE is symmetric.        @rtype: L{Data<escript.Data>}
      @rtype : C{escript.Data}  
   
750        @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.        @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
751        """        """
752        verbose=verbose or self.debug()        verbose=verbose or self.__debug
753        out=True        out=True
754        if self.getNumSolutions()!=self.getNumEquations():        if self.getNumSolutions()!=self.getNumEquations():
755           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           if verbose: print "non-symmetric PDE because of different number of equations and solutions"
# Line 445  class LinearPDE: Line 757  class LinearPDE:
757        else:        else:
758           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
759           if not A.isEmpty():           if not A.isEmpty():
760              tol=util.Lsup(A)*self.TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
761              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
762                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
763                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 469  class LinearPDE: Line 781  class LinearPDE:
781              if verbose: print "non-symmetric PDE because C is not present but B is"              if verbose: print "non-symmetric PDE because C is not present but B is"
782              out=False              out=False
783           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
784              tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
785              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
786                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
787                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 485  class LinearPDE: Line 797  class LinearPDE:
797           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
798             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
799             if not D.isEmpty():             if not D.isEmpty():
800               tol=util.Lsup(D)*self.TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
801               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
802                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
803                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
804                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
805                        out=False                        out=False
806               d=self.getCoefficientOfGeneralPDE("d")
807               if not d.isEmpty():
808                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
809                 for i in range(self.getNumEquations()):
810                    for k in range(self.getNumSolutions()):
811                      if util.Lsup(d[i,k]-d[k,i])>tol:
812                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
813                          out=False
814               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
815               if not d_contact.isEmpty():
816                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
817                 for i in range(self.getNumEquations()):
818                    for k in range(self.getNumSolutions()):
819                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
820                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
821                          out=False
822             # and now the reduced coefficients
823             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
824             if not A_reduced.isEmpty():
825                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
826                if self.getNumSolutions()>1:
827                   for i in range(self.getNumEquations()):
828                      for j in range(self.getDim()):
829                         for k in range(self.getNumSolutions()):
830                            for l in range(self.getDim()):
831                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
832                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
833                                   out=False
834                else:
835                   for j in range(self.getDim()):
836                      for l in range(self.getDim()):
837                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
838                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
839                            out=False
840             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
841             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
842             if B_reduced.isEmpty() and not C_reduced.isEmpty():
843                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
844                out=False
845             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
849                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
850                if self.getNumSolutions()>1:
851                   for i in range(self.getNumEquations()):
852                       for j in range(self.getDim()):
853                          for k in range(self.getNumSolutions()):
854                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
855                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
856                                  out=False
857                else:
858                   for j in range(self.getDim()):
859                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
860                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
861                         out=False
862             if self.getNumSolutions()>1:
863               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
864               if not D_reduced.isEmpty():
865                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
866                 for i in range(self.getNumEquations()):
867                    for k in range(self.getNumSolutions()):
868                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
869                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
870                          out=False
871               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
872               if not d_reduced.isEmpty():
873                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
874                 for i in range(self.getNumEquations()):
875                    for k in range(self.getNumSolutions()):
876                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
877                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
878                          out=False
879               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
880               if not d_contact_reduced.isEmpty():
881                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
882                 for i in range(self.getNumEquations()):
883                    for k in range(self.getNumSolutions()):
884                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
885                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
886                          out=False
887        return out        return out
888    
889     def getSolution(self,**options):     def getSolution(self,**options):
890         """         """
891         returns the solution of the PDE. If the solution is not valid the PDE is solved.         returns the solution of the PDE. If the solution is not valid the PDE is solved.
892    
893         @return: the solution         @return: the solution
894         @rtype: L{escript.Data}         @rtype: L{Data<escript.Data>}
895         @param options: solver options         @param options: solver options
896         @keyword verbose:         @keyword verbose: True to get some information during PDE solution
897         @keyword reordering: reordering scheme to be used during elimination         @type verbose: C{bool}
898         @keyword preconditioner: preconditioner method to be used         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
899                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
900         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
901         @keyword drop_tolerance:         @keyword drop_tolerance: threshold for drupping in L{ILUT}
902         @keyword drop_storage:         @keyword drop_storage: maximum of allowed memory in L{ILUT}
903         @keyword truncation:         @keyword truncation: maximum number of residuals in L{GMRES}
904         @keyword restart:         @keyword restart: restart cycle length in L{GMRES}
905         """         """
906         if not self.__solution_isValid:         if not self.__solution_isValid:
907            mat,f=self.getSystem()            mat,f=self.getSystem()
908            if self.isUsingLumping():            if self.isUsingLumping():
909               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
910            else:            else:
911               options[self.TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
912               options[self.METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
913               options[self.SYMMETRY_KEY]=self.isSymmetric()               options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
914                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
915                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
916               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
917               self.trace("solver options: %s"%str(options))               self.trace("solver options: %s"%str(options))
918               self.__solution=mat.solve(f,options)               self.__solution=mat.solve(f,options)
# Line 526  class LinearPDE: Line 921  class LinearPDE:
921    
922     def getFlux(self,u=None):     def getFlux(self,u=None):
923       """       """
924       returns the flux J_ij for a given u       returns the flux M{J} for a given M{u}
925    
926         \f[       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]}
        J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}  
        \f]  
927    
928       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.       or
      @type u: L{escript.Data} or None  
      @return : flux  
      @rtype : L{escript.Data}  
929    
930         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
931    
932         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
933         @type u: L{Data<escript.Data>} or None
934         @return: flux
935         @rtype: L{Data<escript.Data>}
936       """       """
937       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
938       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
939               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
940               -util.self.getCoefficientOfGeneralPDE("X") \
941               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X_reduced")
944     # =============================================================================     # =============================================================================
945     #   solver settings:     #   solver settings:
946     # =============================================================================     # =============================================================================
947     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
948         """         """
949         sets a new solver         sets a new solver
950    
951         @param solver: sets a new solver method.         @param solver: sets a new solver method.
952         @type solver: C{int}         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
953           @param preconditioner: sets a new solver method.
954         """         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
955         if solver==None: solve=self.DEFAULT_METHOD         """
956         if not solver==self.getSolverMethod():         if solver==None: solver=self.__solver_method
957           if preconditioner==None: preconditioner=self.__preconditioner
958           if solver==None: solver=self.DEFAULT
959           if preconditioner==None: preconditioner=self.DEFAULT
960           if not (solver,preconditioner)==self.getSolverMethod():
961             self.__solver_method=solver             self.__solver_method=solver
962               self.__preconditioner=preconditioner
963             self.__checkMatrixType()             self.__checkMatrixType()
964             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
965    
# Line 562  class LinearPDE: Line 967  class LinearPDE:
967         """         """
968         returns the name of the solver currently used         returns the name of the solver currently used
969    
970         @return : the name of the solver currently used.         @return: the name of the solver currently used.
971         @rtype: C{string}         @rtype: C{string}
972         """         """
973    
974         m=self.getSolverMethod()         m=self.getSolverMethod()
975         if m==self.DEFAULT_METHOD: return "DEFAULT_METHOD"         p=self.getSolverPackage()
976         elif m==self.DIRECT: return "DIRECT"         method=""
977         elif m==self.CHOLEVSKY: return "CHOLEVSKY"         if m[0]==self.DEFAULT: method="DEFAULT"
978         elif m==self.PCG: return "PCG"         elif m[0]==self.DIRECT: method= "DIRECT"
979         elif m==self.CR: return "CR"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
980         elif m==self.CGS: return "CGS"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
981         elif m==self.BICGSTAB: return "BICGSTAB"         elif m[0]==self.PCG: method= "PCG"
982         elif m==self.SSOR: return "SSOR"         elif m[0]==self.CR: method= "CR"
983         elif m==self.GMRES: return "GMRES"         elif m[0]==self.CGS: method= "CGS"
984         elif m==self.PRES20: return "PRES20"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
985         elif m==self.LUMPING: return "LUMPING"         elif m[0]==self.SSOR: method= "SSOR"
986         return None         elif m[0]==self.GMRES: method= "GMRES"
987                 elif m[0]==self.PRES20: method= "PRES20"
988           elif m[0]==self.LUMPING: method= "LUMPING"
989           elif m[0]==self.AMG: method= "AMG"
990           if m[1]==self.DEFAULT: method+="+DEFAULT"
991           elif m[1]==self.JACOBI: method+= "+JACOBI"
992           elif m[1]==self.ILU0: method+= "+ILU0"
993           elif m[1]==self.ILUT: method+= "+ILUT"
994           elif m[1]==self.SSOR: method+= "+SSOR"
995           elif m[1]==self.AMG: method+= "+AMG"
996           elif m[1]==self.RILU: method+= "+RILU"
997           if p==self.DEFAULT: package="DEFAULT"
998           elif p==self.PASO: package= "PASO"
999           elif p==self.MKL: package= "MKL"
1000           elif p==self.SCSL: package= "SCSL"
1001           elif p==self.UMFPACK: package= "UMFPACK"
1002           elif p==self.TRILINOS: package= "TRILINOS"
1003           else : method="unknown"
1004           return "%s solver of %s package"%(method,package)
1005    
1006    
1007     def getSolverMethod(self):     def getSolverMethod(self):
1008         """         """
1009         returns the solver method         returns the solver method
1010      
1011         @return : the solver method currently be used.         @return: the solver method currently be used.
1012         @rtype : C{int}         @rtype: C{int}
1013           """
1014           return self.__solver_method,self.__preconditioner
1015    
1016       def setSolverPackage(self,package=None):
1017           """
1018           sets a new solver package
1019    
1020           @param package: sets a new solver method.
1021           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1022         """         """
1023         return self.__solver_method         if package==None: package=self.DEFAULT
1024           if not package==self.getSolverPackage():
1025               self.__solver_package=package
1026               self.__checkMatrixType()
1027               self.trace("New solver is %s"%self.getSolverMethodName())
1028    
1029       def getSolverPackage(self):
1030           """
1031           returns the package of the solver
1032    
1033           @return: the solver package currently being used.
1034           @rtype: C{int}
1035           """
1036           return self.__solver_package
1037    
1038     def isUsingLumping(self):     def isUsingLumping(self):
1039        """        """
1040        checks if matrix lumping is used a solver method        checks if matrix lumping is used a solver method
1041    
1042        @return : True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
1043        @rtype: C{bool}        @rtype: C{bool}
1044        """        """
1045        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
1046    
1047     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1048         """         """
1049         resets the tolerance for the solver method to tol where for an appropriate norm |.|         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1050    
1051                 |self.getResidual()|<tol*|self.getRightHandSide()|         M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1052    
1053         defines the stopping criterion.         defines the stopping criterion.
1054    
1055         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1056                     the system will be resolved.                     the system will be resolved.
1057         @type solver: C{float}         @type tol: positive C{float}
1058         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1059         """         """
1060         if not tol>0:         if not tol>0:
1061             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1062         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1063         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1064         self.__tolerance=tol         self.__tolerance=tol
# Line 634  class LinearPDE: Line 1079  class LinearPDE:
1079     def isSymmetric(self):     def isSymmetric(self):
1080        """        """
1081        checks if symmetry is indicated.        checks if symmetry is indicated.
1082        
1083        @return : True is a symmetric PDE is indicated, otherwise False is returned        @return: True is a symmetric PDE is indicated, otherwise False is returned
1084        @rtype : C{bool}        @rtype: C{bool}
1085        """        """
1086        return self.__sym        return self.__sym
1087    
# Line 661  class LinearPDE: Line 1106  class LinearPDE:
1106     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1107        """        """
1108        sets the symmetry flag to flag        sets the symmetry flag to flag
1109    
1110        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1111        @type flag: C{bool}        @type flag: C{bool}
1112        """        """
# Line 670  class LinearPDE: Line 1115  class LinearPDE:
1115        else:        else:
1116           self.setSymmetryOff()           self.setSymmetryOff()
1117    
     
1118     # =============================================================================     # =============================================================================
1119     # function space handling for the equation as well as the solution     # function space handling for the equation as well as the solution
1120     # =============================================================================     # =============================================================================
1121     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1122       """       """
1123       switches on reduced order for solution and equation representation       switches on reduced order for solution and equation representation
1124    
1125         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1126       """       """
1127       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1128       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
# Line 684  class LinearPDE: Line 1130  class LinearPDE:
1130     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1131       """       """
1132       switches off reduced order for solution and equation representation       switches off reduced order for solution and equation representation
1133    
1134         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1135       """       """
1136       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1137       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1138    
1139     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1140       """       """
1141       sets order reduction for both solution and equation representation according to flag.       sets order reduction for both solution and equation representation according to flag.
1142         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
      @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or  
1143                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1144       @type flag: C{bool}       @type flag: C{bool}
1145         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1146       """       """
1147       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1148       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
# Line 703  class LinearPDE: Line 1151  class LinearPDE:
1151     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1152       """       """
1153       switches on reduced order for solution representation       switches on reduced order for solution representation
1154    
1155         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1156       """       """
1157       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1158       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1159                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1160           self.trace("Reduced order is used to solution representation.")           self.trace("Reduced order is used to solution representation.")
1161           self.__column_function_space=new_fs           self.__reduce_solution_order=True
1162           self.__resetSystem()           self.__resetSystem()
1163    
1164     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1165       """       """
1166       switches off reduced order for solution representation       switches off reduced order for solution representation
1167    
1168         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1169       """       """
1170       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1171       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1172                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1173           self.trace("Full order is used to interpolate solution.")           self.trace("Full order is used to interpolate solution.")
1174           self.__column_function_space=new_fs           self.__reduce_solution_order=False
1175           self.__resetSystem()           self.__resetSystem()
1176    
1177     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1178       """       """
1179       sets order for test functions according to flag       sets order for test functions according to flag
1180    
1181       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1182                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1183       @type flag: C{bool}       @type flag: C{bool}
1184         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1185       """       """
1186       if flag:       if flag:
1187          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
# Line 736  class LinearPDE: Line 1191  class LinearPDE:
1191     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1192       """       """
1193       switches on reduced order for equation representation       switches on reduced order for equation representation
1194    
1195         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1196       """       """
1197       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1198       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1199                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1200           self.trace("Reduced order is used for test functions.")           self.trace("Reduced order is used for test functions.")
1201           self.__row_function_space=new_fs           self.__reduce_equation_order=True
1202           self.__resetSystem()           self.__resetSystem()
1203    
1204     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1205       """       """
1206       switches off reduced order for equation representation       switches off reduced order for equation representation
1207    
1208         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1209       """       """
1210       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1211       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1212                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1213           self.trace("Full order is used for test functions.")           self.trace("Full order is used for test functions.")
1214           self.__row_function_space=new_fs           self.__reduce_equation_order=False
1215           self.__resetSystem()           self.__resetSystem()
1216    
1217     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1218       """       """
1219       sets order for test functions according to flag       sets order for test functions according to flag
1220    
1221       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1222                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1223       @type flag: C{bool}       @type flag: C{bool}
1224         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1225       """       """
1226       if flag:       if flag:
1227          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
# Line 773  class LinearPDE: Line 1235  class LinearPDE:
1235       """       """
1236       reassess the matrix type and, if a new matrix is needed, resets the system.       reassess the matrix type and, if a new matrix is needed, resets the system.
1237       """       """
1238       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1239       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1240           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1241           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
1242           self.__resetSystem()           self.__resetSystem()
1243     #     #
1244     #   rebuild switches :     #   rebuild switches :
1245     #     #
1246     def __invalidateSolution(self):     def __invalidateSolution(self):
1247         """         """
1248         indicates the PDE has to be resolved if the solution is requested         indicates the PDE has to be resolved if the solution is requested
# Line 792  class LinearPDE: Line 1254  class LinearPDE:
1254         """         """
1255         indicates the operator has to be rebuilt next time it is used         indicates the operator has to be rebuilt next time it is used
1256         """         """
1257         if self.__operator_isValid: self.trace("Operator has to be rebuilt.")         if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1258         self.__invalidateSolution()         self.__invalidateSolution()
1259         self.__operator_isValid=False         self.__operator_is_Valid=False
1260    
1261     def __invalidateRightHandSide(self):     def __invalidateRightHandSide(self):
1262         """         """
# Line 819  class LinearPDE: Line 1281  class LinearPDE:
1281         """         """
1282         self.trace("New System is built from scratch.")         self.trace("New System is built from scratch.")
1283         self.__operator=escript.Operator()         self.__operator=escript.Operator()
1284         self.__operator_isValid=False         self.__operator_is_Valid=False
1285         self.__righthandside=escript.Data()         self.__righthandside=escript.Data()
1286         self.__righthandside_isValid=False         self.__righthandside_isValid=False
1287         self.__solution=escript.Data()         self.__solution=escript.Data()
1288         self.__solution_isValid=False         self.__solution_isValid=False
1289     #     #
1290     #    system initialization:     #    system initialization:
1291     #     #
1292     def __getNewOperator(self):     def __getNewOperator(self):
1293         """         """
1294         returns an instance of a new operator         returns an instance of a new operator
# Line 877  class LinearPDE: Line 1339  class LinearPDE:
1339         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1340             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1341         else:         else:
1342             self.__righthandside*=0             self.__righthandside.setToZero()
1343             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1344         return self.__righthandside         return self.__righthandside
1345    
# Line 888  class LinearPDE: Line 1350  class LinearPDE:
1350         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1351             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
1352         else:         else:
1353             self.__operator.setValue(0.)             self.__operator.resetValues()
1354             self.trace("Operator reset to zero")             self.trace("Operator reset to zero")
1355         return self.__operator         return self.__operator
1356    
# Line 909  class LinearPDE: Line 1371  class LinearPDE:
1371               else:               else:
1372                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1373               u.copyWithMask(r_s,col_q)               u.copyWithMask(r_s,col_q)
1374               if not self.__righthandside.isEmpty():               if not self.__righthandside.isEmpty():
1375                  self.__righthandside-=self.__operator*u                  self.__righthandside-=self.__operator*u
1376                  self.__righthandside=self.copyConstraint(self.__righthandside)                  self.__righthandside=self.copyConstraint(self.__righthandside)
1377               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
# Line 920  class LinearPDE: Line 1382  class LinearPDE:
1382       """       """
1383       return the value of the coefficient name of the general PDE.       return the value of the coefficient name of the general PDE.
1384    
1385       @note This method is called by the assembling routine it can be overwritten       @note: This method is called by the assembling routine it can be overwritten
1386             to map coefficients of a particular PDE to the general PDE.             to map coefficients of a particular PDE to the general PDE.
1387         @param name: name of the coefficient requested.
      @param name: name of the coefficient requested.  
1388       @type name: C{string}       @type name: C{string}
1389       @return : the value of the coefficient  name       @return: the value of the coefficient  name
1390       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1391       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1392                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1393                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1394       """       """
1395       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1396          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 938  class LinearPDE: Line 1400  class LinearPDE:
1400     def hasCoefficientOfGeneralPDE(self,name):     def hasCoefficientOfGeneralPDE(self,name):
1401       """       """
1402       checks if name is a the name of a coefficient of the general PDE.       checks if name is a the name of a coefficient of the general PDE.
1403        
1404       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1405       @type name: C{string}       @type name: C{string}
1406       @return : True if name is the name of a coefficient of the general PDE. Otherwise False.       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1407       @rtype : C{bool}       @rtype: C{bool}
1408        
1409       """       """
1410       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1411    
# Line 953  class LinearPDE: Line 1415  class LinearPDE:
1415    
1416       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1417       @type name: C{string}       @type name: C{string}
1418       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1419       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1420       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1421                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1422                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1423       """       """
1424       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1425          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 965  class LinearPDE: Line 1428  class LinearPDE:
1428    
1429     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1430       """       """
1431       return the L{escript.FunctionSpace} to be used for coefficient name of the general PDE       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1432    
1433       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1434       @type name: C{string}       @type name: C{string}
1435       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1436       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1437       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1438                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1439                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1440       """       """
1441       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1442          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 985  class LinearPDE: Line 1449  class LinearPDE:
1449    
1450       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1451       @type name: C{string}       @type name: C{string}
1452       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1453       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1454       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1455                    "A", "B", "C", "D", "X", "Y", "d", "y", "d_contact", "y_contact", "r" or "q".                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1456                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1457       """       """
1458       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1459          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1003  class LinearPDE: Line 1467  class LinearPDE:
1467       """       """
1468       returns the value of the coefficient name       returns the value of the coefficient name
1469    
1470       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1471       @type name: C{string}       @type name: C{string}
1472       @return : the value of the coefficient name       @return: the value of the coefficient name
1473       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1474       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1475       """       """
1476       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1020  class LinearPDE: Line 1484  class LinearPDE:
1484    
1485       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1486       @type name: C{string}       @type name: C{string}
1487       @return : True if name is the name of a coefficient of the general PDE. Otherwise False.       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1488       @rtype : C{bool}       @rtype: C{bool}
1489       """       """
1490       return self.COEFFICIENTS.has_key(name)       return self.COEFFICIENTS.has_key(name)
1491    
1492     def createCoefficient(self, name):     def createCoefficient(self, name):
1493       """       """
1494       create a L{escript.Data} object corresponding to coefficient name       create a L{Data<escript.Data>} object corresponding to coefficient name
1495    
1496       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1497       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1498       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1499       """       """
1500       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1040  class LinearPDE: Line 1504  class LinearPDE:
1504    
1505     def getFunctionSpaceForCoefficient(self,name):     def getFunctionSpaceForCoefficient(self,name):
1506       """       """
1507       return the L{escript.FunctionSpace} to be used for coefficient name       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1508    
1509       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1510       @type name: C{string}       @type name: C{string}
1511       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1512       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1513       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1514       """       """
1515       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1516          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1517       else:       else:
1518          raise ValueError,"unknown coefficient %s requested"%name          raise ValueError,"unknown coefficient %s requested"%name
   
1519     def getShapeOfCoefficient(self,name):     def getShapeOfCoefficient(self,name):
1520       """       """
1521       return the shape of the coefficient name       return the shape of the coefficient name
1522    
1523       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1524       @type name: C{string}       @type name: C{string}
1525       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1526       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1527       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1528       """       """
1529       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1082  class LinearPDE: Line 1545  class LinearPDE:
1545       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1546       @type name: C{string}       @type name: C{string}
1547       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1548         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1549       """       """
1550       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1551          self.trace("Coefficient %s has been altered."%name)          self.trace("Coefficient %s has been altered."%name)
1552          if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()          if not ((name=="q" or name=="r") and self.isUsingLumping()):
1553          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()             if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1554               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1555       else:       else:
1556          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1557    
1558     def copyConstraint(self,u):     def copyConstraint(self,u):
1559        """        """
1560        copies the constraint into u and returns u.        copies the constraint into u and returns u.
   
       @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs  
       @type u: L{escript.Data}  
       @return : the input u modified by the constraints.  
       @rtype : L{escript.Data}  
       @warning: u is altered if it has the appropriate L{escript.FunctionSpace}  
1561    
1562          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1563          @type u: L{Data<escript.Data>}
1564          @return: the input u modified by the constraints.
1565          @rtype: L{Data<escript.Data>}
1566          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1567        """        """
1568        q=self.getCoefficientOfGeneralPDE("q")        q=self.getCoefficientOfGeneralPDE("q")
1569        r=self.getCoefficientOfGeneralPDE("r")        r=self.getCoefficientOfGeneralPDE("r")
# Line 1116  class LinearPDE: Line 1580  class LinearPDE:
1580        """        """
1581        sets new values to coefficients        sets new values to coefficients
1582    
1583        @note This method is called by the assembling routine it can be overwritten        @param coefficients: new values assigned to coefficients
1584             to map coefficients of a particular PDE to the general PDE.        @keyword A: value for coefficient A.
1585          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1586        @param name: name of the coefficient requested.        @keyword A_reduced: value for coefficient A_reduced.
1587        @type name: C{string}        @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
       @keyword A: value for coefficient A.  
       @type A: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.  
1588        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1589        @type B: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1590          @keyword B_reduced: value for coefficient B_reduced
1591          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1592        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1593        @type C: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1594          @keyword C_reduced: value for coefficient C_reduced
1595          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1596        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1597        @type D: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1598          @keyword D_reduced: value for coefficient D_reduced
1599          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1600        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1601        @type X: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1602          @keyword X_reduced: value for coefficient X_reduced
1603          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1604        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1605        @type Y: any type that can be interpreted as L{escript.Data} object on L{escript.Function}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1606          @keyword Y_reduced: value for coefficient Y_reduced
1607          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1608        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1609        @type d: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1610          @keyword d_reduced: value for coefficient d_reduced
1611          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1612        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1613        @type y: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnBoundary}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1614        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1615        @type d_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1616                         or  L{escript.FunctionOnContactZero}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1617          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1618        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1619        @type y_contact: any type that can be interpreted as L{escript.Data} object on L{escript.FunctionOnContactOne}.        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1620                         or  L{escript.FunctionOnContactZero}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1621          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1622        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1623        @type r: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1624                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
1625        @keyword q: mask for location of constraints        @keyword q: mask for location of constraints
1626        @type q: any type that can be interpreted as L{escript.Data} object on L{escript.Solution} or L{escript.ReducedSolution}        @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1628        @raise IllegalCoefficient: if an unknown coefficient keyword is used.        @raise IllegalCoefficient: if an unknown coefficient keyword is used.
   
1629        """        """
1630        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1631        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
# Line 1178  class LinearPDE: Line 1653  class LinearPDE:
1653        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1654        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1655          try:          try:
1656             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1657                                             self.getNumEquations(),self.getNumSolutions(),
1658                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1659               self.alteredCoefficient(i)
1660            except IllegalCoefficientFunctionSpace,m:
1661                # if the function space is wrong then we try the reduced version:
1662                i_red=i+"_reduced"
1663                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1664                    try:
1665                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1666                                                          self.getNumEquations(),self.getNumSolutions(),
1667                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1668                        self.alteredCoefficient(i_red)
1669                    except IllegalCoefficientValue,m:
1670                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1671                    except IllegalCoefficientFunctionSpace,m:
1672                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673                else:
1674                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1675          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1676             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677          self.alteredCoefficient(i)        self.__altered_coefficients=True
   
1678        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1679        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
1680           q=self.getCoefficientOfGeneralPDE("q")           q=self.getCoefficientOfGeneralPDE("q")
1681           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1682           homogeneous_constraint=True           homogeneous_constraint=True
1683           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1684               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1685                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1686                 self.__invalidateSystem()                 self.__invalidateSystem()
1687    
   
1688     def getSystem(self):     def getSystem(self):
1689         """         """
1690         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1691    
1692           @return: the discrete version of the PDE
1693           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1694         """         """
1695         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1696            if self.isUsingLumping():            if self.isUsingLumping():
1697                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1698                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1699                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient A"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1700                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient B"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1701                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1702                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1703                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1704                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1705                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1706                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1707                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1708                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1709                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1710                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1711                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1712                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1713                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1714                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1715                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1716                     D=self.getCoefficientOfGeneralPDE("D")
1717                     d=self.getCoefficientOfGeneralPDE("d")
1718                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1719                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1720                     if not D.isEmpty():
1721                         if self.getNumSolutions()>1:
1722                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1723                         else:
1724                            D_times_e=D
1725                     else:
1726                        D_times_e=escript.Data()
1727                     if not d.isEmpty():
1728                         if self.getNumSolutions()>1:
1729                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1730                         else:
1731                            d_times_e=d
1732                     else:
1733                        d_times_e=escript.Data()
1734          
1735                     if not D_reduced.isEmpty():
1736                         if self.getNumSolutions()>1:
1737                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1738                         else:
1739                            D_reduced_times_e=D_reduced
1740                     else:
1741                        D_reduced_times_e=escript.Data()
1742                     if not d_reduced.isEmpty():
1743                         if self.getNumSolutions()>1:
1744                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1745                         else:
1746                            d_reduced_times_e=d_reduced
1747                     else:
1748                        d_reduced_times_e=escript.Data()
1749    
1750                     self.__operator=self.__getNewRightHandSide()
1751                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1752                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1753                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1754                     else:
1755                        self.getDomain().addPDEToRHS(self.__operator, \
1756                                                     escript.Data(), \
1757                                                     D_times_e, \
1758                                                     d_times_e,\
1759                                                     escript.Data())
1760                        self.getDomain().addPDEToRHS(self.__operator, \
1761                                                     escript.Data(), \
1762                                                     D_reduced_times_e, \
1763                                                     d_reduced_times_e,\
1764                                                     escript.Data())
1765                     self.__operator=1./self.__operator
1766                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1767                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1768                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1769                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1770                                 self.getCoefficientOfGeneralPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1771                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1772                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1773                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1774                     self.getDomain().addPDEToRHS(self.__righthandside, \
1775                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1776                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1778                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1779                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1780                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1781            else:            else:
1782               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1783                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1784                                 self.getCoefficientOfGeneralPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1785                                 self.getCoefficientOfGeneralPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
# Line 1242  class LinearPDE: Line 1791  class LinearPDE:
1791                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1792                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1793                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1794                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1795                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1805                   self.__applyConstraint()                   self.__applyConstraint()
1806                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1807                   self.trace("New system has been built.")                   self.trace("New system has been built.")
1808                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1809                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1810               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1811                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
# Line 1253  class LinearPDE: Line 1813  class LinearPDE:
1813                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1814                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1815                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1816                     self.getDomain().addPDEToRHS(self.__righthandside, \
1817                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1818                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1820                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1821                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1822                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1823                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1824               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1825                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1826                              self.getCoefficientOfGeneralPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1827                              self.getCoefficientOfGeneralPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
# Line 1268  class LinearPDE: Line 1833  class LinearPDE:
1833                              escript.Data(),\                              escript.Data(),\
1834                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1835                              escript.Data())                              escript.Data())
1836                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1837                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1840                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1841                                escript.Data(), \
1842                                escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1844                                escript.Data(),\
1845                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1846                                escript.Data())
1847                   self.__applyConstraint()                   self.__applyConstraint()
1848                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1849                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1850         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1851    
1852    
1853    class Poisson(LinearPDE):
   
 class AdvectivePDE(LinearPDE):  
1854     """     """
1855     Class to handle a linear PDE dominated by advective terms:     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1856    
1857     class to define a linear PDE of the form     M{-grad(grad(u)[j])[j] = f}
1858    
1859     \f[     with natural boundary conditons
    -(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  
    \f]  
1860    
1861     with boundary conditons:     M{n[j]*grad(u)[j] = 0 }
   
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
   
    and contact conditions  
   
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}  
    \f]  
1862    
1863     and constraints:     and constraints:
1864    
1865     \f[     M{u=0} where M{q>0}
1866     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1867     """     """
    def __init__(self,domain,numEquations=0,numSolutions=0,xi=None,debug=False):  
       LinearPDE.__init__(self,domain,numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
1868    
1869     def __calculateXi(self,peclet_factor,Z,h):     def __init__(self,domain,debug=False):
1870         Z_max=util.Lsup(Z)       """
1871         if Z_max>0.:       initializes a new Poisson equation
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
        else:  
           return 0.  
1872    
1873     def setValue(self,**args):       @param domain: domain of the PDE
1874         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       @type domain: L{Domain<escript.Domain>}
1875         LinearPDE.setValue(**args)       @param debug: if True debug informations are printed.
   
    def ELMAN_RAMAGE(P):  
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
    def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(P):  
     """ """  
     return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2  
                 else:  
                    if self.getNumSolutions()>1:  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2  
                    else:  
                       for l in range(self.getDim()): Z2+=(C[l]-B[l])**2  
                 length_of_Z=util.sqrt(Z2)  
             elif C.isEmpty():  
               length_of_Z=util.length(B)  
             else:  
               length_of_Z=util.length(C)  
1876    
1877              Z_max=util.Lsup(length_of_Z)       """
1878              if Z_max>0.:       super(Poisson, self).__init__(domain,1,1,debug)
1879                 length_of_A=util.length(A)       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                 A_max=util.Lsup(length_of_A)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1881                 if A_max>0:                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1882                      inv_A=1./(length_of_A+A_max*self.TOL)       self.setSymmetryOn()
1883                 else:  
1884                      inv_A=1./self.TOL     def setValue(self,**coefficients):
1885                 peclet_number=length_of_Z*h/2*inv_A       """
1886                 xi=self.__xi(peclet_number)       sets new values to coefficients
                self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)  
                print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)  
       return self.__Xi  
1887    
1888         @param coefficients: new values assigned to coefficients
1889         @keyword f: value for right hand side M{f}
1890         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1891         @keyword q: mask for location of constraints
1892         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1893                   depending of reduced order is used for the representation of the equation.
1894         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1895         """
1896         super(Poisson, self).setValue(**coefficients)
1897    
1898     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1899       """       """
1900       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
1901         @param name: name of the coefficient requested.
1902       @param name:       @type name: C{string}
1903         @return: the value of the coefficient  name
1904         @rtype: L{Data<escript.Data>}
1905         @raise IllegalCoefficient: if name is not one of coefficients
1906                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1907         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1908       """       """
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
1909       if name == "A" :       if name == "A" :
1910           A=self.getCoefficient("A")           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.createNewCoefficient("A")  
             else:  
                Aout=A[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                 for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
             else:  
                 for j in range(self.getDim()):  
                    for l in range(self.getDim()):  
                       if not C.isEmpty() and not B.isEmpty():  
                           Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])  
                       elif C.isEmpty():  
                           Aout[j,l]+=Xi*B[j]*B[l]  
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
          return Aout  
1911       elif name == "B" :       elif name == "B" :
1912           B=self.getCoefficient("B")           return escript.Data()
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.getXi()  
             if B.isEmpty():  
                 Bout=self.createNewCoefficient("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
          return Bout  
1913       elif name == "C" :       elif name == "C" :
1914           B=self.getCoefficient("B")           return escript.Data()
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.getXi()  
             if C.isEmpty():  
                 Cout=self.createNewCoefficient("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
          return Cout  
1915       elif name == "D" :       elif name == "D" :
1916           return self.getCoefficient("D")           return escript.Data()
1917       elif name == "X" :       elif name == "X" :
1918           X=self.getCoefficient("X")           return escript.Data()
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
          else:  
             if X.isEmpty():  
                 Xout=self.createNewCoefficient("X")  
             else:  
                 Xout=X[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
             else:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                     else:  
                        Xout[j]+=tmp*C[j]  
          return Xout  
1919       elif name == "Y" :       elif name == "Y" :
1920           return self.getCoefficient("Y")           return self.getCoefficient("f")
1921       elif name == "d" :       elif name == "d" :
1922           return self.getCoefficient("d")           return escript.Data()
1923       elif name == "y" :       elif name == "y" :
1924           return self.getCoefficient("y")           return escript.Data()
1925       elif name == "d_contact" :       elif name == "d_contact" :
1926           return self.getCoefficient("d_contact")           return escript.Data()
1927       elif name == "y_contact" :       elif name == "y_contact" :
1928           return self.getCoefficient("y_contact")           return escript.Data()
1929         elif name == "A_reduced" :
1930             return escript.Data()
1931         elif name == "B_reduced" :
1932             return escript.Data()
1933         elif name == "C_reduced" :
1934             return escript.Data()
1935         elif name == "D_reduced" :
1936             return escript.Data()
1937         elif name == "X_reduced" :
1938             return escript.Data()
1939         elif name == "Y_reduced" :
1940             return self.getCoefficient("f_reduced")
1941         elif name == "d_reduced" :
1942             return escript.Data()
1943         elif name == "y_reduced" :
1944             return escript.Data()
1945         elif name == "d_contact_reduced" :
1946             return escript.Data()
1947         elif name == "y_contact_reduced" :
1948             return escript.Data()
1949       elif name == "r" :       elif name == "r" :
1950           return self.getCoefficient("r")           return escript.Data()
1951       elif name == "q" :       elif name == "q" :
1952           return self.getCoefficient("q")           return self.getCoefficient("q")
1953       else:       else:
1954           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
1955    
1956  class Poisson(LinearPDE):  class Helmholtz(LinearPDE):
1957     """     """
1958     Class to define a Poisson equation problem:     Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1959    
1960       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1961    
1962       with natural boundary conditons
1963    
1964     class to define a linear PDE of the form     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    \f[  
    -u_{,jj} = f  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
1965    
1966     and constraints:     and constraints:
1967    
1968     \f[     M{u=r} where M{q>0}
1969     u=0 \quad \mathrm{where} \quad q>0  
    \f]  
1970     """     """
1971    
1972     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
1973         LinearPDE.__init__(self,domain,1,1,debug)       """
1974         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),       initializes a new Poisson equation
1975                            "q": PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
1976         self.setSymmetryOn()       @param domain: domain of the PDE
1977         self.setValue(f,q)       @type domain: L{Domain<escript.Domain>}
1978         @param debug: if True debug informations are printed.
1979     def setValue(self,f=escript.Data(),q=escript.Data()):  
1980         """set value of PDE parameters f and q"""       """
1981         self._LinearPDE__setValue(f=f,q=q)       super(Helmholtz, self).__init__(domain,1,1,debug)
1982         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1984                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1990                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1991         self.setSymmetryOn()
1992    
1993       def setValue(self,**coefficients):
1994         """
1995         sets new values to coefficients
1996    
1997         @param coefficients: new values assigned to coefficients
1998         @keyword omega: value for coefficient M{S{omega}}
1999         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000         @keyword k: value for coefficeint M{k}
2001         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002         @keyword f: value for right hand side M{f}
2003         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2004         @keyword alpha: value for right hand side M{S{alpha}}
2005         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006         @keyword g: value for right hand side M{g}
2007         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2008         @keyword r: prescribed values M{r} for the solution in constraints.
2009         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2010                   depending of reduced order is used for the representation of the equation.
2011         @keyword q: mask for location of constraints
2012         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                   depending of reduced order is used for the representation of the equation.
2014         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2015         """
2016         super(Helmholtz, self).setValue(**coefficients)
2017    
2018     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2019       """       """
2020       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2021    
2022       @param name:       @param name: name of the coefficient requested.
2023         @type name: C{string}
2024         @return: the value of the coefficient  name
2025         @rtype: L{Data<escript.Data>}
2026         @raise IllegalCoefficient: if name is not one of coefficients
2027                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2028         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2029       """       """
2030       if name == "A" :       if name == "A" :
2031           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2032       elif name == "B" :       elif name == "B" :
2033           return escript.Data()           return escript.Data()
2034       elif name == "C" :       elif name == "C" :
2035           return escript.Data()           return escript.Data()
2036       elif name == "D" :       elif name == "D" :
2037           return escript.Data()           return self.getCoefficient("omega")
2038       elif name == "X" :       elif name == "X" :
2039           return escript.Data()           return escript.Data()
2040       elif name == "Y" :       elif name == "Y" :
2041           return self.getCoefficient("f")           return self.getCoefficient("f")
2042       elif name == "d" :       elif name == "d" :
2043           return escript.Data()           return self.getCoefficient("alpha")
2044       elif name == "y" :       elif name == "y" :
2045           return escript.Data()           return self.getCoefficient("g")
2046       elif name == "d_contact" :       elif name == "d_contact" :
2047           return escript.Data()           return escript.Data()
2048       elif name == "y_contact" :       elif name == "y_contact" :
2049           return escript.Data()           return escript.Data()
2050       elif name == "r" :       elif name == "A_reduced" :
2051             return escript.Data()
2052         elif name == "B_reduced" :
2053             return escript.Data()
2054         elif name == "C_reduced" :
2055             return escript.Data()
2056         elif name == "D_reduced" :
2057             return escript.Data()
2058         elif name == "X_reduced" :
2059             return escript.Data()
2060         elif name == "Y_reduced" :
2061             return self.getCoefficient("f_reduced")
2062         elif name == "d_reduced" :
2063             return escript.Data()
2064         elif name == "y_reduced" :
2065            return self.getCoefficient("g_reduced")
2066         elif name == "d_contact_reduced" :
2067           return escript.Data()           return escript.Data()
2068         elif name == "y_contact_reduced" :
2069             return escript.Data()
2070         elif name == "r" :
2071             return self.getCoefficient("r")
2072       elif name == "q" :       elif name == "q" :
2073           return self.getCoefficient("q")           return self.getCoefficient("q")
2074       else:       else:
2075           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2076    
2077  class LameEquation(LinearPDE):  class LameEquation(LinearPDE):
2078     """     """
2079     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2080    
2081     class to define a linear PDE of the form     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] }
2082     \f[  
2083     -(\mu (u_{i,j}+u_{j,i}))_{,j} - \lambda u_{j,ji}} = F_i -\sigma_{ij,j}     with natural boundary conditons:
2084     \f]  
2085       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] }
    with boundary conditons:  
   
    \f[  
    n_j(\mu (u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\lambda u_{j,j} = f_i  
    \f]  
2086    
2087     and constraints:     and constraints:
2088    
2089     \f[     M{u[i]=r[i]} where M{q[i]>0}
2090     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
2091     """     """
2092    
2093     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
2094         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim(),debug)        super(LameEquation, self).__init__(domain,\
2095         self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                                           domain.getDim(),domain.getDim(),debug)
2096          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2097                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2098                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2100                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2101                            "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2102                            "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2103         self.setSymmetryOn()        self.setSymmetryOn()
2104    
2105     def setValue(self,lame_lambda=escript.Data(),lame_mu=escript.Data(),F=escript.Data(),sigma=escript.Data(),f=escript.Data(),r=escript.Data(),q=escript.Data()):     def setValues(self,**coefficients):
2106         """set value of PDE parameters"""       """
2107         self._LinearPDE__setValue(lame_lambda=lame_lambda, \       sets new values to coefficients
2108                                   lame_mu=lame_mu, \  
2109                                   F=F, \       @param coefficients: new values assigned to coefficients
2110                                   sigma=sigma, \       @keyword lame_mu: value for coefficient M{S{mu}}
2111                                   f=f, \       @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112                                   r=r, \       @keyword lame_lambda: value for coefficient M{S{lambda}}
2113                                   q=q)       @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2114         @keyword F: value for internal force M{F}
2115         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2116         @keyword sigma: value for initial stress M{S{sigma}}
2117         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2118         @keyword f: value for extrenal force M{f}
2119         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2120         @keyword r: prescribed values M{r} for the solution in constraints.
2121         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2122                   depending of reduced order is used for the representation of the equation.
2123         @keyword q: mask for location of constraints
2124         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2127         """
2128         super(LameEquation, self).setValues(**coefficients)
2129    
2130     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2131       """       """
2132       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2133    
2134       @param name:       @param name: name of the coefficient requested.
2135         @type name: C{string}
2136         @return: the value of the coefficient  name
2137         @rtype: L{Data<escript.Data>}
2138         @raise IllegalCoefficient: if name is not one of coefficients
2139                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2140         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2141       """       """
2142       if name == "A" :       if name == "A" :
2143           out =self.createCoefficientOfGeneralPDE("A")           out =self.createCoefficientOfGeneralPDE("A")
# Line 1662  class LameEquation(LinearPDE): Line 2165  class LameEquation(LinearPDE):
2165           return escript.Data()           return escript.Data()
2166       elif name == "y_contact" :       elif name == "y_contact" :
2167           return escript.Data()           return escript.Data()
2168         elif name == "A_reduced" :
2169             return escript.Data()
2170         elif name == "B_reduced" :
2171             return escript.Data()
2172         elif name == "C_reduced" :
2173             return escript.Data()
2174         elif name == "D_reduced" :
2175             return escript.Data()
2176         elif name == "X_reduced" :
2177             return escript.Data()
2178         elif name == "Y_reduced" :
2179             return escript.Data()
2180         elif name == "d_reduced" :
2181             return escript.Data()
2182         elif name == "y_reduced" :
2183             return escript.Data()
2184         elif name == "d_contact_reduced" :
2185             return escript.Data()
2186         elif name == "y_contact_reduced" :
2187             return escript.Data()
2188       elif name == "r" :       elif name == "r" :
2189           return self.getCoefficient("r")           return self.getCoefficient("r")
2190       elif name == "q" :       elif name == "q" :
2191           return self.getCoefficient("q")           return self.getCoefficient("q")
2192       else:       else:
2193           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2194    
2195  # $Log$  def LinearSinglePDE(domain,debug=False):
2196  # Revision 1.11  2005/08/23 01:24:28  jgs     """
2197  # Merge of development branch dev-02 back to main trunk on 2005-08-23     defines a single linear PDEs
2198  #  
2199  # Revision 1.10  2005/08/12 01:45:36  jgs     @param domain: domain of the PDE
2200  # erge of development branch dev-02 back to main trunk on 2005-08-12     @type domain: L{Domain<escript.Domain>}
2201  #     @param debug: if True debug informations are printed.
2202  # Revision 1.9.2.4  2005/08/22 07:11:09  gross     @rtype: L{LinearPDE}
2203  # some problems with LinearPDEs fixed.     """
2204  #     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2205  # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
2206  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  def LinearPDESystem(domain,debug=False):
2207  #     """
2208  # Revision 1.9.2.2  2005/08/18 04:39:32  gross     defines a system of linear PDEs
2209  # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
2210  #     @param domain: domain of the PDE
2211  # Revision 1.9.2.1  2005/07/29 07:10:27  gross     @type domain: L{Domain<escript.Domain>}
2212  # new functions in util and a new pde type in linearPDEs     @param debug: if True debug informations are printed.
2213  #     @rtype: L{LinearPDE}
2214  # Revision 1.1.2.25  2005/07/28 04:21:09  gross     """
2215  # Lame equation: (linear elastic, isotropic) added     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2216  #  
2217  # Revision 1.1.2.24  2005/07/22 06:37:11  gross  class TransportPDE(object):
2218  # some extensions to modellib and linearPDEs       """
2219  #       Warning: This is still a very experimental. The class is still changing!
2220  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
2221  # Fixed up some docstrings.  Moved module-level functions to top of file so       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2222  # that epydoc and doxygen can pick them up properly.      
2223  #       u=r where q>0
2224  # Revision 1.1.2.22  2005/05/12 11:41:30  gross      
2225  # some basic Models have been added       all coefficients are constant over time.
2226  #  
2227  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane       typical usage:
2228  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
2229  # file so that the AdvectivePDE class is picked up by doxygen.  Some           p=TransportPDE(dom)
2230  # reformatting of docstrings.  Addition of code to make equations come out           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2231  # as proper LaTeX.           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2232  #           t=0
2233  # Revision 1.1.2.20  2005/04/15 07:09:08  gross           dt=0.1
2234  # some problems with functionspace and linearPDEs fixed.           while (t<1.):
2235  #                u=p.solve(dt)
2236  # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
2237  # bug in SystemPattern fixed.       """
2238  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2239  # Revision 1.1.2.18  2005/02/08 06:16:45  gross          self.__domain=domain
2240  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed          self.__num_equations=num_equations
2241  #          self.__useSUPG=useSUPG
2242  # Revision 1.1.2.17  2005/02/08 05:56:19  gross          self.__trace=trace
2243  # Reference Number handling added          self.__theta=theta
2244  #          self.__matrix_type=0
2245  # Revision 1.1.2.16  2005/02/07 04:41:28  gross          self.__reduced=True
2246  # some function exposed to python to make mesh merging running          self.__reassemble=True
2247  #          if self.__useSUPG:
2248  # Revision 1.1.2.15  2005/02/03 00:14:44  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2249  # timeseries add and ESySParameter.py renames esysXML.py for consistence             self.__pde.setSymmetryOn()
2250  #             self.__pde.setReducedOrderOn()
2251  # Revision 1.1.2.14  2005/02/01 06:44:10  gross          else:
2252  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working             self.__transport_problem=self.__getNewTransportProblem()
2253  #          self.setTolerance()
2254  # Revision 1.1.2.13  2005/01/25 00:47:07  gross          self.__M=escript.Data()
2255  # updates in the documentation          self.__A=escript.Data()
2256  #          self.__B=escript.Data()
2257  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__C=escript.Data()
2258  # Added createCoefficient method for linearPDEs.          self.__D=escript.Data()
2259  #          self.__X=escript.Data()
2260  # Revision 1.1.2.11  2005/01/11 01:55:34  gross          self.__Y=escript.Data()
2261  # a problem in linearPDE class fixed          self.__d=escript.Data()
2262  #          self.__y=escript.Data()
2263  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          self.__d_contact=escript.Data()
2264  # some bugs in linearPDE fixed          self.__y_contact=escript.Data()
2265  #          self.__r=escript.Data()
2266  # Revision 1.1.2.9  2005/01/06 06:24:58  gross          self.__q=escript.Data()
2267  # some bugs in slicing fixed  
2268  #       def trace(self,text):
2269  # Revision 1.1.2.8  2005/01/05 04:21:40  gross               if self.__trace: print text
2270  # FunctionSpace checking/matchig in slicing added       def getSafeTimeStepSize(self):
2271  #          if self.__useSUPG:
2272  # Revision 1.1.2.7  2004/12/29 10:03:41  gross              if self.__reassemble:
2273  # bug in setValue fixed                 h=self.__domain.getSize()
2274  #                 dt=None
2275  # Revision 1.1.2.6  2004/12/29 05:29:59  gross                 if not self.__A.isEmpty():
2276  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2277  #                    if dt == None:
2278  # Revision 1.1.2.5  2004/12/29 00:18:41  gross                       dt = dt2
2279  # AdvectivePDE added                    else:
2280  #                       dt=1./(1./dt+1./dt2)
2281  # Revision 1.1.2.4  2004/12/24 06:05:41  gross                 if not self.__B.isEmpty():
2282  # some changes in linearPDEs to add AdevectivePDE                    dt2=util.inf(h*self.__M/util.length(self.__B))
2283  #                    if dt == None:
2284  # Revision 1.1.2.3  2004/12/16 00:12:34  gross                       dt = dt2
2285  # __init__ of LinearPDE does not accept any coefficient anymore                    else:
2286  #                       dt=1./(1./dt+1./dt2)
2287  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs                 if not  self.__C.isEmpty():
2288  # *** empty log message ***                    dt2=util.inf(h*self.__M/util.length(self.__C))
2289  #                    if dt == None:
2290  # Revision 1.1.2.1  2004/12/12 22:53:47  gross                       dt = dt2
2291  # linearPDE has been renamed LinearPDE                    else:
2292  #                       dt=1./(1./dt+1./dt2)
2293  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__D.isEmpty():
2294  # GMRES added                    dt2=util.inf(self.__M/util.length(self.__D))
2295  #                    if dt == None:
2296  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2297  # options for GMRES and PRES20 added                    else:
2298  #                       dt=1./(1./dt+1./dt2)
2299  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 self.__dt = dt/2
2300  # some small changes              return self.__dt
2301  #          else:
2302  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross              return self.__getTransportProblem().getSafeTimeStepSize()
2303  # Finley solves 4M unknowns now       def getDomain(self):
2304  #          return self.__domain
2305  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross       def getTheta(self):
2306  # poisson solver added          return self.__theta
2307  #       def getNumEquations(self):
2308  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross          return self.__num_equations
2309  # 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       def setReducedOn(self):
2310  #            if not self.reduced():
2311  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                if self.__useSUPG:
2312  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                   self.__pde.setReducedOrderOn()
2313  #                else:
2314  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                   self.__transport_problem=self.__getNewTransportProblem()
2315  # initial import of project esys2            self.__reduced=True
2316  #       def setReducedOff(self):
2317  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs            if self.reduced():
2318  # committing Lutz's and Paul's changes to brach jgs                if self.__useSUPG:
2319  #                   self.__pde.setReducedOrderOff()
2320  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                else:
2321  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.                   self.__transport_problem=self.__getNewTransportProblem()
2322  #            self.__reduced=False
2323  # Revision 1.3  2004/09/23 00:53:23  jgs       def reduced(self):
2324  # minor fixes           return self.__reduced
2325  #       def getFunctionSpace(self):
2326  # Revision 1.1  2004/08/28 12:58:06  gross          if self.reduced():
2327  # SimpleSolve is not running yet: problem with == of functionsspace             return escript.ReducedSolution(self.getDomain())
2328  #          else:
2329  #             return escript.Solution(self.getDomain())
2330    
2331         def setTolerance(self,tol=1.e-8):
2332            self.__tolerance=tol
2333            if self.__useSUPG:
2334                  self.__pde.setTolerance(self.__tolerance)
2335    
2336         def __getNewTransportProblem(self):
2337           """
2338           returns an instance of a new operator
2339           """
2340           self.trace("New Transport problem is allocated.")
2341           return self.getDomain().newTransportProblem( \
2342                                   self.getTheta(),
2343                                   self.getNumEquations(), \
2344                                   self.getFunctionSpace(), \
2345                                   self.__matrix_type)
2346              
2347         def __getNewSolutionVector(self):
2348             if self.getNumEquations() ==1 :
2349                    out=escript.Data(0.0,(),self.getFunctionSpace())
2350             else:
2351                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2352             return out
2353    
2354         def __getTransportProblem(self):
2355           if self.__reassemble:
2356                 self.__source=self.__getNewSolutionVector()
2357                 self.__transport_problem.reset()
2358                 self.getDomain().addPDEToTransportProblem(
2359                             self.__transport_problem,
2360                             self.__source,
2361                             self.__M,
2362                             self.__A,
2363                             self.__B,
2364                             self.__C,
2365                             self.__D,
2366                             self.__X,
2367                             self.__Y,
2368                             self.__d,
2369                             self.__y,
2370                             self.__d_contact,
2371                             self.__y_contact)
2372                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2373                 self.__reassemble=False
2374           return self.__transport_problem
2375         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2376                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2377                 if not M==None:
2378                      self.__reassemble=True
2379                      self.__M=M
2380                 if not A==None:
2381                      self.__reassemble=True
2382                      self.__A=A
2383                 if not B==None:
2384                      self.__reassemble=True
2385                      self.__B=B
2386                 if not C==None:
2387                      self.__reassemble=True
2388                      self.__C=C
2389                 if not D==None:
2390                      self.__reassemble=True
2391                      self.__D=D
2392                 if not X==None:
2393                      self.__reassemble=True
2394                      self.__X=X
2395                 if not Y==None:
2396                      self.__reassemble=True
2397                      self.__Y=Y
2398                 if not d==None:
2399                      self.__reassemble=True
2400                      self.__d=d
2401                 if not y==None:
2402                      self.__reassemble=True
2403                      self.__y=y
2404                 if not d_contact==None:
2405                      self.__reassemble=True
2406                      self.__d_contact=d_contact
2407                 if not y_contact==None:
2408                      self.__reassemble=True
2409                      self.__y_contact=y_contact
2410                 if not q==None:
2411                      self.__reassemble=True
2412                      self.__q=q
2413                 if not r==None:
2414                      self.__reassemble=True
2415                      self.__r=r
2416    
2417         def setInitialSolution(self,u):
2418                 if self.__useSUPG:
2419                     self.__u=util.interpolate(u,self.getFunctionSpace())
2420                 else:
2421                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2422    
2423         def solve(self,dt,**kwarg):
2424               if self.__useSUPG:
2425                    if self.__reassemble:
2426                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2427                        self.__reassemble=False
2428                    dt2=self.getSafeTimeStepSize()
2429                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2430                    dt2=dt/nn
2431                    nnn=0
2432                    u=self.__u
2433                    self.trace("number of substeps is %d."%nn)
2434                    while nnn<nn :
2435                        self.__setSUPG(u,u,dt2/2)
2436                        u_half=self.__pde.getSolution(verbose=True)
2437                        self.__setSUPG(u,u_half,dt2)
2438                        u=self.__pde.getSolution(verbose=True)
2439                        nnn+=1
2440                    self.__u=u
2441                    return self.__u
2442               else:
2443                   kwarg["tolerance"]=self.__tolerance
2444                   tp=self.__getTransportProblem()
2445                   return tp.solve(self.__source,dt,kwarg)
2446         def __setSUPG(self,u0,u,dt):
2447                g=util.grad(u)
2448                X=0
2449                Y=self.__M*u0
2450                X=0
2451                self.__pde.setValue(r=u0)
2452                if not self.__A.isEmpty():
2453                   X=X+dt*util.matrixmult(self.__A,g)
2454                if not self.__B.isEmpty():
2455                   X=X+dt*self.__B*u
2456                if not  self.__C.isEmpty():
2457                   Y=Y+dt*util.inner(self.__C,g)
2458                if not self.__D.isEmpty():
2459                   Y=Y+dt*self.__D*u
2460                if not self.__X.isEmpty():
2461                   X=X+dt*self.__X
2462                if not self.__Y.isEmpty():
2463                   Y=Y+dt*self.__Y
2464                self.__pde.setValue(X=X,Y=Y)
2465                if not self.__y.isEmpty():
2466                   self.__pde.setValue(y=dt*self.__y)
2467                if not self.__y_contact.isEmpty():
2468                   self.__pde.setValue(y=dt*self.__y_contact)
2469                self.__pde.setValue(r=u0)

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