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trunk/esys2/escript/py_src/linearPDEs.py revision 148 by jgs, Tue Aug 23 01:24:31 2005 UTC temp_trunk_copy/escript/py_src/linearPDEs.py revision 1384 by phornby, Fri Jan 11 02:29:38 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 escript  import escript
38  import util  import util
39  import numarray  import numarray
40    
41    __author__="Lutz Gross, l.gross@uq.edu.au"
42    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
43                        http://www.access.edu.au
44                    Primary Business: Queensland, Australia"""
45    __license__="""Licensed under the Open Software License version 3.0
46                 http://www.opensource.org/licenses/osl-3.0.php"""
47    __url__="http://www.iservo.edu.au/esys"
48    __version__="$Revision$"
49    __date__="$Date$"
50    
51    
52  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
53     """     """
54     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.
55     """     """
56       pass
57    
58  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
59     """     """
60     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
61     """     """
62       pass
63    
64    class IllegalCoefficientFunctionSpace(ValueError):
65       """
66       raised if an incorrect function space for a coefficient is used.
67       """
68    
69  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
70     """     """
71     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
72     """     """
73       pass
74    
75  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:  
76      """      """
77      A class for PDE coefficients      A class for describing a PDE coefficient
78    
79        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
80        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
81        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
82        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
83        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
84        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
85        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
86        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
87        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
88        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
89        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
90        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
91        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
92        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
93    
94      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
95      INTERIOR=0      INTERIOR=0
96      BOUNDARY=1      BOUNDARY=1
97      CONTACT=2      CONTACT=2
98      CONTINUOUS=3      SOLUTION=3
99      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
100      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
101      # number of unknowns.      BY_SOLUTION=6
102      EQUATION=3      BY_DIM=7
103      SOLUTION=4      OPERATOR=10
104      DIM=5      RIGHTHANDSIDE=11
105      # indicator for what is altered if the coefficient is altered:      BOTH=12
106      OPERATOR=5      INTERIOR_REDUCED=13
107      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
108      BOTH=7      CONTACT_REDUCED=15
109      def __init__(self,where,pattern,altering):  
110        def __init__(self, where, pattern, altering):
111         """         """
112         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
113    
114           @param where: describes where the coefficient lives
115           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
116                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
117           @param pattern: describes the shape of the coefficient and how the shape is build for a given
118                  spatial dimension and numbers of equation and solution in then PDE. For instance,
119                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
120                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
121                  on a 2-dimensional domain. In the case of single equation and a single solution component
122                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
123                  the example would be read as (2,).
124           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
125           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
126           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
127           @param reduced: indicates if reduced
128           @type reduced: C{bool}
129         """         """
130           super(PDECoefficient, self).__init__()
131         self.what=where         self.what=where
132         self.pattern=pattern         self.pattern=pattern
133         self.altering=altering         self.altering=altering
# Line 74  class PDECoefficient: Line 139  class PDECoefficient:
139         """         """
140         self.value=escript.Data()         self.value=escript.Data()
141    
142      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
143         """         """
144         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
145    
146         @param domain:         @param domain: domain on which the PDE uses the coefficient
147         """         @type domain: L{Domain<escript.Domain>}
148         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
149         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
150         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
151         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
152           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
153           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
154           """
155           if self.what==self.INTERIOR:
156                return escript.Function(domain)
157           elif self.what==self.INTERIOR_REDUCED:
158                return escript.ReducedFunction(domain)
159           elif self.what==self.BOUNDARY:
160                return escript.FunctionOnBoundary(domain)
161           elif self.what==self.BOUNDARY_REDUCED:
162                return escript.ReducedFunctionOnBoundary(domain)
163           elif self.what==self.CONTACT:
164                return escript.FunctionOnContactZero(domain)
165           elif self.what==self.CONTACT_REDUCED:
166                return escript.ReducedFunctionOnContactZero(domain)
167           elif self.what==self.SOLUTION:
168                if reducedEquationOrder and reducedSolutionOrder:
169                    return escript.ReducedSolution(domain)
170                else:
171                    return escript.Solution(domain)
172           elif self.what==self.REDUCED:
173                return escript.ReducedSolution(domain)
174    
175      def getValue(self):      def getValue(self):
176         """         """
177         returns the value of the coefficient:         returns the value of the coefficient
178    
179           @return:  value of the coefficient
180           @rtype:  L{Data<escript.Data>}
181         """         """
182         return self.value         return self.value
183    
184      def setValue(self,domain,numEquations=1,numSolutions=1,newValue=None):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
185         """         """
186         set the value of the coefficient to new value         set the value of the coefficient to a new value
187    
188           @param domain: domain on which the PDE uses the coefficient
189           @type domain: L{Domain<escript.Domain>}
190           @param numEquations: number of equations of the PDE
191           @type numEquations: C{int}
192           @param numSolutions: number of components of the PDE solution
193           @type numSolutions: C{int}
194           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
195           @type reducedEquationOrder: C{bool}
196           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
197           @type reducedSolutionOrder: C{bool}
198           @param newValue: number of components of the PDE solution
199           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
200           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
201           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
202         """         """
203         if newValue==None:         if newValue==None:
204             newValue=escript.Data()             newValue=escript.Data()
205         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
206             if not newValue.isEmpty():             if not newValue.isEmpty():
207                newValue=escript.Data(newValue,self.getFunctionSpace(domain))                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
208                    try:
209                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
210                    except:
211                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
212         else:         else:
213             newValue=escript.Data(newValue,self.getFunctionSpace(domain))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
214         if not newValue.isEmpty():         if not newValue.isEmpty():
215             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():             if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
216                 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())
217         self.value=newValue         self.value=newValue
218    
219      def isAlteringOperator(self):      def isAlteringOperator(self):
220          """          """
221      return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
222    
223            @return:  True if the operator of the PDE is changed when the coefficient is changed
224            @rtype:  C{bool}
225      """      """
226          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
227              return not None              return not None
# Line 118  class PDECoefficient: Line 230  class PDECoefficient:
230    
231      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
232          """          """
233      return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
234    
235        @rtype:  C{bool}
236            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
237      """      """
238          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
239              return not None              return not None
# Line 127  class PDECoefficient: Line 242  class PDECoefficient:
242    
243      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
244         """         """
245         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
246    
247         @param shape:         @param domain: domain on which the PDE uses the coefficient
248         @param dim:         @type domain: L{Domain<escript.Domain>}
249           @param shape: suggested shape of the coefficient
250           @type shape: C{tuple} of C{int} values
251           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
252                     If no appropriate numbers could be identified, C{None} is returned
253           @rtype: C{tuple} of two C{int} values or C{None}
254         """         """
255         dim=domain.getDim()         dim=domain.getDim()
256         if len(shape)>0:         if len(shape)>0:
# Line 138  class PDECoefficient: Line 258  class PDECoefficient:
258         else:         else:
259             num=1             num=1
260         search=[]         search=[]
261         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
262            for e in range(num):            for u in range(num):
263               search.append((e,u))               for e in range(num):
264         search.sort(_CompTuple2)                  search.append((e,u))
265         for item in search:            search.sort(self.__CompTuple2)
266              for item in search:
267               s=self.getShape(domain,item[0],item[1])               s=self.getShape(domain,item[0],item[1])
268               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
269                   return (1,1)                   return (1,1)
270               else:               else:
271                   if s==shape: return item                   if s==shape: return item
272           elif self.definesNumEquation():
273              for e in range(num,0,-1):
274                 s=self.getShape(domain,e,0)
275                 if len(s)==0 and len(shape)==0:
276                     return (1,None)
277                 else:
278                     if s==shape: return (e,None)
279    
280           elif self.definesNumSolutions():
281              for u in range(num,0,-1):
282                 s=self.getShape(domain,0,u)
283                 if len(s)==0 and len(shape)==0:
284                     return (None,1)
285                 else:
286                     if s==shape: return (None,u)
287         return None         return None
288        def definesNumSolutions(self):
289           """
290           checks if the coefficient allows to estimate the number of solution components
291    
292           @return: True if the coefficient allows an estimate of the number of solution components
293           @rtype: C{bool}
294           """
295           for i in self.pattern:
296                 if i==self.BY_SOLUTION: return True
297           return False
298    
299        def definesNumEquation(self):
300           """
301           checks if the coefficient allows to estimate the number of equations
302    
303           @return: True if the coefficient allows an estimate of the number of equations
304           @rtype: C{bool}
305           """
306           for i in self.pattern:
307                 if i==self.BY_EQUATION: return True
308           return False
309    
310        def __CompTuple2(self,t1,t2):
311          """
312          Compare two tuples of possible number of equations and number of solutions
313    
314          @param t1: The first tuple
315          @param t2: The second tuple
316    
317          """
318    
319          dif=t1[0]+t1[1]-(t2[0]+t2[1])
320          if dif<0: return 1
321          elif dif>0: return -1
322          else: return 0
323    
324      def getShape(self,domain,numEquations=1,numSolutions=1):      def getShape(self,domain,numEquations=1,numSolutions=1):
325          """         """
326      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
327    
328      @param e:         @param domain: domain on which the PDE uses the coefficient
329      @param u:         @type domain: L{Domain<escript.Domain>}
330      @param dim:         @param numEquations: number of equations of the PDE
331      """         @type numEquations: C{int}
332          dim=domain.getDim()         @param numSolutions: number of components of the PDE solution
333          s=()         @type numSolutions: C{int}
334          for i in self.pattern:         @return: shape of the coefficient
335               if i==self.EQUATION:         @rtype: C{tuple} of C{int} values
336           """
337           dim=domain.getDim()
338           s=()
339           for i in self.pattern:
340                 if i==self.BY_EQUATION:
341                  if numEquations>1: s=s+(numEquations,)                  if numEquations>1: s=s+(numEquations,)
342               elif i==self.SOLUTION:               elif i==self.BY_SOLUTION:
343                  if numSolutions>1: s=s+(numSolutions,)                  if numSolutions>1: s=s+(numSolutions,)
344               else:               else:
345                  s=s+(dim,)                  s=s+(dim,)
346          return s         return s
347    
348  class LinearPDE:  class LinearPDE(object):
349     """     """
350     Class to define a linear PDE of the form     This class is used to define a general linear, steady, second order PDE
351       for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
352    
353     \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]  
354    
355     with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
356    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
357    
358     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
359       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
360       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
361       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
362       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
363       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
364       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
365    
366     \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]  
367    
368     and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
369    
370       where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
371    
372    
373       Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
374    
375       M{u=r}  where M{q>0}
376    
377       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
378       The constraints override any other condition set by the PDE or the boundary condition.
379    
380       The PDE is symmetrical if
381    
382       M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
383    
384       For a system of PDEs and a solution with several components the PDE has the form
385    
386       M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
387    
388       M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
389       The natural boundary conditions take the form:
390    
391       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
392    
393     \f[  
394     u_i=r_i \quad \mathrm{where} \quad q_i>0     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
395     \f]  
396       Constraints take the form
397    
398       M{u[i]=r[i]}  where  M{q[i]>0}
399    
400       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
401    
402       The system of PDEs is symmetrical if
403    
404            - M{A[i,j,k,l]=A[k,l,i,j]}
405            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
406            - M{B[i,j,k]=C[k,i,j]}
407            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
408            - M{D[i,k]=D[i,k]}
409            - M{D_reduced[i,k]=D_reduced[i,k]}
410            - M{d[i,k]=d[k,i]}
411            - M{d_reduced[i,k]=d_reduced[k,i]}
412    
413       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
414       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
415       defined as
416    
417       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
418    
419       For the case of single solution component and single PDE M{J} is defined
420    
421       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
422    
423       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
424       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
425       the contact condition takes the form
426    
427       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
428    
429       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
430       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
431       L{jump<util.jump>}.
432       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
433       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
434       In case of a single PDE and a single component solution the contact condition takes the form
435    
436       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
437    
438       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
439    
440       @cvar DEFAULT: The default method used to solve the system of linear equations
441       @cvar DIRECT: The direct solver based on LDU factorization
442       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
443       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
444       @cvar CR: The conjugate residual method
445       @cvar CGS: The conjugate gardient square method
446       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
447       @cvar SSOR: The symmetric overrealaxtion method
448       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449       @cvar ILUT: The incomplete LU factorization preconditioner with will in
450       @cvar JACOBI: The Jacobi preconditioner
451       @cvar GMRES: The Gram-Schmidt minimum residual method
452       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
453       @cvar LUMPING: Matrix lumping.
454       @cvar NO_REORDERING: No matrix reordering allowed
455       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
456       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
457       @cvar PASO: PASO solver package
458       @cvar SCSL: SGI SCSL solver library
459       @cvar MKL: Intel's MKL solver library
460       @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462       @cvar ITERATIVE: The default iterative solver
463       @cvar AMG: algebraic multi grid
464       @cvar RILU: recursive ILU
465    
466     """     """
467     TOL=1.e-13     DEFAULT= 0
468     # solver methods     DIRECT= 1
469     UNKNOWN=-1     CHOLEVSKY= 2
470     DEFAULT_METHOD=0     PCG= 3
471     DIRECT=1     CR= 4
472     CHOLEVSKY=2     CGS= 5
473     PCG=3     BICGSTAB= 6
474     CR=4     SSOR= 7
475     CGS=5     ILU0= 8
476     BICGSTAB=6     ILUT= 9
477     SSOR=7     JACOBI= 10
478     ILU0=8     GMRES= 11
479     ILUT=9     PRES20= 12
480     JACOBI=10     LUMPING= 13
481     GMRES=11     NO_REORDERING= 17
482     PRES20=12     MINIMUM_FILL_IN= 18
483     LUMPING=13     NESTED_DISSECTION= 19
484     # matrix reordering:     SCSL= 14
485     NO_REORDERING=0     MKL= 15
486     MINIMUM_FILL_IN=1     UMFPACK= 16
487     NESTED_DISSECTION=2     ITERATIVE= 20
488     # important keys in the dictonary used to hand over options to the solver library:     PASO= 21
489     METHOD_KEY="method"     AMG= 22
490     SYMMETRY_KEY="symmetric"     RILU = 23
491     TOLERANCE_KEY="tolerance"     TRILINOS = 24
492    
493       SMALL_TOLERANCE=1.e-13
494       __PACKAGE_KEY="package"
495       __METHOD_KEY="method"
496       __SYMMETRY_KEY="symmetric"
497       __TOLERANCE_KEY="tolerance"
498       __PRECONDITIONER_KEY="preconditioner"
499    
500    
501     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
# Line 228  class LinearPDE: Line 503  class LinearPDE:
503       initializes a new linear PDE       initializes a new linear PDE
504    
505       @param domain: domain of the PDE       @param domain: domain of the PDE
506       @type domain: L{Domain}       @type domain: L{Domain<escript.Domain>}
507       @param numEquations: number of equations. If numEquations==None the number of equations       @param numEquations: number of equations. If numEquations==None the number of equations
508                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
509       @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
510                            is exracted from the PDE coefficients.                            is exracted from the PDE coefficients.
511       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
512    
   
513       """       """
514         super(LinearPDE, self).__init__()
515       #       #
516       #   the coefficients of the general PDE:       #   the coefficients of the general PDE:
517       #       #
518       self.__COEFFICIENTS_OF_GENEARL_PDE={       self.__COEFFICIENTS_OF_GENEARL_PDE={
519         "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),
520         "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),
521         "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),
522         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
524         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
525         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
526         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529         "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),
530         "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),
531           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
534           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
540           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
541    
542       # COEFFICIENTS can be overwritten by subclasses:       # COEFFICIENTS can be overwritten by subclasses:
543       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE       self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
544         self.__altered_coefficients=False
545       # initialize attributes       # initialize attributes
546       self.__debug=debug       self.__debug=debug
547       self.__domain=domain       self.__domain=domain
# Line 264  class LinearPDE: Line 550  class LinearPDE:
550       self.__resetSystem()       self.__resetSystem()
551    
552       # set some default values:       # set some default values:
553       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
554       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
555       self.__tolerance=1.e-8       self.__tolerance=1.e-8
556       self.__solver_method=self.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
557       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
558         self.__preconditioner=self.DEFAULT
559         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
560       self.__sym=False       self.__sym=False
561    
562       self.resetCoefficients()       self.resetCoefficients()
# Line 278  class LinearPDE: Line 565  class LinearPDE:
565     #    general stuff:     #    general stuff:
566     # =============================================================================     # =============================================================================
567     def __str__(self):     def __str__(self):
568         return "<LinearPDE %d>"%id(self)       """
569         returns string representation of the PDE
570    
571         @return: a simple representation of the PDE
572         @rtype: C{str}
573         """
574         return "<LinearPDE %d>"%id(self)
575     # =============================================================================     # =============================================================================
576     #    debug :     #    debug :
577     # =============================================================================     # =============================================================================
578     def setDebugOn(self):     def setDebugOn(self):
579       """       """
580       switches on debugging       switches on debugging
581       """       """
582       self.__debug=not None       self.__debug=not None
# Line 296  class LinearPDE: Line 589  class LinearPDE:
589    
590     def trace(self,text):     def trace(self,text):
591       """       """
592       print the text message if debugging is swiched on.       print the text message if debugging is swiched on.
593         @param text: message
594       @param name: name of the coefficient enquired.       @type text: C{string}
      @type name: C{string}  
595       """       """
596       if self.__debug: print "%s: %s"%(str(self),text)       if self.__debug: print "%s: %s"%(str(self),text)
597    
# Line 309  class LinearPDE: Line 601  class LinearPDE:
601     def getDomain(self):     def getDomain(self):
602       """       """
603       returns the domain of the PDE       returns the domain of the PDE
       
      @return : the domain of the PDE  
      @rtype : C{Domain}  
604    
605         @return: the domain of the PDE
606         @rtype: L{Domain<escript.Domain>}
607       """       """
608       return self.__domain       return self.__domain
609    
# Line 320  class LinearPDE: Line 611  class LinearPDE:
611       """       """
612       returns the spatial dimension of the PDE       returns the spatial dimension of the PDE
613    
614       @return : the spatial dimension of the PDE domain       @return: the spatial dimension of the PDE domain
615       @rtype : C{int}       @rtype: C{int}
616       """       """
617       return self.getDomain().getDim()       return self.getDomain().getDim()
618    
# Line 329  class LinearPDE: Line 620  class LinearPDE:
620       """       """
621       returns the number of equations       returns the number of equations
622    
623       @return : the number of equations       @return: the number of equations
624       @rtype : C{int}       @rtype: C{int}
625       @raise UndefinedPDEError: if the number of equations is not be specified yet.       @raise UndefinedPDEError: if the number of equations is not be specified yet.
626       """       """
627       if self.__numEquations==None:       if self.__numEquations==None:
# Line 342  class LinearPDE: Line 633  class LinearPDE:
633       """       """
634       returns the number of unknowns       returns the number of unknowns
635    
636       @return : the number of unknowns       @return: the number of unknowns
637       @rtype : C{int}       @rtype: C{int}
638       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.       @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
639       """       """
640       if self.__numSolutions==None:       if self.__numSolutions==None:
# Line 351  class LinearPDE: Line 642  class LinearPDE:
642       else:       else:
643          return self.__numSolutions          return self.__numSolutions
644    
645       def reduceEquationOrder(self):
646         """
647         return status for order reduction for equation
648    
649         @return: return True is reduced interpolation order is used for the represenation of the equation
650         @rtype: L{bool}
651         """
652         return self.__reduce_equation_order
653    
654       def reduceSolutionOrder(self):
655         """
656         return status for order reduction for the solution
657    
658         @return: return True is reduced interpolation order is used for the represenation of the solution
659         @rtype: L{bool}
660         """
661         return self.__reduce_solution_order
662    
663     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
664       """       """
665       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}  
666    
667         @return: representation space of equation
668         @rtype: L{FunctionSpace<escript.FunctionSpace>}
669       """       """
670       return self.__row_function_space       if self.reduceEquationOrder():
671             return escript.ReducedSolution(self.getDomain())
672         else:
673             return escript.Solution(self.getDomain())
674    
675     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
676       """       """
677       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}  
678    
679         @return: representation space of solution
680         @rtype: L{FunctionSpace<escript.FunctionSpace>}
681       """       """
682       return self.__column_function_space       if self.reduceSolutionOrder():
683             return escript.ReducedSolution(self.getDomain())
684         else:
685             return escript.Solution(self.getDomain())
686    
687    
688     def getOperator(self):     def getOperator(self):
689       """       """
690       provides access to the operator of the PDE       provides access to the operator of the PDE
691    
692       @return : the operator of the PDE       @return: the operator of the PDE
693       @rtype : L{Operator}       @rtype: L{Operator<escript.Operator>}
694       """       """
695       m=self.getSystem()[0]       m=self.getSystem()[0]
696       if self.isUsingLumping():       if self.isUsingLumping():
# Line 388  class LinearPDE: Line 701  class LinearPDE:
701     def getRightHandSide(self):     def getRightHandSide(self):
702       """       """
703       provides access to the right hand side of the PDE       provides access to the right hand side of the PDE
704         @return: the right hand side of the PDE
705       @return : the right hand side of the PDE       @rtype: L{Data<escript.Data>}
      @rtype : L{escript.Data}  
706       """       """
707       r=self.getSystem()[1]       r=self.getSystem()[1]
708       if self.isUsingLumping():       if self.isUsingLumping():
# Line 404  class LinearPDE: Line 716  class LinearPDE:
716    
717       @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}
718                 the current solution is used.                 the current solution is used.
719       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
720       @return : image of u       @return: image of u
721       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
722       """       """
723       if u==None:       if u==None:
724            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
725       else:       else:
726          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
727    
728     def getResidual(self,u=None):     def getResidual(self,u=None):
729       """       """
# Line 419  class LinearPDE: Line 731  class LinearPDE:
731    
732       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
733                 the current solution is used.                 the current solution is used.
734       @type u: L{escript.Data} or None       @type u: L{Data<escript.Data>} or None
735       @return : residual of u       @return: residual of u
736       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
737       """       """
738       return self.applyOperator(u)-self.getRightHandSide()       return self.applyOperator(u)-self.getRightHandSide()
739    
# Line 429  class LinearPDE: Line 741  class LinearPDE:
741        """        """
742        test the PDE for symmetry.        test the PDE for symmetry.
743    
744          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
745       @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.        @type verbose: C{bool}
746       @type verbose: C{bool}        @return:  True if the PDE is symmetric.
747       @return:  True if the PDE is symmetric.        @rtype: L{Data<escript.Data>}
      @rtype : C{escript.Data}  
   
748        @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.
749        """        """
750        verbose=verbose or self.debug()        verbose=verbose or self.__debug
751        out=True        out=True
752        if self.getNumSolutions()!=self.getNumEquations():        if self.getNumSolutions()!=self.getNumEquations():
753           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 755  class LinearPDE:
755        else:        else:
756           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
757           if not A.isEmpty():           if not A.isEmpty():
758              tol=util.Lsup(A)*self.TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
759              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
760                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
761                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 469  class LinearPDE: Line 779  class LinearPDE:
779              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"
780              out=False              out=False
781           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
782              tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
783              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
784                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
785                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 485  class LinearPDE: Line 795  class LinearPDE:
795           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
796             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
797             if not D.isEmpty():             if not D.isEmpty():
798               tol=util.Lsup(D)*self.TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
799               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
800                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
801                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
802                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
803                        out=False                        out=False
804               d=self.getCoefficientOfGeneralPDE("d")
805               if not d.isEmpty():
806                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
807                 for i in range(self.getNumEquations()):
808                    for k in range(self.getNumSolutions()):
809                      if util.Lsup(d[i,k]-d[k,i])>tol:
810                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
811                          out=False
812               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
813               if not d_contact.isEmpty():
814                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
815                 for i in range(self.getNumEquations()):
816                    for k in range(self.getNumSolutions()):
817                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
818                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
819                          out=False
820             # and now the reduced coefficients
821             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
822             if not A_reduced.isEmpty():
823                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
824                if self.getNumSolutions()>1:
825                   for i in range(self.getNumEquations()):
826                      for j in range(self.getDim()):
827                         for k in range(self.getNumSolutions()):
828                            for l in range(self.getDim()):
829                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
830                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
831                                   out=False
832                else:
833                   for j in range(self.getDim()):
834                      for l in range(self.getDim()):
835                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
836                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
837                            out=False
838             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
839             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
840             if B_reduced.isEmpty() and not C_reduced.isEmpty():
841                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
842                out=False
843             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
847                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
848                if self.getNumSolutions()>1:
849                   for i in range(self.getNumEquations()):
850                       for j in range(self.getDim()):
851                          for k in range(self.getNumSolutions()):
852                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
853                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
854                                  out=False
855                else:
856                   for j in range(self.getDim()):
857                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
858                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
859                         out=False
860             if self.getNumSolutions()>1:
861               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
862               if not D_reduced.isEmpty():
863                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
870               if not d_reduced.isEmpty():
871                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
872                 for i in range(self.getNumEquations()):
873                    for k in range(self.getNumSolutions()):
874                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
875                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
876                          out=False
877               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
878               if not d_contact_reduced.isEmpty():
879                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
880                 for i in range(self.getNumEquations()):
881                    for k in range(self.getNumSolutions()):
882                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
883                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
884                          out=False
885        return out        return out
886    
887     def getSolution(self,**options):     def getSolution(self,**options):
888         """         """
889         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.
890    
891         @return: the solution         @return: the solution
892         @rtype: L{escript.Data}         @rtype: L{Data<escript.Data>}
893         @param options: solver options         @param options: solver options
894         @keyword verbose:         @keyword verbose: True to get some information during PDE solution
895         @keyword reordering: reordering scheme to be used during elimination         @type verbose: C{bool}
896         @keyword preconditioner: preconditioner method to be used         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
897                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
898         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
899         @keyword drop_tolerance:         @keyword drop_tolerance: threshold for drupping in L{ILUT}
900         @keyword drop_storage:         @keyword drop_storage: maximum of allowed memory in L{ILUT}
901         @keyword truncation:         @keyword truncation: maximum number of residuals in L{GMRES}
902         @keyword restart:         @keyword restart: restart cycle length in L{GMRES}
903         """         """
904         if not self.__solution_isValid:         if not self.__solution_isValid:
905            mat,f=self.getSystem()            mat,f=self.getSystem()
906            if self.isUsingLumping():            if self.isUsingLumping():
907               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
908            else:            else:
909               options[self.TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
910               options[self.METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
911               options[self.SYMMETRY_KEY]=self.isSymmetric()               options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
912                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
913                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
914               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
915               self.trace("solver options: %s"%str(options))               self.trace("solver options: %s"%str(options))
916               self.__solution=mat.solve(f,options)               self.__solution=mat.solve(f,options)
# Line 526  class LinearPDE: Line 919  class LinearPDE:
919    
920     def getFlux(self,u=None):     def getFlux(self,u=None):
921       """       """
922       returns the flux J_ij for a given u       returns the flux M{J} for a given M{u}
923    
924         \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]  
925    
926       @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}  
927    
928         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
929    
930         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
931         @type u: L{Data<escript.Data>} or None
932         @return: flux
933         @rtype: L{Data<escript.Data>}
934       """       """
935       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
936       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))) \
937               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
938               -util.self.getCoefficientOfGeneralPDE("X") \
939               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X_reduced")
942     # =============================================================================     # =============================================================================
943     #   solver settings:     #   solver settings:
944     # =============================================================================     # =============================================================================
945     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
946         """         """
947         sets a new solver         sets a new solver
948    
949         @param solver: sets a new solver method.         @param solver: sets a new solver method.
950         @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}
951           @param preconditioner: sets a new solver method.
952         """         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
953         if solver==None: solve=self.DEFAULT_METHOD         """
954         if not solver==self.getSolverMethod():         if solver==None: solver=self.__solver_method
955           if preconditioner==None: preconditioner=self.__preconditioner
956           if solver==None: solver=self.DEFAULT
957           if preconditioner==None: preconditioner=self.DEFAULT
958           if not (solver,preconditioner)==self.getSolverMethod():
959             self.__solver_method=solver             self.__solver_method=solver
960               self.__preconditioner=preconditioner
961             self.__checkMatrixType()             self.__checkMatrixType()
962             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
963    
# Line 562  class LinearPDE: Line 965  class LinearPDE:
965         """         """
966         returns the name of the solver currently used         returns the name of the solver currently used
967    
968         @return : the name of the solver currently used.         @return: the name of the solver currently used.
969         @rtype: C{string}         @rtype: C{string}
970         """         """
971    
972         m=self.getSolverMethod()         m=self.getSolverMethod()
973         if m==self.DEFAULT_METHOD: return "DEFAULT_METHOD"         p=self.getSolverPackage()
974         elif m==self.DIRECT: return "DIRECT"         method=""
975         elif m==self.CHOLEVSKY: return "CHOLEVSKY"         if m[0]==self.DEFAULT: method="DEFAULT"
976         elif m==self.PCG: return "PCG"         elif m[0]==self.DIRECT: method= "DIRECT"
977         elif m==self.CR: return "CR"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
978         elif m==self.CGS: return "CGS"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
979         elif m==self.BICGSTAB: return "BICGSTAB"         elif m[0]==self.PCG: method= "PCG"
980         elif m==self.SSOR: return "SSOR"         elif m[0]==self.CR: method= "CR"
981         elif m==self.GMRES: return "GMRES"         elif m[0]==self.CGS: method= "CGS"
982         elif m==self.PRES20: return "PRES20"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
983         elif m==self.LUMPING: return "LUMPING"         elif m[0]==self.SSOR: method= "SSOR"
984         return None         elif m[0]==self.GMRES: method= "GMRES"
985                 elif m[0]==self.PRES20: method= "PRES20"
986           elif m[0]==self.LUMPING: method= "LUMPING"
987           elif m[0]==self.AMG: method= "AMG"
988           if m[1]==self.DEFAULT: method+="+DEFAULT"
989           elif m[1]==self.JACOBI: method+= "+JACOBI"
990           elif m[1]==self.ILU0: method+= "+ILU0"
991           elif m[1]==self.ILUT: method+= "+ILUT"
992           elif m[1]==self.SSOR: method+= "+SSOR"
993           elif m[1]==self.AMG: method+= "+AMG"
994           elif m[1]==self.RILU: method+= "+RILU"
995           if p==self.DEFAULT: package="DEFAULT"
996           elif p==self.PASO: package= "PASO"
997           elif p==self.MKL: package= "MKL"
998           elif p==self.SCSL: package= "SCSL"
999           elif p==self.UMFPACK: package= "UMFPACK"
1000           elif p==self.TRILINOS: package= "TRILINOS"
1001           else : method="unknown"
1002           return "%s solver of %s package"%(method,package)
1003    
1004    
1005     def getSolverMethod(self):     def getSolverMethod(self):
1006         """         """
1007         returns the solver method         returns the solver method
1008      
1009         @return : the solver method currently be used.         @return: the solver method currently be used.
1010         @rtype : C{int}         @rtype: C{int}
1011           """
1012           return self.__solver_method,self.__preconditioner
1013    
1014       def setSolverPackage(self,package=None):
1015           """
1016           sets a new solver package
1017    
1018           @param package: sets a new solver method.
1019           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1020           """
1021           if package==None: package=self.DEFAULT
1022           if not package==self.getSolverPackage():
1023               self.__solver_package=package
1024               self.__checkMatrixType()
1025               self.trace("New solver is %s"%self.getSolverMethodName())
1026    
1027       def getSolverPackage(self):
1028         """         """
1029         return self.__solver_method         returns the package of the solver
1030    
1031           @return: the solver package currently being used.
1032           @rtype: C{int}
1033           """
1034           return self.__solver_package
1035    
1036     def isUsingLumping(self):     def isUsingLumping(self):
1037        """        """
1038        checks if matrix lumping is used a solver method        checks if matrix lumping is used a solver method
1039    
1040        @return : True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
1041        @rtype: C{bool}        @rtype: C{bool}
1042        """        """
1043        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
1044    
1045     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1046         """         """
1047         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{|.|}
1048    
1049                 |self.getResidual()|<tol*|self.getRightHandSide()|         M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1050    
1051         defines the stopping criterion.         defines the stopping criterion.
1052    
1053         @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
1054                     the system will be resolved.                     the system will be resolved.
1055         @type solver: C{float}         @type tol: positive C{float}
1056         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1057         """         """
1058         if not tol>0:         if not tol>0:
1059             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1060         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1061         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1062         self.__tolerance=tol         self.__tolerance=tol
# Line 634  class LinearPDE: Line 1077  class LinearPDE:
1077     def isSymmetric(self):     def isSymmetric(self):
1078        """        """
1079        checks if symmetry is indicated.        checks if symmetry is indicated.
1080        
1081        @return : True is a symmetric PDE is indicated, otherwise False is returned        @return: True is a symmetric PDE is indicated, otherwise False is returned
1082        @rtype : C{bool}        @rtype: C{bool}
1083        """        """
1084        return self.__sym        return self.__sym
1085    
# Line 661  class LinearPDE: Line 1104  class LinearPDE:
1104     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1105        """        """
1106        sets the symmetry flag to flag        sets the symmetry flag to flag
1107    
1108        @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.
1109        @type flag: C{bool}        @type flag: C{bool}
1110        """        """
# Line 670  class LinearPDE: Line 1113  class LinearPDE:
1113        else:        else:
1114           self.setSymmetryOff()           self.setSymmetryOff()
1115    
     
1116     # =============================================================================     # =============================================================================
1117     # function space handling for the equation as well as the solution     # function space handling for the equation as well as the solution
1118     # =============================================================================     # =============================================================================
1119     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1120       """       """
1121       switches on reduced order for solution and equation representation       switches on reduced order for solution and equation representation
1122    
1123         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1124       """       """
1125       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1126       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
# Line 684  class LinearPDE: Line 1128  class LinearPDE:
1128     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1129       """       """
1130       switches off reduced order for solution and equation representation       switches off reduced order for solution and equation representation
1131    
1132         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1133       """       """
1134       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1135       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1136    
1137     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1138       """       """
1139       sets order reduction for both solution and equation representation according to flag.       sets order reduction for both solution and equation representation according to flag.
1140         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
      @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or  
1141                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1142       @type flag: C{bool}       @type flag: C{bool}
1143         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1144       """       """
1145       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1146       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
# Line 703  class LinearPDE: Line 1149  class LinearPDE:
1149     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1150       """       """
1151       switches on reduced order for solution representation       switches on reduced order for solution representation
1152    
1153         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1154       """       """
1155       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1156       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1157                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1158           self.trace("Reduced order is used to solution representation.")           self.trace("Reduced order is used to solution representation.")
1159           self.__column_function_space=new_fs           self.__reduce_solution_order=True
1160           self.__resetSystem()           self.__resetSystem()
1161    
1162     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1163       """       """
1164       switches off reduced order for solution representation       switches off reduced order for solution representation
1165    
1166         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1167       """       """
1168       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1169       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1170                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1171           self.trace("Full order is used to interpolate solution.")           self.trace("Full order is used to interpolate solution.")
1172           self.__column_function_space=new_fs           self.__reduce_solution_order=False
1173           self.__resetSystem()           self.__resetSystem()
1174    
1175     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1176       """       """
1177       sets order for test functions according to flag       sets order for test functions according to flag
1178    
1179       @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
1180                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1181       @type flag: C{bool}       @type flag: C{bool}
1182         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1183       """       """
1184       if flag:       if flag:
1185          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
# Line 736  class LinearPDE: Line 1189  class LinearPDE:
1189     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1190       """       """
1191       switches on reduced order for equation representation       switches on reduced order for equation representation
1192    
1193         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1194       """       """
1195       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1196       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1197                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1198           self.trace("Reduced order is used for test functions.")           self.trace("Reduced order is used for test functions.")
1199           self.__row_function_space=new_fs           self.__reduce_equation_order=True
1200           self.__resetSystem()           self.__resetSystem()
1201    
1202     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1203       """       """
1204       switches off reduced order for equation representation       switches off reduced order for equation representation
1205    
1206         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1207       """       """
1208       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1209       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1210                  raise RuntimeError,"order cannot be altered after coefficients have been defined."
1211           self.trace("Full order is used for test functions.")           self.trace("Full order is used for test functions.")
1212           self.__row_function_space=new_fs           self.__reduce_equation_order=False
1213           self.__resetSystem()           self.__resetSystem()
1214    
1215     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1216       """       """
1217       sets order for test functions according to flag       sets order for test functions according to flag
1218    
1219       @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
1220                    if flag is not present order reduction is switched off                    if flag is not present order reduction is switched off
1221       @type flag: C{bool}       @type flag: C{bool}
1222         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1223       """       """
1224       if flag:       if flag:
1225          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
# Line 773  class LinearPDE: Line 1233  class LinearPDE:
1233       """       """
1234       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.
1235       """       """
1236       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1237       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1238           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1239           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
1240           self.__resetSystem()           self.__resetSystem()
1241     #     #
1242     #   rebuild switches :     #   rebuild switches :
1243     #     #
1244     def __invalidateSolution(self):     def __invalidateSolution(self):
1245         """         """
1246         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 1252  class LinearPDE:
1252         """         """
1253         indicates the operator has to be rebuilt next time it is used         indicates the operator has to be rebuilt next time it is used
1254         """         """
1255         if self.__operator_isValid: self.trace("Operator has to be rebuilt.")         if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1256         self.__invalidateSolution()         self.__invalidateSolution()
1257         self.__operator_isValid=False         self.__operator_is_Valid=False
1258    
1259     def __invalidateRightHandSide(self):     def __invalidateRightHandSide(self):
1260         """         """
# Line 819  class LinearPDE: Line 1279  class LinearPDE:
1279         """         """
1280         self.trace("New System is built from scratch.")         self.trace("New System is built from scratch.")
1281         self.__operator=escript.Operator()         self.__operator=escript.Operator()
1282         self.__operator_isValid=False         self.__operator_is_Valid=False
1283         self.__righthandside=escript.Data()         self.__righthandside=escript.Data()
1284         self.__righthandside_isValid=False         self.__righthandside_isValid=False
1285         self.__solution=escript.Data()         self.__solution=escript.Data()
1286         self.__solution_isValid=False         self.__solution_isValid=False
1287     #     #
1288     #    system initialization:     #    system initialization:
1289     #     #
1290     def __getNewOperator(self):     def __getNewOperator(self):
1291         """         """
1292         returns an instance of a new operator         returns an instance of a new operator
# Line 877  class LinearPDE: Line 1337  class LinearPDE:
1337         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1338             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1339         else:         else:
1340             self.__righthandside*=0             self.__righthandside.setToZero()
1341             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1342         return self.__righthandside         return self.__righthandside
1343    
# Line 888  class LinearPDE: Line 1348  class LinearPDE:
1348         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1349             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
1350         else:         else:
1351             self.__operator.setValue(0.)             self.__operator.resetValues()
1352             self.trace("Operator reset to zero")             self.trace("Operator reset to zero")
1353         return self.__operator         return self.__operator
1354    
# Line 909  class LinearPDE: Line 1369  class LinearPDE:
1369               else:               else:
1370                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())                  r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1371               u.copyWithMask(r_s,col_q)               u.copyWithMask(r_s,col_q)
1372               if not self.__righthandside.isEmpty():               if not self.__righthandside.isEmpty():
1373                  self.__righthandside-=self.__operator*u                  self.__righthandside-=self.__operator*u
1374                  self.__righthandside=self.copyConstraint(self.__righthandside)                  self.__righthandside=self.copyConstraint(self.__righthandside)
1375               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)               self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
# Line 920  class LinearPDE: Line 1380  class LinearPDE:
1380       """       """
1381       return the value of the coefficient name of the general PDE.       return the value of the coefficient name of the general PDE.
1382    
1383       @note This method is called by the assembling routine it can be overwritten       @note: This method is called by the assembling routine it can be overwritten
1384             to map coefficients of a particular PDE to the general PDE.             to map coefficients of a particular PDE to the general PDE.
1385         @param name: name of the coefficient requested.
      @param name: name of the coefficient requested.  
1386       @type name: C{string}       @type name: C{string}
1387       @return : the value of the coefficient  name       @return: the value of the coefficient  name
1388       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1389       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1390                    "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},
1391                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1392       """       """
1393       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1394          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 938  class LinearPDE: Line 1398  class LinearPDE:
1398     def hasCoefficientOfGeneralPDE(self,name):     def hasCoefficientOfGeneralPDE(self,name):
1399       """       """
1400       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.
1401        
1402       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1403       @type name: C{string}       @type name: C{string}
1404       @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.
1405       @rtype : C{bool}       @rtype: C{bool}
1406        
1407       """       """
1408       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1409    
# Line 953  class LinearPDE: Line 1413  class LinearPDE:
1413    
1414       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1415       @type name: C{string}       @type name: C{string}
1416       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1417       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1418       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1419                    "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},
1420                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1421       """       """
1422       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1423          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 1426  class LinearPDE:
1426    
1427     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1428       """       """
1429       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
1430    
1431       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1432       @type name: C{string}       @type name: C{string}
1433       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1434       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1435       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1436                    "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},
1437                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1438       """       """
1439       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1440          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 1447  class LinearPDE:
1447    
1448       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1449       @type name: C{string}       @type name: C{string}
1450       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1451       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1452       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1453                    "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},
1454                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1455       """       """
1456       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1457          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 1465  class LinearPDE:
1465       """       """
1466       returns the value of the coefficient name       returns the value of the coefficient name
1467    
1468       @param name: name of the coefficient requested.       @param name: name of the coefficient requested.
1469       @type name: C{string}       @type name: C{string}
1470       @return : the value of the coefficient name       @return: the value of the coefficient name
1471       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1472       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1473       """       """
1474       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1020  class LinearPDE: Line 1482  class LinearPDE:
1482    
1483       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1484       @type name: C{string}       @type name: C{string}
1485       @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.
1486       @rtype : C{bool}       @rtype: C{bool}
1487       """       """
1488       return self.COEFFICIENTS.has_key(name)       return self.COEFFICIENTS.has_key(name)
1489    
1490     def createCoefficient(self, name):     def createCoefficient(self, name):
1491       """       """
1492       create a L{escript.Data} object corresponding to coefficient name       create a L{Data<escript.Data>} object corresponding to coefficient name
1493    
1494       @return : a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1495       @rtype : L{escript.Data}       @rtype: L{Data<escript.Data>}
1496       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1497       """       """
1498       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1040  class LinearPDE: Line 1502  class LinearPDE:
1502    
1503     def getFunctionSpaceForCoefficient(self,name):     def getFunctionSpaceForCoefficient(self,name):
1504       """       """
1505       return the L{escript.FunctionSpace} to be used for coefficient name       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1506    
1507       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1508       @type name: C{string}       @type name: C{string}
1509       @return : the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1510       @rtype : L{escript.FunctionSpace}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1511       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1512       """       """
1513       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1514          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1515       else:       else:
1516          raise ValueError,"unknown coefficient %s requested"%name          raise ValueError,"unknown coefficient %s requested"%name
   
1517     def getShapeOfCoefficient(self,name):     def getShapeOfCoefficient(self,name):
1518       """       """
1519       return the shape of the coefficient name       return the shape of the coefficient name
1520    
1521       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1522       @type name: C{string}       @type name: C{string}
1523       @return : the shape of the coefficient name       @return: the shape of the coefficient name
1524       @rtype : C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1525       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1526       """       """
1527       if self.hasCoefficient(name):       if self.hasCoefficient(name):
# Line 1082  class LinearPDE: Line 1543  class LinearPDE:
1543       @param name: name of the coefficient enquired.       @param name: name of the coefficient enquired.
1544       @type name: C{string}       @type name: C{string}
1545       @raise IllegalCoefficient: if name is not a coefficient of the PDE.       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1546         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1547       """       """
1548       if self.hasCoefficient(name):       if self.hasCoefficient(name):
1549          self.trace("Coefficient %s has been altered."%name)          self.trace("Coefficient %s has been altered."%name)
1550          if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()          if not ((name=="q" or name=="r") and self.isUsingLumping()):
1551          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()             if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1552               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1553       else:       else:
1554          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1555    
1556     def copyConstraint(self,u):     def copyConstraint(self,u):
1557        """        """
1558        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}  
1559    
1560          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1561          @type u: L{Data<escript.Data>}
1562          @return: the input u modified by the constraints.
1563          @rtype: L{Data<escript.Data>}
1564          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1565        """        """
1566        q=self.getCoefficientOfGeneralPDE("q")        q=self.getCoefficientOfGeneralPDE("q")
1567        r=self.getCoefficientOfGeneralPDE("r")        r=self.getCoefficientOfGeneralPDE("r")
# Line 1116  class LinearPDE: Line 1578  class LinearPDE:
1578        """        """
1579        sets new values to coefficients        sets new values to coefficients
1580    
1581        @note This method is called by the assembling routine it can be overwritten        @param coefficients: new values assigned to coefficients
1582             to map coefficients of a particular PDE to the general PDE.        @keyword A: value for coefficient A.
1583          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584        @param name: name of the coefficient requested.        @keyword A_reduced: value for coefficient A_reduced.
1585        @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}.  
1586        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1587        @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>}.
1588          @keyword B_reduced: value for coefficient B_reduced
1589          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1590        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1591        @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>}.
1592          @keyword C_reduced: value for coefficient C_reduced
1593          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1595        @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>}.
1596          @keyword D_reduced: value for coefficient D_reduced
1597          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1599        @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>}.
1600          @keyword X_reduced: value for coefficient X_reduced
1601          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1603        @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>}.
1604          @keyword Y_reduced: value for coefficient Y_reduced
1605          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1606        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1607        @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>}.
1608          @keyword d_reduced: value for coefficient d_reduced
1609          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1610        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1611        @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>}.
1612        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1613        @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>}.
1614                         or  L{escript.FunctionOnContactZero}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1615          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1616        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1617        @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>}.
1618                         or  L{escript.FunctionOnContactZero}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1619          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1620        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1621        @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>}
1622                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
1623        @keyword q: mask for location of constraints        @keyword q: mask for location of constraints
1624        @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>}
1625                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1626        @raise IllegalCoefficient: if an unknown coefficient keyword is used.        @raise IllegalCoefficient: if an unknown coefficient keyword is used.
   
1627        """        """
1628        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1629        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
# Line 1178  class LinearPDE: Line 1651  class LinearPDE:
1651        # 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:
1652        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1653          try:          try:
1654             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1655                                             self.getNumEquations(),self.getNumSolutions(),
1656                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1657               self.alteredCoefficient(i)
1658            except IllegalCoefficientFunctionSpace,m:
1659                # if the function space is wrong then we try the reduced version:
1660                i_red=i+"_reduced"
1661                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1662                    try:
1663                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1664                                                          self.getNumEquations(),self.getNumSolutions(),
1665                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1666                        self.alteredCoefficient(i_red)
1667                    except IllegalCoefficientValue,m:
1668                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1669                    except IllegalCoefficientFunctionSpace,m:
1670                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1671                else:
1672                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1674             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1675          self.alteredCoefficient(i)        self.__altered_coefficients=True
   
1676        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1677        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
1678           q=self.getCoefficientOfGeneralPDE("q")           q=self.getCoefficientOfGeneralPDE("q")
1679           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1680           homogeneous_constraint=True           homogeneous_constraint=True
1681           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1682               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1683                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1684                 self.__invalidateSystem()                 self.__invalidateSystem()
1685    
   
1686     def getSystem(self):     def getSystem(self):
1687         """         """
1688         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1689    
1690           @return: the discrete version of the PDE
1691           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1692         """         """
1693         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1694            if self.isUsingLumping():            if self.isUsingLumping():
1695                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1696                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1697                   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"
1698                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Lumped matrix does not allow coefficient B"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1699                   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."
1700                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1701                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1702                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1703                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1704                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1705                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1706                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1707                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1708                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1709                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1710                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1711                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1712                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1713                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1714                     D=self.getCoefficientOfGeneralPDE("D")
1715                     d=self.getCoefficientOfGeneralPDE("d")
1716                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1717                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1718                     if not D.isEmpty():
1719                         if self.getNumSolutions()>1:
1720                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1721                         else:
1722                            D_times_e=D
1723                     else:
1724                        D_times_e=escript.Data()
1725                     if not d.isEmpty():
1726                         if self.getNumSolutions()>1:
1727                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1728                         else:
1729                            d_times_e=d
1730                     else:
1731                        d_times_e=escript.Data()
1732          
1733                     if not D_reduced.isEmpty():
1734                         if self.getNumSolutions()>1:
1735                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1736                         else:
1737                            D_reduced_times_e=D_reduced
1738                     else:
1739                        D_reduced_times_e=escript.Data()
1740                     if not d_reduced.isEmpty():
1741                         if self.getNumSolutions()>1:
1742                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1743                         else:
1744                            d_reduced_times_e=d_reduced
1745                     else:
1746                        d_reduced_times_e=escript.Data()
1747    
1748                     self.__operator=self.__getNewRightHandSide()
1749                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1750                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1751                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1752                     else:
1753                        self.getDomain().addPDEToRHS(self.__operator, \
1754                                                     escript.Data(), \
1755                                                     D_times_e, \
1756                                                     d_times_e,\
1757                                                     escript.Data())
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_reduced_times_e, \
1761                                                     d_reduced_times_e,\
1762                                                     escript.Data())
1763                     self.__operator=1./self.__operator
1764                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1765                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1766                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1767                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1768                                 self.getCoefficientOfGeneralPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1769                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1770                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1771                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1772                     self.getDomain().addPDEToRHS(self.__righthandside, \
1773                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1774                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1775                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1777                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1778                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1779            else:            else:
1780               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1781                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1782                                 self.getCoefficientOfGeneralPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1783                                 self.getCoefficientOfGeneralPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
# Line 1242  class LinearPDE: Line 1789  class LinearPDE:
1789                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1790                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1791                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1792                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1793                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1803                   self.__applyConstraint()                   self.__applyConstraint()
1804                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1805                   self.trace("New system has been built.")                   self.trace("New system has been built.")
1806                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1807                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1808               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1809                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
# Line 1253  class LinearPDE: Line 1811  class LinearPDE:
1811                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1812                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1813                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1814                     self.getDomain().addPDEToRHS(self.__righthandside, \
1815                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1816                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1817                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1819                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1820                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1821                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1822               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1823                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1824                              self.getCoefficientOfGeneralPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1825                              self.getCoefficientOfGeneralPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
# Line 1268  class LinearPDE: Line 1831  class LinearPDE:
1831                              escript.Data(),\                              escript.Data(),\
1832                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1833                              escript.Data())                              escript.Data())
1834                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1836                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1839                                escript.Data(), \
1840                                escript.Data(), \
1841                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1842                                escript.Data(),\
1843                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1844                                escript.Data())
1845                   self.__applyConstraint()                   self.__applyConstraint()
1846                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1847                   self.__operator_isValid=True                   self.__operator_is_Valid=True
1848         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1849    
1850    
1851    class Poisson(LinearPDE):
   
 class AdvectivePDE(LinearPDE):  
1852     """     """
1853     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
   
    class to define a linear PDE of the form  
1854    
1855     \f[     M{-grad(grad(u)[j])[j] = f}
    -(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]  
1856    
1857     with boundary conditons:     with natural boundary conditons
1858    
1859     \f[     M{n[j]*grad(u)[j] = 0 }
    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]  
1860    
1861     and constraints:     and constraints:
1862    
1863     \f[     M{u=0} where M{q>0}
1864     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1865     """     """
    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()  
1866    
1867     def __calculateXi(self,peclet_factor,Z,h):     def __init__(self,domain,debug=False):
1868         Z_max=util.Lsup(Z)       """
1869         if Z_max>0.:       initializes a new Poisson equation
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
        else:  
           return 0.  
1870    
1871     def setValue(self,**args):       @param domain: domain of the PDE
1872         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>}
1873         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)  
1874    
1875              Z_max=util.Lsup(length_of_Z)       """
1876              if Z_max>0.:       super(Poisson, self).__init__(domain,1,1,debug)
1877                 length_of_A=util.length(A)       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1878                 A_max=util.Lsup(length_of_A)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                 if A_max>0:                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1880                      inv_A=1./(length_of_A+A_max*self.TOL)       self.setSymmetryOn()
                else:  
                     inv_A=1./self.TOL  
                peclet_number=length_of_Z*h/2*inv_A  
                xi=self.__xi(peclet_number)  
                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  
1881    
1882       def setValue(self,**coefficients):
1883         """
1884         sets new values to coefficients
1885    
1886         @param coefficients: new values assigned to coefficients
1887         @keyword f: value for right hand side M{f}
1888         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1889         @keyword q: mask for location of constraints
1890         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1891                   depending of reduced order is used for the representation of the equation.
1892         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1893         """
1894         super(Poisson, self).setValue(**coefficients)
1895    
1896     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1897       """       """
1898       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
1899         @param name: name of the coefficient requested.
1900       @param name:       @type name: C{string}
1901         @return: the value of the coefficient  name
1902         @rtype: L{Data<escript.Data>}
1903         @raise IllegalCoefficient: if name is not one of coefficients
1904                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1905         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1906       """       """
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
1907       if name == "A" :       if name == "A" :
1908           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  
1909       elif name == "B" :       elif name == "B" :
1910           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  
1911       elif name == "C" :       elif name == "C" :
1912           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  
1913       elif name == "D" :       elif name == "D" :
1914           return self.getCoefficient("D")           return escript.Data()
1915       elif name == "X" :       elif name == "X" :
1916           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  
1917       elif name == "Y" :       elif name == "Y" :
1918           return self.getCoefficient("Y")           return self.getCoefficient("f")
1919       elif name == "d" :       elif name == "d" :
1920           return self.getCoefficient("d")           return escript.Data()
1921       elif name == "y" :       elif name == "y" :
1922           return self.getCoefficient("y")           return escript.Data()
1923       elif name == "d_contact" :       elif name == "d_contact" :
1924           return self.getCoefficient("d_contact")           return escript.Data()
1925       elif name == "y_contact" :       elif name == "y_contact" :
1926           return self.getCoefficient("y_contact")           return escript.Data()
1927         elif name == "A_reduced" :
1928             return escript.Data()
1929         elif name == "B_reduced" :
1930             return escript.Data()
1931         elif name == "C_reduced" :
1932             return escript.Data()
1933         elif name == "D_reduced" :
1934             return escript.Data()
1935         elif name == "X_reduced" :
1936             return escript.Data()
1937         elif name == "Y_reduced" :
1938             return self.getCoefficient("f_reduced")
1939         elif name == "d_reduced" :
1940             return escript.Data()
1941         elif name == "y_reduced" :
1942             return escript.Data()
1943         elif name == "d_contact_reduced" :
1944             return escript.Data()
1945         elif name == "y_contact_reduced" :
1946             return escript.Data()
1947       elif name == "r" :       elif name == "r" :
1948           return self.getCoefficient("r")           return escript.Data()
1949       elif name == "q" :       elif name == "q" :
1950           return self.getCoefficient("q")           return self.getCoefficient("q")
1951       else:       else:
1952           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
1953    
1954  class Poisson(LinearPDE):  class Helmholtz(LinearPDE):
1955     """     """
1956     Class to define a Poisson equation problem:     Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1957    
1958     class to define a linear PDE of the form     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1959     \f[  
1960     -u_{,jj} = f     with natural boundary conditons
1961     \f]  
1962       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
1963    
1964     and constraints:     and constraints:
1965    
1966     \f[     M{u=r} where M{q>0}
1967     u=0 \quad \mathrm{where} \quad q>0  
    \f]  
1968     """     """
1969    
1970     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
1971         LinearPDE.__init__(self,domain,1,1,debug)       """
1972         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),       initializes a new Poisson equation
1973                            "q": PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
1974         self.setSymmetryOn()       @param domain: domain of the PDE
1975         self.setValue(f,q)       @type domain: L{Domain<escript.Domain>}
1976         @param debug: if True debug informations are printed.
1977     def setValue(self,f=escript.Data(),q=escript.Data()):  
1978         """set value of PDE parameters f and q"""       """
1979         self._LinearPDE__setValue(f=f,q=q)       super(Helmholtz, self).__init__(domain,1,1,debug)
1980         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1981                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1983                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1988                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1989         self.setSymmetryOn()
1990    
1991       def setValue(self,**coefficients):
1992         """
1993         sets new values to coefficients
1994    
1995         @param coefficients: new values assigned to coefficients
1996         @keyword omega: value for coefficient M{S{omega}}
1997         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1998         @keyword k: value for coefficeint M{k}
1999         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000         @keyword f: value for right hand side M{f}
2001         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002         @keyword alpha: value for right hand side M{S{alpha}}
2003         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2004         @keyword g: value for right hand side M{g}
2005         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006         @keyword r: prescribed values M{r} for the solution in constraints.
2007         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2008                   depending of reduced order is used for the representation of the equation.
2009         @keyword q: mask for location of constraints
2010         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2011                   depending of reduced order is used for the representation of the equation.
2012         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2013         """
2014         super(Helmholtz, self).setValue(**coefficients)
2015    
2016     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2017       """       """
2018       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2019    
2020       @param name:       @param name: name of the coefficient requested.
2021         @type name: C{string}
2022         @return: the value of the coefficient  name
2023         @rtype: L{Data<escript.Data>}
2024         @raise IllegalCoefficient: if name is not one of coefficients
2025                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2026         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2027       """       """
2028       if name == "A" :       if name == "A" :
2029           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")
2030       elif name == "B" :       elif name == "B" :
2031           return escript.Data()           return escript.Data()
2032       elif name == "C" :       elif name == "C" :
2033           return escript.Data()           return escript.Data()
2034       elif name == "D" :       elif name == "D" :
2035           return escript.Data()           return self.getCoefficient("omega")
2036       elif name == "X" :       elif name == "X" :
2037           return escript.Data()           return escript.Data()
2038       elif name == "Y" :       elif name == "Y" :
2039           return self.getCoefficient("f")           return self.getCoefficient("f")
2040       elif name == "d" :       elif name == "d" :
2041           return escript.Data()           return self.getCoefficient("alpha")
2042       elif name == "y" :       elif name == "y" :
2043           return escript.Data()           return self.getCoefficient("g")
2044       elif name == "d_contact" :       elif name == "d_contact" :
2045           return escript.Data()           return escript.Data()
2046       elif name == "y_contact" :       elif name == "y_contact" :
2047           return escript.Data()           return escript.Data()
2048       elif name == "r" :       elif name == "A_reduced" :
2049             return escript.Data()
2050         elif name == "B_reduced" :
2051             return escript.Data()
2052         elif name == "C_reduced" :
2053             return escript.Data()
2054         elif name == "D_reduced" :
2055             return escript.Data()
2056         elif name == "X_reduced" :
2057             return escript.Data()
2058         elif name == "Y_reduced" :
2059             return self.getCoefficient("f_reduced")
2060         elif name == "d_reduced" :
2061           return escript.Data()           return escript.Data()
2062         elif name == "y_reduced" :
2063            return self.getCoefficient("g_reduced")
2064         elif name == "d_contact_reduced" :
2065             return escript.Data()
2066         elif name == "y_contact_reduced" :
2067             return escript.Data()
2068         elif name == "r" :
2069             return self.getCoefficient("r")
2070       elif name == "q" :       elif name == "q" :
2071           return self.getCoefficient("q")           return self.getCoefficient("q")
2072       else:       else:
2073           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2074    
2075  class LameEquation(LinearPDE):  class LameEquation(LinearPDE):
2076     """     """
2077     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2078    
2079     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] }
2080     \f[  
2081     -(\mu (u_{i,j}+u_{j,i}))_{,j} - \lambda u_{j,ji}} = F_i -\sigma_{ij,j}     with natural boundary conditons:
2082     \f]  
2083       M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
    with boundary conditons:  
   
    \f[  
    n_j(\mu (u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\lambda u_{j,j} = f_i  
    \f]  
2084    
2085     and constraints:     and constraints:
2086    
2087     \f[     M{u[i]=r[i]} where M{q[i]>0}
2088     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
2089     """     """
2090    
2091     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
2092         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim(),debug)        super(LameEquation, self).__init__(domain,\
2093         self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                                           domain.getDim(),domain.getDim(),debug)
2094          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2095                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2096                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2097                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2098                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099                            "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2100                            "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2101         self.setSymmetryOn()        self.setSymmetryOn()
2102    
2103     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):
2104         """set value of PDE parameters"""       """
2105         self._LinearPDE__setValue(lame_lambda=lame_lambda, \       sets new values to coefficients
2106                                   lame_mu=lame_mu, \  
2107                                   F=F, \       @param coefficients: new values assigned to coefficients
2108                                   sigma=sigma, \       @keyword lame_mu: value for coefficient M{S{mu}}
2109                                   f=f, \       @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2110                                   r=r, \       @keyword lame_lambda: value for coefficient M{S{lambda}}
2111                                   q=q)       @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112         @keyword F: value for internal force M{F}
2113         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2114         @keyword sigma: value for initial stress M{S{sigma}}
2115         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2116         @keyword f: value for extrenal force M{f}
2117         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2118         @keyword r: prescribed values M{r} for the solution in constraints.
2119         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2120                   depending of reduced order is used for the representation of the equation.
2121         @keyword q: mask for location of constraints
2122         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2123                   depending of reduced order is used for the representation of the equation.
2124         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2125         """
2126         super(LameEquation, self).setValues(**coefficients)
2127    
2128     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2129       """       """
2130       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2131    
2132       @param name:       @param name: name of the coefficient requested.
2133         @type name: C{string}
2134         @return: the value of the coefficient  name
2135         @rtype: L{Data<escript.Data>}
2136         @raise IllegalCoefficient: if name is not one of coefficients
2137                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2138         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2139       """       """
2140       if name == "A" :       if name == "A" :
2141           out =self.createCoefficientOfGeneralPDE("A")           out =self.createCoefficientOfGeneralPDE("A")
# Line 1662  class LameEquation(LinearPDE): Line 2163  class LameEquation(LinearPDE):
2163           return escript.Data()           return escript.Data()
2164       elif name == "y_contact" :       elif name == "y_contact" :
2165           return escript.Data()           return escript.Data()
2166         elif name == "A_reduced" :
2167             return escript.Data()
2168         elif name == "B_reduced" :
2169             return escript.Data()
2170         elif name == "C_reduced" :
2171             return escript.Data()
2172         elif name == "D_reduced" :
2173             return escript.Data()
2174         elif name == "X_reduced" :
2175             return escript.Data()
2176         elif name == "Y_reduced" :
2177             return escript.Data()
2178         elif name == "d_reduced" :
2179             return escript.Data()
2180         elif name == "y_reduced" :
2181             return escript.Data()
2182         elif name == "d_contact_reduced" :
2183             return escript.Data()
2184         elif name == "y_contact_reduced" :
2185             return escript.Data()
2186       elif name == "r" :       elif name == "r" :
2187           return self.getCoefficient("r")           return self.getCoefficient("r")
2188       elif name == "q" :       elif name == "q" :
2189           return self.getCoefficient("q")           return self.getCoefficient("q")
2190       else:       else:
2191           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2192    
 # $Log$  
 # Revision 1.11  2005/08/23 01:24:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-08-23  
 #  
 # Revision 1.10  2005/08/12 01:45:36  jgs  
 # erge of development branch dev-02 back to main trunk on 2005-08-12  
 #  
 # Revision 1.9.2.4  2005/08/22 07:11:09  gross  
 # some problems with LinearPDEs fixed.  
 #  
 # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
 # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
 #  
 # Revision 1.9.2.2  2005/08/18 04:39:32  gross  
 # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
 #  
 # Revision 1.9.2.1  2005/07/29 07:10:27  gross  
 # new functions in util and a new pde type in linearPDEs  
 #  
 # Revision 1.1.2.25  2005/07/28 04:21:09  gross  
 # Lame equation: (linear elastic, isotropic) added  
 #  
 # Revision 1.1.2.24  2005/07/22 06:37:11  gross  
 # some extensions to modellib and linearPDEs  
 #  
 # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
 # Fixed up some docstrings.  Moved module-level functions to top of file so  
 # that epydoc and doxygen can pick them up properly.  
 #  
 # Revision 1.1.2.22  2005/05/12 11:41:30  gross  
 # some basic Models have been added  
 #  
 # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
 # file so that the AdvectivePDE class is picked up by doxygen.  Some  
 # reformatting of docstrings.  Addition of code to make equations come out  
 # as proper LaTeX.  
 #  
 # Revision 1.1.2.20  2005/04/15 07:09:08  gross  
 # some problems with functionspace and linearPDEs fixed.  
 #  
 # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
 # bug in SystemPattern fixed.  
 #  
 # Revision 1.1.2.18  2005/02/08 06:16:45  gross  
 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
 #  
 # Revision 1.1.2.17  2005/02/08 05:56:19  gross  
 # Reference Number handling added  
 #  
 # Revision 1.1.2.16  2005/02/07 04:41:28  gross  
 # some function exposed to python to make mesh merging running  
 #  
 # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
 # timeseries add and ESySParameter.py renames esysXML.py for consistence  
 #  
 # Revision 1.1.2.14  2005/02/01 06:44:10  gross  
 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working  
 #  
 # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
 # updates in the documentation  
 #  
 # Revision 1.1.2.12  2005/01/12 01:28:04  matt  
 # Added createCoefficient method for linearPDEs.  
 #  
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # 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  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  
 #  

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