/[escript]/trunk/escript/py_src/linearPDEs.py
ViewVC logotype

Diff of /trunk/escript/py_src/linearPDEs.py

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

trunk/esys2/escript/py_src/linearPDEs.py revision 108 by jgs, Thu Jan 27 06:21:59 2005 UTC trunk/escript/py_src/linearPDEs.py revision 720 by gross, Thu Apr 27 10:16:05 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 ## @file linearPDEs.py  
   
2  """  """
3  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
4    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
5    solver capabilities in itself but hands the PDE over to
6    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
7    The general interface is provided through the L{LinearPDE} class. The
8    L{AdvectivePDE} which is derived from the L{LinearPDE} class
9    provides an interface to PDE dominated by its advective terms. The L{Poisson},
10    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11    classs which are also derived form the L{LinearPDE} class should be used
12    to define of solve these sepecial PDEs.
13    
14    @var __author__: name of author
15    @var __copyright__: copyrights
16    @var __license__: licence agreement
17    @var __url__: url entry point on documentation
18    @var __version__: version
19    @var __date__: date of the version
20  """  """
21    
22  import escript  import escript
23  import util  import util
24  import numarray  import numarray
25    
26    __author__="Lutz Gross, l.gross@uq.edu.au"
27    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28                        http://www.access.edu.au
29                    Primary Business: Queensland, Australia"""
30    __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32    __url__="http://www.iservo.edu.au/esys"
33    __version__="$Revision$"
34    __date__="$Date$"
35    
36    
37    class IllegalCoefficient(ValueError):
38       """
39       raised if an illegal coefficient of the general ar particular PDE is requested.
40       """
41    
42  def _CompTuple2(t1,t2):  class IllegalCoefficientValue(ValueError):
43       """
44       raised if an incorrect value for a coefficient is used.
45     """     """
    @brief  
46    
47     @param t1  class UndefinedPDEError(ValueError):
48     @param t2     """
49       raised if a PDE is not fully defined yet.
50     """     """
    dif=t1[0]+t1[1]-(t2[0]+t2[1])  
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
51    
52  class PDECoefficient:  class PDECoefficient(object):
53      """      """
54      @brief      A class for describing a PDE coefficient
55    
56        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
57        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
58        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
59        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
60        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
61        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
62        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
63        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
64        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
65        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
66        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
67    
68      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
69      INTERIOR=0      INTERIOR=0
70      BOUNDARY=1      BOUNDARY=1
71      CONTACT=2      CONTACT=2
72      CONTINUOUS=3      SOLUTION=3
73      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
74      # 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
75      # number of unknowns.      BY_SOLUTION=6
76      EQUATION=3      BY_DIM=7
77      SOLUTION=4      OPERATOR=10
78      DIM=5      RIGHTHANDSIDE=11
79      # indicator for what is altered if the coefficient is altered:      BOTH=12
80      OPERATOR=5  
     RIGHTHANDSIDE=6  
     BOTH=7  
81      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
82         """         """
83         @brief Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
84    
85           @param where: describes where the coefficient lives
86           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
87           @param pattern: describes the shape of the coefficient and how the shape is build for a given
88                  spatial dimension and numbers of equation and solution in then PDE. For instance,
89                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
90                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
91                  on a 2-dimensional domain. In the case of single equation and a single solution component
92                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
93                  the example would be read as (2,).
94           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
95           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
96           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
97    
98         """         """
99           super(PDECoefficient, self).__init__()
100         self.what=where         self.what=where
101         self.pattern=pattern         self.pattern=pattern
102         self.altering=altering         self.altering=altering
# Line 53  class PDECoefficient: Line 104  class PDECoefficient:
104    
105      def resetValue(self):      def resetValue(self):
106         """         """
107         @brief resets coefficient value to default         resets coefficient value to default
108         """         """
109         self.value=escript.Data()         self.value=escript.Data()
110    
111      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
112         """         """
113         @brief defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
114    
115         @param domain         @param domain: domain on which the PDE uses the coefficient
116         """         @type domain: L{Domain<escript.Domain>}
117         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
118         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
119         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
120         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
121           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
122           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
123           """
124           if self.what==self.INTERIOR:
125                return escript.Function(domain)
126           elif self.what==self.BOUNDARY:
127                return escript.FunctionOnBoundary(domain)
128           elif self.what==self.CONTACT:
129                return escript.FunctionOnContactZero(domain)
130           elif self.what==self.SOLUTION:
131                if reducedEquationOrder and reducedSolutionOrder:
132                    return escript.ReducedSolution(domain)
133                else:
134                    return escript.Solution(domain)
135           elif self.what==self.REDUCED:
136                return escript.ReducedSolution(domain)
137    
138      def getValue(self):      def getValue(self):
139         """         """
140         @brief returns the value of the coefficient:         returns the value of the coefficient
141    
142           @return:  value of the coefficient
143           @rtype:  L{Data<escript.Data>}
144         """         """
145         return self.value         return self.value
146        
147      def setValue(self,newValue):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
        """  
        @brief set the value of the coefficient to new value  
148         """         """
149           set the value of the coefficient to a new value
150    
151           @param domain: domain on which the PDE uses the coefficient
152           @type domain: L{Domain<escript.Domain>}
153           @param numEquations: number of equations of the PDE
154           @type numEquations: C{int}
155           @param numSolutions: number of components of the PDE solution
156           @type numSolutions: C{int}
157           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
158           @type reducedEquationOrder: C{bool}
159           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
160           @type reducedSolutionOrder: C{bool}
161           @param newValue: number of components of the PDE solution
162           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
163           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
164           """
165           if newValue==None:
166               newValue=escript.Data()
167           elif isinstance(newValue,escript.Data):
168               if not newValue.isEmpty():
169                  try:
170                     newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
171                  except:
172                     raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
173           else:
174               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
175           if not newValue.isEmpty():
176               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
177                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
178         self.value=newValue         self.value=newValue
179        
180      def isAlteringOperator(self):      def isAlteringOperator(self):
181          """          """
182      @brief return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
183    
184            @return:  True if the operator of the PDE is changed when the coefficient is changed
185            @rtype:  C{bool}
186      """      """
187          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
188              return not None              return not None
# Line 91  class PDECoefficient: Line 191  class PDECoefficient:
191    
192      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
193          """          """
194      @brief return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
195    
196        @rtype:  C{bool}
197            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
198      """      """
199          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
200              return not None              return not None
201          else:          else:
202              return None              return None
203    
204      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
205         """         """
206         @brief tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
207    
208         @param shape         @param domain: domain on which the PDE uses the coefficient
209         @param dim         @type domain: L{Domain<escript.Domain>}
210           @param shape: suggested shape of the coefficient
211           @type shape: C{tuple} of C{int} values
212           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
213                     If no appropriate numbers could be identified, C{None} is returned
214           @rtype: C{tuple} of two C{int} values or C{None}
215         """         """
216           dim=domain.getDim()
217         if len(shape)>0:         if len(shape)>0:
218             num=max(shape)+1             num=max(shape)+1
219         else:         else:
220             num=1             num=1
221         search=[]         search=[]
222         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
223            for e in range(num):            for u in range(num):
224               search.append((e,u))               for e in range(num):
225         search.sort(_CompTuple2)                  search.append((e,u))
226         for item in search:            search.sort(self.__CompTuple2)
227               s=self.buildShape(item[0],item[1],dim)            for item in search:
228                 s=self.getShape(domain,item[0],item[1])
229               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
230                   return (1,1)                   return (1,1)
231               else:               else:
232                   if s==shape: return item                   if s==shape: return item
233           elif self.definesNumEquation():
234              for e in range(num,0,-1):
235                 s=self.getShape(domain,e,0)
236                 if len(s)==0 and len(shape)==0:
237                     return (1,None)
238                 else:
239                     if s==shape: return (e,None)
240    
241           elif self.definesNumSolutions():
242              for u in range(num,0,-1):
243                 s=self.getShape(domain,0,u)
244                 if len(s)==0 and len(shape)==0:
245                     return (None,1)
246                 else:
247                     if s==shape: return (None,u)
248         return None         return None
249        def definesNumSolutions(self):
250           """
251           checks if the coefficient allows to estimate the number of solution components
252    
253      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
254          """         @rtype: C{bool}
255      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
256           for i in self.pattern:
257                 if i==self.BY_SOLUTION: return True
258           return False
259    
260      @param e      def definesNumEquation(self):
261      @param u         """
262      @param dim         checks if the coefficient allows to estimate the number of equations
263      """  
264          s=()         @return: True if the coefficient allows an estimate of the number of equations
265          for i in self.pattern:         @rtype: C{bool}
266               if i==self.EQUATION:         """
267                  if e>1: s=s+(e,)         for i in self.pattern:
268               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
269                  if u>1: s=s+(u,)         return False
270    
271        def __CompTuple2(self,t1,t2):
272          """
273          Compare two tuples of possible number of equations and number of solutions
274    
275          @param t1: The first tuple
276          @param t2: The second tuple
277    
278          """
279    
280          dif=t1[0]+t1[1]-(t2[0]+t2[1])
281          if dif<0: return 1
282          elif dif>0: return -1
283          else: return 0
284    
285        def getShape(self,domain,numEquations=1,numSolutions=1):
286           """
287           builds the required shape of the coefficient
288    
289           @param domain: domain on which the PDE uses the coefficient
290           @type domain: L{Domain<escript.Domain>}
291           @param numEquations: number of equations of the PDE
292           @type numEquations: C{int}
293           @param numSolutions: number of components of the PDE solution
294           @type numSolutions: C{int}
295           @return: shape of the coefficient
296           @rtype: C{tuple} of C{int} values
297           """
298           dim=domain.getDim()
299           s=()
300           for i in self.pattern:
301                 if i==self.BY_EQUATION:
302                    if numEquations>1: s=s+(numEquations,)
303                 elif i==self.BY_SOLUTION:
304                    if numSolutions>1: s=s+(numSolutions,)
305               else:               else:
306                  s=s+(dim,)                  s=s+(dim,)
307          return s         return s
308    
309  class LinearPDE:  class LinearPDE(object):
310     """     """
311     @brief Class to handel a linear PDE     This class is used to define a general linear, steady, second order PDE
312         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
313    
314       -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
315    
316       with boundary conditons:     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}
317    
318          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
319       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
320       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
321       L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
322       M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
323    
324      and contact conditions     The following natural boundary conditions are considered:
325    
326          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
327    
328      and constraints:     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
329       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
330       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
331    
          u_i=r_i where q_i>0  
332    
333     """     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
    TOL=1.e-13  
    DEFAULT_METHOD=util.DEFAULT_METHOD  
    DIRECT=util.DIRECT  
    CHOLEVSKY=util.CHOLEVSKY  
    PCG=util.PCG  
    CR=util.CR  
    CGS=util.CGS  
    BICGSTAB=util.BICGSTAB  
    SSOR=util.SSOR  
    GMRES=util.GMRES  
    PRES20=util.PRES20  
334    
335     def __init__(self,domain,numEquations=0,numSolutions=0):     M{u=r}  where M{q>0}
      """  
      @brief initializes a new linear PDE.  
336    
337       @param args     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
338       """     The constraints override any other condition set by the PDE or the boundary condition.
339       # COEFFICIENTS can be overwritten by subclasses:  
340       self.COEFFICIENTS={     The PDE is symmetrical if
341         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
342         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}
343         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
344         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     For a system of PDEs and a solution with several components the PDE has the form
345         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
346         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }
347         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
348         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.
349         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The natural boundary conditions take the form:
350         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
351         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}
352         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
353    
354       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
355    
356    
357       M{u[i]=r[i]}  where  M{q[i]>0}
358    
359       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
360    
361       The system of PDEs is symmetrical if
362    
363            - M{A[i,j,k,l]=A[k,l,i,j]}
364            - M{B[i,j,k]=C[k,i,j]}
365            - M{D[i,k]=D[i,k]}
366            - M{d[i,k]=d[k,i]}
367    
368       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
369       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
370       defined as
371    
372       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
373    
374       For the case of single solution component and single PDE M{J} is defined
375    
376       M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
377    
378       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
379       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
380       the contact condition takes the form
381    
382       M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
383    
384       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
385       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
386       L{jump<util.jump>}.
387       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>}.
388       In case of a single PDE and a single component solution the contact condition takes the form
389    
390       M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
391    
392       In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
393       both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
394    
395       @cvar DEFAULT: The default method used to solve the system of linear equations
396       @cvar DIRECT: The direct solver based on LDU factorization
397       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
398       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
399       @cvar CR: The conjugate residual method
400       @cvar CGS: The conjugate gardient square method
401       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
402       @cvar SSOR: The symmetric overrealaxtion method
403       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
404       @cvar ILUT: The incomplete LU factorization preconditioner with will in
405       @cvar JACOBI: The Jacobi preconditioner
406       @cvar GMRES: The Gram-Schmidt minimum residual method
407       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
408       @cvar LUMPING: Matrix lumping.
409       @cvar NO_REORDERING: No matrix reordering allowed
410       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
411       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
412       @cvar PASO: PASO solver package
413       @cvar SCSL: SGI SCSL solver library
414       @cvar MKL: Intel's MKL solver library
415       @cvar UMFPACK: the UMFPACK library
416       @cvar ITERATIVE: The default iterative solver
417       @cvar AMG: algebraic multi grid
418       @cvar RILU: recursive ILU
419    
420       """
421       DEFAULT= 0
422       DIRECT= 1
423       CHOLEVSKY= 2
424       PCG= 3
425       CR= 4
426       CGS= 5
427       BICGSTAB= 6
428       SSOR= 7
429       ILU0= 8
430       ILUT= 9
431       JACOBI= 10
432       GMRES= 11
433       PRES20= 12
434       LUMPING= 13
435       NO_REORDERING= 17
436       MINIMUM_FILL_IN= 18
437       NESTED_DISSECTION= 19
438       SCSL= 14
439       MKL= 15
440       UMFPACK= 16
441       ITERATIVE= 20
442       PASO= 21
443       AMG= 22
444       RILU = 23
445    
446       SMALL_TOLERANCE=1.e-13
447       __PACKAGE_KEY="package"
448       __METHOD_KEY="method"
449       __SYMMETRY_KEY="symmetric"
450       __TOLERANCE_KEY="tolerance"
451       __PRECONDITIONER_KEY="preconditioner"
452    
453    
454       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
455         """
456         initializes a new linear PDE
457    
458         @param domain: domain of the PDE
459         @type domain: L{Domain<escript.Domain>}
460         @param numEquations: number of equations. If numEquations==None the number of equations
461                              is exracted from the PDE coefficients.
462         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
463                              is exracted from the PDE coefficients.
464         @param debug: if True debug informations are printed.
465    
466         """
467         super(LinearPDE, self).__init__()
468         #
469         #   the coefficients of the general PDE:
470         #
471         self.__COEFFICIENTS_OF_GENEARL_PDE={
472           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
473           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
474           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
475           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
476           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
477           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
478           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
480           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
482           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
483           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
484    
485         # COEFFICIENTS can be overwritten by subclasses:
486         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
487         self.__altered_coefficients=False
488       # initialize attributes       # initialize attributes
489       self.__debug=None       self.__debug=debug
490       self.__domain=domain       self.__domain=domain
491       self.__numEquations=numEquations       self.__numEquations=numEquations
492       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
493       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
494    
495       # set some default values:       # set some default values:
496       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
497       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
498       self.__tolerance=1.e-8       self.__tolerance=1.e-8
499       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
500       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
501         self.__preconditioner=self.DEFAULT
502         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
503       self.__sym=False       self.__sym=False
      self.__lumping=False  
504    
505     def createCoefficient(self, name):       self.resetCoefficients()
506         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
507       # =============================================================================
508       #    general stuff:
509       # =============================================================================
510       def __str__(self):
511         """
512         returns string representation of the PDE
513    
514         @return: a simple representation of the PDE
515         @rtype: C{str}
516         """
517         return "<LinearPDE %d>"%id(self)
518       # =============================================================================
519       #    debug :
520       # =============================================================================
521       def setDebugOn(self):
522       """       """
523       @brief create a data object corresponding to coefficient name       switches on debugging
      @param name  
524       """       """
525       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceOfCoefficient(name))  
526    
527     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
528       """       """
529       @brief return the value of the parameter name       switches off debugging
530         """
531         self.__debug=None
532    
533       @param name     def trace(self,text):
534       """       """
535       return self.COEFFICIENTS[name].getValue()       print the text message if debugging is swiched on.
536         @param text: message
537         @type text: C{string}
538         """
539         if self.__debug: print "%s: %s"%(str(self),text)
540    
541     def getCoefficientOfPDE(self,name):     # =============================================================================
542       # some service functions:
543       # =============================================================================
544       def getDomain(self):
545       """       """
546       @brief return the value of the coefficient name of the general PDE. This method is called by the assembling routine       returns the domain of the PDE
547              it can be overwritten to map coefficients of a particualr PDE to the general PDE.  
548       @param name       @return: the domain of the PDE
549         @rtype: L{Domain<escript.Domain>}
550       """       """
551       return self.getCoefficient(name)       return self.__domain
552    
553     def hasCoefficient(self,name):     def getDim(self):
554        """       """
555        @brief return true if name is the name of a coefficient       returns the spatial dimension of the PDE
556    
557        @param name       @return: the spatial dimension of the PDE domain
558        """       @rtype: C{int}
559        return self.COEFFICIENTS.has_key(name)       """
560         return self.getDomain().getDim()
561    
562     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
563       """       """
564       @brief return true if the test functions should use reduced order       returns the number of equations
565    
566         @return: the number of equations
567         @rtype: C{int}
568         @raise UndefinedPDEError: if the number of equations is not be specified yet.
569       """       """
570       return self.__row_function_space       if self.__numEquations==None:
571             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
572         else:
573             return self.__numEquations
574    
575     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
576       """       """
577       @brief return true if the interpolation of the solution should use reduced order       returns the number of unknowns
578    
579         @return: the number of unknowns
580         @rtype: C{int}
581         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
582       """       """
583       return self.__column_function_space       if self.__numSolutions==None:
584            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
585         else:
586            return self.__numSolutions
587    
588     def setValue(self,**coefficients):     def reduceEquationOrder(self):
589        """       """
590        @brief sets new values to coefficients       return status for order reduction for equation
591    
592        @param coefficients       @return: return True is reduced interpolation order is used for the represenation of the equation
593        """       @rtype: L{bool}
594        self._setValue(**coefficients)       """
595               return self.__reduce_equation_order
596    
597     def cleanCoefficients(self):     def reduceSolutionOrder(self):
598       """       """
599       @brief resets all coefficients to default values.       return status for order reduction for the solution
600    
601         @return: return True is reduced interpolation order is used for the represenation of the solution
602         @rtype: L{bool}
603       """       """
604       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
605    
606     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
607       """       """
608       @brief returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
609    
610         @return: representation space of equation
611         @rtype: L{FunctionSpace<escript.FunctionSpace>}
612       """       """
613       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
614                   return escript.ReducedSolution(self.getDomain())
615         else:
616             return escript.Solution(self.getDomain())
617    
618     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
619       """       """
620       @brief return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
621    
622       @param name       @return: representation space of solution
623         @rtype: L{FunctionSpace<escript.FunctionSpace>}
624       """       """
625       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
626          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
627       else:       else:
628          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
629    
630     def getFunctionSpaceForCoefficient(self,name):  
631       def getOperator(self):
632       """       """
633       @brief return the atoms of the coefficient name       provides access to the operator of the PDE
634    
635       @param name       @return: the operator of the PDE
636         @rtype: L{Operator<escript.Operator>}
637       """       """
638       if self.hasCoefficient(name):       m=self.getSystem()[0]
639          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
640             return self.copyConstraint(1./m)
641       else:       else:
642          raise ValueError,"Solution coefficient %s requested"%name           return m
643    
644     def alteredCoefficient(self,name):     def getRightHandSide(self):
645       """       """
646       @brief annonced that coefficient name has been changed       provides access to the right hand side of the PDE
647         @return: the right hand side of the PDE
648         @rtype: L{Data<escript.Data>}
649         """
650         r=self.getSystem()[1]
651         if self.isUsingLumping():
652             return self.copyConstraint(r)
653         else:
654             return r
655    
656       @param name     def applyOperator(self,u=None):
657       """       """
658       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
659          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
660          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
661                   the current solution is used.
662         @type u: L{Data<escript.Data>} or None
663         @return: image of u
664         @rtype: L{Data<escript.Data>}
665         """
666         if u==None:
667              return self.getOperator()*self.getSolution()
668       else:       else:
669          raise ValueError,"unknown coefficient %s requested"%name          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
670    
671     # ===== debug ==============================================================     def getResidual(self,u=None):
672     def setDebugOn(self):       """
673         return the residual of u or the current solution if u is not present.
674    
675         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
676                   the current solution is used.
677         @type u: L{Data<escript.Data>} or None
678         @return: residual of u
679         @rtype: L{Data<escript.Data>}
680         """
681         return self.applyOperator(u)-self.getRightHandSide()
682    
683       def checkSymmetry(self,verbose=True):
684          """
685          test the PDE for symmetry.
686    
687          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
688          @type verbose: C{bool}
689          @return:  True if the PDE is symmetric.
690          @rtype: L{Data<escript.Data>}
691          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
692          """
693          verbose=verbose or self.__debug
694          out=True
695          if self.getNumSolutions()!=self.getNumEquations():
696             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
697             out=False
698          else:
699             A=self.getCoefficientOfGeneralPDE("A")
700             if not A.isEmpty():
701                tol=util.Lsup(A)*self.SMALL_TOLERANCE
702                if self.getNumSolutions()>1:
703                   for i in range(self.getNumEquations()):
704                      for j in range(self.getDim()):
705                         for k in range(self.getNumSolutions()):
706                            for l in range(self.getDim()):
707                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
708                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
709                                   out=False
710                else:
711                   for j in range(self.getDim()):
712                      for l in range(self.getDim()):
713                         if util.Lsup(A[j,l]-A[l,j])>tol:
714                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
715                            out=False
716             B=self.getCoefficientOfGeneralPDE("B")
717             C=self.getCoefficientOfGeneralPDE("C")
718             if B.isEmpty() and not C.isEmpty():
719                if verbose: print "non-symmetric PDE because B is not present but C is"
720                out=False
721             elif not B.isEmpty() and C.isEmpty():
722                if verbose: print "non-symmetric PDE because C is not present but B is"
723                out=False
724             elif not B.isEmpty() and not C.isEmpty():
725                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
726                if self.getNumSolutions()>1:
727                   for i in range(self.getNumEquations()):
728                       for j in range(self.getDim()):
729                          for k in range(self.getNumSolutions()):
730                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
731                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
732                                  out=False
733                else:
734                   for j in range(self.getDim()):
735                      if util.Lsup(B[j]-C[j])>tol:
736                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
737                         out=False
738             if self.getNumSolutions()>1:
739               D=self.getCoefficientOfGeneralPDE("D")
740               if not D.isEmpty():
741                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
742                 for i in range(self.getNumEquations()):
743                    for k in range(self.getNumSolutions()):
744                      if util.Lsup(D[i,k]-D[k,i])>tol:
745                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
746                          out=False
747               d=self.getCoefficientOfGeneralPDE("d")
748               if not d.isEmpty():
749                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
750                 for i in range(self.getNumEquations()):
751                    for k in range(self.getNumSolutions()):
752                      if util.Lsup(d[i,k]-d[k,i])>tol:
753                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
754                          out=False
755               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
756               if not d_contact.isEmpty():
757                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
758                 for i in range(self.getNumEquations()):
759                    for k in range(self.getNumSolutions()):
760                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
761                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
762                          out=False
763          return out
764    
765       def getSolution(self,**options):
766         """         """
767         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
768    
769           @return: the solution
770           @rtype: L{Data<escript.Data>}
771           @param options: solver options
772           @keyword verbose: True to get some information during PDE solution
773           @type verbose: C{bool}
774           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
775                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
776           @keyword iter_max: maximum number of iteration steps allowed.
777           @keyword drop_tolerance: threshold for drupping in L{ILUT}
778           @keyword drop_storage: maximum of allowed memory in L{ILUT}
779           @keyword truncation: maximum number of residuals in L{GMRES}
780           @keyword restart: restart cycle length in L{GMRES}
781         """         """
782         self.__debug=not None         if not self.__solution_isValid:
783              mat,f=self.getSystem()
784              if self.isUsingLumping():
785                 self.__solution=self.copyConstraint(f*mat)
786              else:
787                 options[self.__TOLERANCE_KEY]=self.getTolerance()
788                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
789                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
790                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
791                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
792                 self.trace("PDE is resolved.")
793                 self.trace("solver options: %s"%str(options))
794                 self.__solution=mat.solve(f,options)
795              self.__solution_isValid=True
796           return self.__solution
797    
798     def setDebugOff(self):     def getFlux(self,u=None):
799         """
800         returns the flux M{J} for a given M{u}
801    
802         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
803    
804         or
805    
806         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
807    
808         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
809         @type u: L{Data<escript.Data>} or None
810         @return: flux
811         @rtype: L{Data<escript.Data>}
812         """
813         if u==None: u=self.getSolution()
814         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
815       # =============================================================================
816       #   solver settings:
817       # =============================================================================
818       def setSolverMethod(self,solver=None,preconditioner=None):
819         """         """
820         @brief         sets a new solver
821    
822           @param solver: sets a new solver method.
823           @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}
824           @param preconditioner: sets a new solver method.
825           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
826         """         """
827         self.__debug=None         if solver==None: solve=self.DEFAULT
828           if preconditioner==None: preconditioner=self.DEFAULT
829           if not (solver,preconditioner)==self.getSolverMethod():
830               self.__solver_method=solver
831               self.__preconditioner=preconditioner
832               self.__checkMatrixType()
833               self.trace("New solver is %s"%self.getSolverMethodName())
834    
835     def debug(self):     def getSolverMethodName(self):
836         """         """
837         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
838    
839           @return: the name of the solver currently used.
840           @rtype: C{string}
841         """         """
        return self.__debug  
842    
843     #===== Lumping ===========================         m=self.getSolverMethod()
844     def setLumpingOn(self):         p=self.getSolverPackage()
845        """         method=""
846        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
847        """         elif m[0]==self.DIRECT: method= "DIRECT"
848        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
849           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
850           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
851           self.__lumping=True         elif m[0]==self.CR: method= "CR"
852           elif m[0]==self.CGS: method= "CGS"
853           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
854           elif m[0]==self.SSOR: method= "SSOR"
855           elif m[0]==self.GMRES: method= "GMRES"
856           elif m[0]==self.PRES20: method= "PRES20"
857           elif m[0]==self.LUMPING: method= "LUMPING"
858           elif m[0]==self.AMG: method= "AMG"
859           if m[1]==self.DEFAULT: method+="+DEFAULT"
860           elif m[1]==self.JACOBI: method+= "+JACOBI"
861           elif m[1]==self.ILU0: method+= "+ILU0"
862           elif m[1]==self.ILUT: method+= "+ILUT"
863           elif m[1]==self.SSOR: method+= "+SSOR"
864           elif m[1]==self.AMG: method+= "+AMG"
865           elif m[1]==self.RILU: method+= "+RILU"
866           if p==self.DEFAULT: package="DEFAULT"
867           elif p==self.PASO: package= "PASO"
868           elif p==self.MKL: package= "MKL"
869           elif p==self.SCSL: package= "SCSL"
870           elif p==self.UMFPACK: package= "UMFPACK"
871           else : method="unknown"
872           return "%s solver of %s package"%(method,package)
873    
    def setLumpingOff(self):  
       """  
       @brief switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
874    
875     def setLumping(self,flag=False):     def getSolverMethod(self):
876        """         """
877        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
878    
879     def isUsingLumping(self):         @return: the solver method currently be used.
880        """         @rtype: C{int}
881        @brief         """
882        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
883    
884     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
885         """         """
886         @brief sets a new solver         sets a new solver package
887    
888           @param package: sets a new solver method.
889           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
890         """         """
891         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
892           if not package==self.getSolverPackage():
893             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
894             self.__checkMatrixType()             self.__checkMatrixType()
895               self.trace("New solver is %s"%self.getSolverMethodName())
896    
897     def getSolverMethod(self):     def getSolverPackage(self):
898         """         """
899         @brief returns the solver method         returns the package of the solver
900    
901           @return: the solver package currently being used.
902           @rtype: C{int}
903         """         """
904         return self.__solver_method         return self.__solver_package
905    
906       def isUsingLumping(self):
907          """
908          checks if matrix lumping is used a solver method
909    
910          @return: True is lumping is currently used a solver method.
911          @rtype: C{bool}
912          """
913          return self.getSolverMethod()[0]==self.LUMPING
914    
    #============ tolerance business =========================================================  
915     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
916         """         """
917         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
918    
919           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
920    
921           defines the stopping criterion.
922    
923           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
924                       the system will be resolved.
925           @type tol: positive C{float}
926           @raise ValueException: if tolerance is not positive.
927         """         """
928         if not tol>0:         if not tol>0:
929             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
930         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
931         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
932         self.__tolerance=tol         self.__tolerance=tol
933         return         return
934    
935     def getTolerance(self):     def getTolerance(self):
936         """         """
937         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
938    
939           @return: tolerance currently used.
940           @rtype: C{float}
941         """         """
942         return self.__tolerance         return self.__tolerance
943    
944     #===== symmetry  flag ==========================     # =============================================================================
945       #    symmetry  flag:
946       # =============================================================================
947     def isSymmetric(self):     def isSymmetric(self):
948        """        """
949        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
950    
951          @return: True is a symmetric PDE is indicated, otherwise False is returned
952          @rtype: C{bool}
953        """        """
954        return self.__sym        return self.__sym
955    
956     def setSymmetryOn(self):     def setSymmetryOn(self):
957        """        """
958        @brief sets the symmetry flag to true        sets the symmetry flag.
959        """        """
960        if not self.isSymmetric():        if not self.isSymmetric():
961           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
962           self.__sym=True           self.__sym=True
963           self.__checkMatrixType()           self.__checkMatrixType()
964    
965     def setSymmetryOff(self):     def setSymmetryOff(self):
966        """        """
967        @brief sets the symmetry flag to false        removes the symmetry flag.
968        """        """
969        if self.isSymmetric():        if self.isSymmetric():
970           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
971           self.__sym=False           self.__sym=False
972           self.__checkMatrixType()           self.__checkMatrixType()
973    
974     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
975       """        """
976       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
977    
978       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
979       """        @type flag: C{bool}
980       if flag:        """
981          self.setSymmetryOn()        if flag:
982       else:           self.setSymmetryOn()
983          self.setSymmetryOff()        else:
984             self.setSymmetryOff()
985    
986     #===== order reduction ==========================     # =============================================================================
987       # function space handling for the equation as well as the solution
988       # =============================================================================
989     def setReducedOrderOn(self):     def setReducedOrderOn(self):
990       """       """
991       @brief switches to on reduced order       switches on reduced order for solution and equation representation
992    
993         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
994       """       """
995       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
996       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
997    
998     def setReducedOrderOff(self):     def setReducedOrderOff(self):
999       """       """
1000       @brief switches to full order       switches off reduced order for solution and equation representation
1001    
1002         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1003       """       """
1004       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1005       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1006    
1007     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1008       """       """
1009       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1010         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1011       @param flag                    if flag is not present order reduction is switched off
1012         @type flag: C{bool}
1013         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1014       """       """
1015       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1016       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1017    
1018     #===== order reduction solution ==========================  
1019     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1020       """       """
1021       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1022    
1023         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1024       """       """
1025       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1026       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1027           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1028           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1029           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1030             self.__resetSystem()
1031    
1032     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1033       """       """
1034       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1035    
1036         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1037       """       """
1038       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1039       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1040           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1041           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1042           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1043             self.__resetSystem()
1044    
1045     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1046       """       """
1047       @brief sets order for test functions according to flag       sets order for test functions according to flag
1048    
1049       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1050                      if flag is not present order reduction is switched off
1051         @type flag: C{bool}
1052         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1053       """       """
1054       if flag:       if flag:
1055          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1056       else:       else:
1057          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1058                                                                                                                                                              
    #===== order reduction equation ==========================  
1059     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1060       """       """
1061       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1062    
1063         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1064       """       """
1065       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1066       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1067           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1068           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1069           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1070             self.__resetSystem()
1071    
1072     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1073       """       """
1074       @brief switches to full order for test functions       switches off reduced order for equation representation
1075    
1076         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1077       """       """
1078       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1079       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1080           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1081           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1082           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1083             self.__resetSystem()
1084    
1085     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1086       """       """
1087       @brief sets order for test functions according to flag       sets order for test functions according to flag
1088    
1089       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1090                      if flag is not present order reduction is switched off
1091         @type flag: C{bool}
1092         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1093       """       """
1094       if flag:       if flag:
1095          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1096       else:       else:
1097          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1098                                                                                                                                                              
1099     # ==== initialization =====================================================================     # =============================================================================
1100     def __makeNewOperator(self):     # private method:
1101       # =============================================================================
1102       def __checkMatrixType(self):
1103         """
1104         reassess the matrix type and, if a new matrix is needed, resets the system.
1105         """
1106         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1107         if not new_matrix_type==self.__matrix_type:
1108             self.trace("Matrix type is now %d."%new_matrix_type)
1109             self.__matrix_type=new_matrix_type
1110             self.__resetSystem()
1111       #
1112       #   rebuild switches :
1113       #
1114       def __invalidateSolution(self):
1115           """
1116           indicates the PDE has to be resolved if the solution is requested
1117           """
1118           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1119           self.__solution_isValid=False
1120    
1121       def __invalidateOperator(self):
1122           """
1123           indicates the operator has to be rebuilt next time it is used
1124           """
1125           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1126           self.__invalidateSolution()
1127           self.__operator_is_Valid=False
1128    
1129       def __invalidateRightHandSide(self):
1130           """
1131           indicates the right hand side has to be rebuild next time it is used
1132           """
1133           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1134           self.__invalidateSolution()
1135           self.__righthandside_isValid=False
1136    
1137       def __invalidateSystem(self):
1138           """
1139           annonced that everthing has to be rebuild:
1140           """
1141           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1142           self.__invalidateSolution()
1143           self.__invalidateOperator()
1144           self.__invalidateRightHandSide()
1145    
1146       def __resetSystem(self):
1147           """
1148           annonced that everthing has to be rebuild:
1149           """
1150           self.trace("New System is built from scratch.")
1151           self.__operator=escript.Operator()
1152           self.__operator_is_Valid=False
1153           self.__righthandside=escript.Data()
1154           self.__righthandside_isValid=False
1155           self.__solution=escript.Data()
1156           self.__solution_isValid=False
1157       #
1158       #    system initialization:
1159       #
1160       def __getNewOperator(self):
1161         """         """
1162         @brief         returns an instance of a new operator
1163         """         """
1164           self.trace("New operator is allocated.")
1165         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1166                             self.getNumEquations(), \                             self.getNumEquations(), \
1167                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 545  class LinearPDE: Line 1169  class LinearPDE:
1169                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1170                             self.__matrix_type)                             self.__matrix_type)
1171    
1172     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1173         """         """
1174         @brief         returns an instance of a new right hand side
1175         """         """
1176         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1177           if self.getNumEquations()>1:
1178               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1179           else:
1180               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1181    
1182     def __makeNewSolution(self):     def __getNewSolution(self):
1183         """         """
1184         @brief         returns an instance of a new solution
1185         """         """
1186         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1187           if self.getNumSolutions()>1:
1188               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1189           else:
1190               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1191    
1192     def __getFreshOperator(self):     def __makeFreshSolution(self):
1193         """         """
1194         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1195         """         """
1196         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1197             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1198         else:         else:
1199             self.__operator.setValue(0.)             self.__solution*=0
1200             self.__operator.resetSolver()             self.trace("Solution is reset to zero.")
1201             if self.debug() : print "PDE Debug: Operator reset to zero"         return self.__solution
        return self.__operator  
1202    
1203     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1204         """         """
1205         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1206         """         """
1207         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1208             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1209         else:         else:
1210             print "fix self.__righthandside*=0"             self.__righthandside*=0
1211             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1212             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1213    
1214     #============ some serivice functions  =====================================================     def __makeFreshOperator(self):
1215     def getDomain(self):         """
1216           makes sure that the operator is instantiated and returns it initialized by zeros
1217           """
1218           if self.__operator.isEmpty():
1219               self.__operator=self.__getNewOperator()
1220           else:
1221               self.__operator.resetValues()
1222               self.trace("Operator reset to zero")
1223           return self.__operator
1224    
1225       def __applyConstraint(self):
1226           """
1227           applies the constraints defined by q and r to the system
1228           """
1229           if not self.isUsingLumping():
1230              q=self.getCoefficientOfGeneralPDE("q")
1231              r=self.getCoefficientOfGeneralPDE("r")
1232              if not q.isEmpty() and not self.__operator.isEmpty():
1233                 # q is the row and column mask to indicate where constraints are set:
1234                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1235                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1236                 u=self.__getNewSolution()
1237                 if r.isEmpty():
1238                    r_s=self.__getNewSolution()
1239                 else:
1240                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1241                 u.copyWithMask(r_s,col_q)
1242                 if not self.__righthandside.isEmpty():
1243                    self.__righthandside-=self.__operator*u
1244                    self.__righthandside=self.copyConstraint(self.__righthandside)
1245                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1246       # =============================================================================
1247       # function giving access to coefficients of the general PDE:
1248       # =============================================================================
1249       def getCoefficientOfGeneralPDE(self,name):
1250         """
1251         return the value of the coefficient name of the general PDE.
1252    
1253         @note: This method is called by the assembling routine it can be overwritten
1254               to map coefficients of a particular PDE to the general PDE.
1255         @param name: name of the coefficient requested.
1256         @type name: C{string}
1257         @return: the value of the coefficient  name
1258         @rtype: L{Data<escript.Data>}
1259         @raise IllegalCoefficient: if name is not one of coefficients
1260                      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}.
1261       """       """
1262       @brief returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1263            return self.getCoefficient(name)
1264         else:
1265            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1266    
1267       def hasCoefficientOfGeneralPDE(self,name):
1268       """       """
1269       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1270    
1271         @param name: name of the coefficient enquired.
1272         @type name: C{string}
1273         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1274         @rtype: C{bool}
1275    
    def getDim(self):  
1276       """       """
1277       @brief returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1278    
1279       def createCoefficientOfGeneralPDE(self,name):
1280       """       """
1281       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1282    
1283     def getNumEquations(self):       @param name: name of the coefficient requested.
1284         @type name: C{string}
1285         @return: a coefficient name initialized to 0.
1286         @rtype: L{Data<escript.Data>}
1287         @raise IllegalCoefficient: if name is not one of coefficients
1288                      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}.
1289       """       """
1290       @brief returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1291            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1292         else:
1293            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1294    
1295       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1296       """       """
1297       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1298           return self.__numEquations  
1299         @param name: name of the coefficient enquired.
1300         @type name: C{string}
1301         @return: the function space to be used for coefficient name
1302         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1303         @raise IllegalCoefficient: if name is not one of coefficients
1304                      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}.
1305         """
1306         if self.hasCoefficientOfGeneralPDE(name):
1307            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1308       else:       else:
1309           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1310    
1311     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1312       """       """
1313       @brief returns the number of unknowns       return the shape of the coefficient name of the general PDE
1314    
1315         @param name: name of the coefficient enquired.
1316         @type name: C{string}
1317         @return: the shape of the coefficient name
1318         @rtype: C{tuple} of C{int}
1319         @raise IllegalCoefficient: if name is not one of coefficients
1320                      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}.
1321       """       """
1322       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1323          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1324       else:       else:
1325          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1326    
1327       # =============================================================================
1328       # functions giving access to coefficients of a particular PDE implementation:
1329       # =============================================================================
1330       def getCoefficient(self,name):
1331         """
1332         returns the value of the coefficient name
1333    
1334     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1335        """       @type name: C{string}
1336        @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.       @return: the value of the coefficient name
1337        """       @rtype: L{Data<escript.Data>}
1338        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1339        out=True       """
1340        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1341           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1342           out=False       else:
1343        else:          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          A=self.getCoefficientOfPDE("A")  
          if not A.isEmpty():  
             tol=util.Lsup(A)*self.TOL  
             if self.getNumSolutions()>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 util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:  
                                if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)  
                                out=False  
             else:  
                for j in range(self.getDim()):  
                   for l in range(self.getDim()):  
                      if util.Lsup(A[j,l]-A[l,j])>tol:  
                         if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)  
                         out=False  
          B=self.getCoefficientOfPDE("B")  
          C=self.getCoefficientOfPDE("C")  
          if B.isEmpty() and not C.isEmpty():  
             if verbose: print "non-symmetric PDE because B is not present but C is"  
             out=False  
          elif not B.isEmpty() and C.isEmpty():  
             if verbose: print "non-symmetric PDE because C is not present but B is"  
             out=False  
          elif not B.isEmpty() and not C.isEmpty():  
             tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          if util.Lsup(B[i,j,k]-C[i,j,k])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,i,j,k)  
                               out=False  
             else:  
                for j in range(self.getDim()):  
                   if util.Lsup(B[j]-C[j])>tol:  
                      if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)  
                      out=False  
          if self.getNumSolutions()>1:  
            D=self.getCoefficientOfPDE("D")  
            if not D.isEmpty():  
              tol=util.Lsup(D)*self.TOL  
              for i in range(self.getNumEquations()):  
                 for k in range(self.getNumSolutions()):  
                   if util.Lsup(D[i,k]-D[k,i])>tol:  
                       if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)  
                       out=False  
               
       return out  
1344    
1345     def getFlux(self,u):     def hasCoefficient(self,name):
1346         """       """
1347         @brief returns the flux J_ij for a given u       return True if name is the name of a coefficient
1348    
1349         @param name: name of the coefficient enquired.
1350         @type name: C{string}
1351         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1352         @rtype: C{bool}
1353         """
1354         return self.COEFFICIENTS.has_key(name)
1355    
1356              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     def createCoefficient(self, name):
1357         """
1358         create a L{Data<escript.Data>} object corresponding to coefficient name
1359    
1360         @param u argument of the operator       @return: a coefficient name initialized to 0.
1361         @rtype: L{Data<escript.Data>}
1362         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1363         """
1364         if self.hasCoefficient(name):
1365            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1366         else:
1367            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1368    
1369         """     def getFunctionSpaceForCoefficient(self,name):
1370         raise SystemError,"getFlux is not implemented yet"       """
1371         return None       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1372    
1373     def applyOperator(self,u):       @param name: name of the coefficient enquired.
1374         """       @type name: C{string}
1375         @brief applies the operator of the PDE to a given solution u in weak from       @return: the function space to be used for coefficient name
1376         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1377         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1378         """
1379         if self.hasCoefficient(name):
1380            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1381         else:
1382            raise ValueError,"unknown coefficient %s requested"%name
1383       def getShapeOfCoefficient(self,name):
1384         """
1385         return the shape of the coefficient name
1386    
1387         @param u argument of the operator       @param name: name of the coefficient enquired.
1388         @type name: C{string}
1389         @return: the shape of the coefficient name
1390         @rtype: C{tuple} of C{int}
1391         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1392         """
1393         if self.hasCoefficient(name):
1394            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1395         else:
1396            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1397    
1398         """     def resetCoefficients(self):
1399         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       """
1400                                                                                                                                                                   resets all coefficients to there default values.
1401     def getResidual(self,u):       """
1402         """       for i in self.COEFFICIENTS.iterkeys():
1403         @brief return the residual of u in the weak from           self.COEFFICIENTS[i].resetValue()
1404    
1405         @param u     def alteredCoefficient(self,name):
1406         """       """
1407         return self.applyOperator(u)-self.getRightHandSide()       announce that coefficient name has been changed
1408    
1409         @param name: name of the coefficient enquired.
1410         @type name: C{string}
1411         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1412         @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.
1413         """
1414         if self.hasCoefficient(name):
1415            self.trace("Coefficient %s has been altered."%name)
1416            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1417               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1418               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1419         else:
1420            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1421    
1422       def copyConstraint(self,u):
1423          """
1424          copies the constraint into u and returns u.
1425    
1426          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1427          @type u: L{Data<escript.Data>}
1428          @return: the input u modified by the constraints.
1429          @rtype: L{Data<escript.Data>}
1430          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1431          """
1432          q=self.getCoefficientOfGeneralPDE("q")
1433          r=self.getCoefficientOfGeneralPDE("r")
1434          if not q.isEmpty():
1435             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1436             if r.isEmpty():
1437                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1438             else:
1439                 r=escript.Data(r,u.getFunctionSpace())
1440             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1441          return u
1442    
1443     def _setValue(self,**coefficients):     def setValue(self,**coefficients):
1444        """        """
1445        @brief sets new values to coefficient        sets new values to coefficients
1446    
1447        @param coefficients        @param coefficients: new values assigned to coefficients
1448          @keyword A: value for coefficient A.
1449          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1450          @keyword B: value for coefficient B
1451          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452          @keyword C: value for coefficient C
1453          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454          @keyword D: value for coefficient D
1455          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1456          @keyword X: value for coefficient X
1457          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458          @keyword Y: value for coefficient Y
1459          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1460          @keyword d: value for coefficient d
1461          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1462          @keyword y: value for coefficient y
1463          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1464          @keyword d_contact: value for coefficient d_contact
1465          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1466                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1467          @keyword y_contact: value for coefficient y_contact
1468          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1469                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1470          @keyword r: values prescribed to the solution at the locations of constraints
1471          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1472                   depending of reduced order is used for the solution.
1473          @keyword q: mask for location of constraints
1474          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1475                   depending of reduced order is used for the representation of the equation.
1476          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1477        """        """
1478        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1479        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1480           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1481              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1482        # if the number of unknowns or equations is still unknown we try to estimate them:        # if the number of unknowns or equations is still unknown we try to estimate them:
1483        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1484           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1485              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1486                  s=d.shape                  s=d.shape
# Line 726  class LinearPDE: Line 1490  class LinearPDE:
1490                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1491              if s!=None:              if s!=None:
1492                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1493                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1494                  if res==None:                  if res==None:
1495                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1496                  else:                  else:
1497                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1498                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1499        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1500        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1501        # 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:
1502        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1503          if d==None:          try:
1504               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1505          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1506               if d.isEmpty():             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
                 d2=d  
              else:  
                 d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))  
         else:  
               d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))  
         if not d2.isEmpty():  
            if not self.getShapeOfCoefficient(i)==d2.getShape():  
                raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())  
         # overwrite new values:  
         if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
         self.COEFFICIENTS[i].setValue(d2)  
1507          self.alteredCoefficient(i)          self.alteredCoefficient(i)
         
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def __setHomogeneousConstraintFlag(self):  
       """  
       @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.  
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficientOfPDE("q")  
       r=self.getCoefficientOfPDE("r")  
       if not q.isEmpty() and not r.isEmpty():  
          if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False  
       if self.debug():  
            if self.__homogeneous_constraint:  
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
   
    # ==== rebuild switches =====================================================================  
    def __rebuildSolution(self,deep=False):  
        """  
        @brief indicates the PDE has to be reolved if the solution is requested  
        """  
        if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."  
        self.__solution_isValid=False  
        if deep: self.__solution=escript.Data()  
   
1508    
1509     def __rebuildOperator(self,deep=False):        self.__altered_coefficients=True
1510         """        # check if the systrem is inhomogeneous:
1511         @brief indicates the operator has to be rebuilt next time it is used        if len(coefficients)>0 and not self.isUsingLumping():
1512         """           q=self.getCoefficientOfGeneralPDE("q")
1513         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."           r=self.getCoefficientOfGeneralPDE("r")
1514         self.__rebuildSolution(deep)           homogeneous_constraint=True
1515         self.__operator_isValid=False           if not q.isEmpty() and not r.isEmpty():
1516         if deep: self.__operator=escript.Operator()               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1517                   self.trace("Inhomogeneous constraint detected.")
1518     def __rebuildRightHandSide(self,deep=False):                 self.__invalidateSystem()
        """  
        @brief indicates the right hand side has to be rebuild next time it is used  
        """  
        if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__righthandside_isValid=False  
        if deep: self.__righthandside=escript.Data()  
   
    def __rebuildSystem(self,deep=False):  
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      @brief reassess the matrix type and, if needed, initiates an operator rebuild  
      """  
      new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())  
      if not new_matrix_type==self.__matrix_type:  
          if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type  
          self.__matrix_type=new_matrix_type  
          self.__rebuildOperator(deep=True)  
   
    #============ assembling =======================================================  
    def __copyConstraint(self):  
       """  
       @brief copies the constrint condition into u  
       """  
       if not self.__righthandside.isEmpty():  
          q=self.getCoefficientOfPDE("q")  
          r=self.getCoefficientOfPDE("r")  
          if not q.isEmpty():  
              if r.isEmpty():  
                 r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace())  
              else:  
                 r2=escript.Data(r,self.__righthandside.getFunctionSpace())  
              self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace()))  
   
    def __applyConstraint(self):  
        """  
        @brief applies the constraints defined by q and r to the system  
        """  
        q=self.getCoefficientOfPDE("q")  
        r=self.getCoefficientOfPDE("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__makeNewSolution()  
           if r.isEmpty():  
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if self.isUsingLumping():  
              self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q)  
           else:  
              if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u  
              self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1519    
1520     def getSystem(self):     def getSystem(self):
1521         """         """
1522         @brief return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1523    
1524           @return: the discrete version of the PDE
1525           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1526         """         """
1527         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1528            if self.isUsingLumping():            if self.isUsingLumping():
1529                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1530                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1531                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1532                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1533                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1534                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1535                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1536                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1537                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1538                   if self.debug() : print "PDE Debug: New lumped operator is built."                   D=self.getCoefficientOfGeneralPDE("D")
1539                   mat=self.__makeNewOperator()                   if not D.isEmpty():
1540                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                       if self.getNumSolutions()>1:
1541                             self.getCoefficientOfPDE("A"), \                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1542                             self.getCoefficientOfPDE("B"), \                       else:
1543                             self.getCoefficientOfPDE("C"), \                          D_times_e=D
1544                             self.getCoefficientOfPDE("D"), \                   else:
1545                             escript.Data(), \                      D_times_e=escript.Data()
1546                             escript.Data(), \                   d=self.getCoefficientOfGeneralPDE("d")
1547                             self.getCoefficientOfPDE("d"), \                   if not d.isEmpty():
1548                             escript.Data(),\                       if self.getNumSolutions()>1:
1549                             self.getCoefficientOfPDE("d_contact"), \                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1550                             escript.Data())                       else:
1551                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                          d_times_e=d
1552                   self.__applyConstraint()                   else:
1553                   self.__operator_isValid=True                      d_times_e=escript.Data()
1554                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1555                     if not d_contact.isEmpty():
1556                         if self.getNumSolutions()>1:
1557                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1558                         else:
1559                            d_contact_times_e=d_contact
1560                     else:
1561                        d_contact_times_e=escript.Data()
1562        
1563                     self.__operator=self.__getNewRightHandSide()
1564                     self.getDomain().addPDEToRHS(self.__operator, \
1565                                                  escript.Data(), \
1566                                                  D_times_e, \
1567                                                  d_times_e,\
1568                                                  d_contact_times_e)
1569                     self.__operator=1./self.__operator
1570                     self.trace("New lumped operator has been built.")
1571                     self.__operator_is_Valid=True
1572                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1573                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1574                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1575                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1576                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1577                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1578                                 self.getCoefficientOfPDE("y_contact"))                   self.trace("New right hand side as been built.")
                  self.__copyConstraint()  
1579                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1580            else:            else:
1581               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1582                   if self.debug() : print "PDE Debug: New system is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1583                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("A"), \
1584                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1585                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1586                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1587                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1588                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1589                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1590                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1591                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1592                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y_contact"))
                                self.getCoefficientOfPDE("y_contact"))  
1593                   self.__applyConstraint()                   self.__applyConstraint()
1594                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1595                   self.__operator_isValid=True                   self.trace("New system has been built.")
1596                     self.__operator_is_Valid=True
1597                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1598               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1599                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1600                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1601                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1602                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1603                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1604                                 self.getCoefficientOfPDE("y_contact"))                   self.__righthandside=self.copyConstraint(self.__righthandside)
1605                   self.__copyConstraint()                   self.trace("New right hand side has been built.")
1606                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1607               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1608                   if self.debug() : print "PDE Debug: New operator is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1609                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),escript.Data(), \                              self.getCoefficientOfGeneralPDE("A"), \
1610                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("B"), \
1611                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("C"), \
1612                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("D"), \
                             self.getCoefficientOfPDE("D"), \  
1613                              escript.Data(), \                              escript.Data(), \
1614                              escript.Data(), \                              escript.Data(), \
1615                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1616                              escript.Data(),\                              escript.Data(),\
1617                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1618                              escript.Data())                              escript.Data())
1619                   self.__applyConstraint()                   self.__applyConstraint()
1620                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1621                     self.__operator_is_Valid=True
1622         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        @brief returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1623    
    def getRightHandSide(self):  
        """  
        @brief returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1624    
1625     def solve(self,**options):  class Poisson(LinearPDE):
1626        """     """
1627        @brief solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1628    
1629        @param options     M{-grad(grad(u)[j])[j] = f}
       """  
       mat,f=self.getSystem()  
       if self.isUsingLumping():  
          out=f/mat  
       else:  
          options[util.TOLERANCE_KEY]=self.getTolerance()  
          options[util.METHOD_KEY]=self.getSolverMethod()  
          options[util.SYMMETRY_KEY]=self.isSymmetric()  
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
1630    
1631     def getSolution(self,**options):     with natural boundary conditons
        """  
        @brief returns the solution of the PDE  
1632    
1633         @param options     M{n[j]*grad(u)[j] = 0 }
1634         """  
1635         if not self.__solution_isValid:     and constraints:
1636             if self.debug() : print "PDE Debug: PDE is resolved."  
1637             self.__solution=self.solve(**options)     M{u=0} where M{q>0}
            self.__solution_isValid=True  
        return self.__solution  
1638    
 class AdvectivePDE(LinearPDE):  
1639     """     """
    @brief Class to handel a linear PDE domineated by advective terms:  
     
    class to define a linear PDE of the form  
1640    
1641       -(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     def __init__(self,domain,debug=False):
1642         """
1643         initializes a new Poisson equation
1644    
1645       with boundary conditons:       @param domain: domain of the PDE
1646         @type domain: L{Domain<escript.Domain>}
1647         @param debug: if True debug informations are printed.
1648    
1649          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       """
1650         super(Poisson, self).__init__(domain,1,1,debug)
1651         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1652                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1653         self.setSymmetryOn()
1654    
1655      and contact conditions     def setValue(self,**coefficients):
1656         """
1657         sets new values to coefficients
1658    
1659          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i       @param coefficients: new values assigned to coefficients
1660         @keyword f: value for right hand side M{f}
1661         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1662         @keyword q: mask for location of constraints
1663         @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>}
1664                   depending of reduced order is used for the representation of the equation.
1665         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1666         """
1667         super(Poisson, self).setValue(**coefficients)
1668    
1669       def getCoefficientOfGeneralPDE(self,name):
1670         """
1671         return the value of the coefficient name of the general PDE
1672         @param name: name of the coefficient requested.
1673         @type name: C{string}
1674         @return: the value of the coefficient  name
1675         @rtype: L{Data<escript.Data>}
1676         @raise IllegalCoefficient: if name is not one of coefficients
1677                      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}.
1678         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1679         """
1680         if name == "A" :
1681             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1682         elif name == "B" :
1683             return escript.Data()
1684         elif name == "C" :
1685             return escript.Data()
1686         elif name == "D" :
1687             return escript.Data()
1688         elif name == "X" :
1689             return escript.Data()
1690         elif name == "Y" :
1691             return self.getCoefficient("f")
1692         elif name == "d" :
1693             return escript.Data()
1694         elif name == "y" :
1695             return escript.Data()
1696         elif name == "d_contact" :
1697             return escript.Data()
1698         elif name == "y_contact" :
1699             return escript.Data()
1700         elif name == "r" :
1701             return escript.Data()
1702         elif name == "q" :
1703             return self.getCoefficient("q")
1704         else:
1705            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1706    
1707      and constraints:  class Helmholtz(LinearPDE):
1708       """
1709       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1710    
1711           u_i=r_i where q_i>0     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1712    
1713      The PDE is solved by stabilizing the advective terms using SUPG approach:     with natural boundary conditons
1714    
1715         A_{ijkl}<-A_{ijkl}+0.5*h*(xi(b_{ik})*B_{ijk}*B_{ilk}/length(B_{i:k})^2)+0.5*h*xi_{c_{ik}}*(C_{ikj}*C_{ikl}/length(C_{ik:})^2)     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1716    
1717      where       and constraints:
1718    
1719             b_{ik}=length(B_{i:k})*h/2/length(A_{i:k:})     M{u=r} where M{q>0}
            c_{ik}=length(C_{i:k})*h/2/length(A_{i:k:})  
1720    
                       alpha/3        alpha<3  
            xi(alpha)=          for                  approximating cotanh(alpha)-1/alpha  
                        1             alpha>=3  
1721     """     """
    def __getXi(self,alpha):  
          c=alpha-3.  
          return c*c.whereNegative()/3.+1.  
   
    def __getUpdateVector(self,V,hover2,alphaByU):  
      v=util.length(V)  
      v_max=util.Lsup(v)  
      if v_max>0:  
          V/=v+v_max*self.TOL  
          alpha=alphaByU*v  
          A_bar=v*hover2*self.__getXi(alpha)  
          print "-------------"  
          print "@ max alpha ",util.Lsup(alpha)  
          print "-------------"  
      else:  
          A_bar=1.  
      return V,A_bar  
   
    def __getAlphaByU(self,A,hover2):  
       a=util.length(A)  
       a_max=util.Lsup(a)  
       if a_max>0:  
          return hover2/(a+a_max*self.TOL)  
       else:  
          return 1./self.TOL  
   
1722    
1723     def getCoefficientOfPDE(self,name):     def __init__(self,domain,debug=False):
1724       """       """
1725       @brief return the value of the coefficient name of the general PDE       initializes a new Poisson equation
1726       @param name  
1727         @param domain: domain of the PDE
1728         @type domain: L{Domain<escript.Domain>}
1729         @param debug: if True debug informations are printed.
1730    
1731         """
1732         super(Helmholtz, self).__init__(domain,1,1,debug)
1733         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1734                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1735                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1736                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1737                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1738                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1739                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1740         self.setSymmetryOn()
1741    
1742       def setValue(self,**coefficients):
1743       """       """
1744       if name == "A" :       sets new values to coefficients
1745           A=self.getCoefficient("A")  
1746           B=self.getCoefficient("B")       @param coefficients: new values assigned to coefficients
1747           C=self.getCoefficient("C")       @keyword omega: value for coefficient M{S{omega}}
1748           if not B.isEmpty() or not C.isEmpty():       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1749               if A.isEmpty():       @keyword k: value for coefficeint M{k}
1750                   A=self.createNewCoefficient("A")       @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1751               else:       @keyword f: value for right hand side M{f}
1752                   A=A[:]       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1753               hover2=self.getDomain().getSize()/2.       @keyword alpha: value for right hand side M{S{alpha}}
1754               if self.getNumEquations()>1:       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1755                  if self.getNumSolutions()>1:       @keyword g: value for right hand side M{g}
1756                     for i in range(self.getNumEquations()):       @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1757                        for k in range(self.getNumSolutions()):       @keyword r: prescribed values M{r} for the solution in constraints.
1758                           alphaByU=self.__getAlphaByU(A[i,:,k,:],hover2)       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1759                           if not B.isEmpty():                 depending of reduced order is used for the representation of the equation.
1760                               b_sub,f=self.__getUpdateVector(B[i,:,k],hover2,alphaByU)       @keyword q: mask for location of constraints
1761                               for j in range(self.getDim()):       @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1762                                  for l in range(self.getDim()):                 depending of reduced order is used for the representation of the equation.
1763                                     A[i,j,k,l]+=f*b_sub[j]*b_sub[l]       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1764                           if not C.isEmpty():       """
1765                               c_sub,f=self.__getUpdateVector(C[i,k,:],hover2,alphaByU)       super(Helmholtz, self).setValue(**coefficients)
1766                               for j in range(self.getDim()):  
1767                                  for l in range(self.getDim()):     def getCoefficientOfGeneralPDE(self,name):
1768                                     A[i,j,k,l]+=f*c_sub[j]*c_sub[l]       """
1769                  else:         return the value of the coefficient name of the general PDE
1770                     for i in range(self.getNumEquations()):  
1771                        alphaByU=self.__getAlphaByU(A[i,:,:],hover2)       @param name: name of the coefficient requested.
1772                        if not B.isEmpty():       @type name: C{string}
1773                            b_sub,f=self.__getUpdateVector(B[i,:],hover2,alphaByU)       @return: the value of the coefficient  name
1774                            for j in range(self.getDim()):       @rtype: L{Data<escript.Data>}
1775                               for l in range(self.getDim()):       @raise IllegalCoefficient: if name is not one of coefficients
1776                                   A[i,j,l]+=f*b_sub[j]*b_sub[l]                    "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}.
1777                        if not C.isEmpty():       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1778                             c_sub,f=self.__getUpdateVector(C[i,:],hover2,alphaByU)       """
1779                             for j in range(self.getDim()):       if name == "A" :
1780                                for l in range(self.getDim()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1781                                   A[i,j,l]+=f*c_sub[j]*c_sub[l]       elif name == "B" :
1782               else:           return escript.Data()
1783                  if self.getNumSolutions()>1:       elif name == "C" :
1784                     for k in range(self.getNumSolutions()):           return escript.Data()
1785                        alphaByU=self.__getAlphaByU(A[:,k,:],hover2)       elif name == "D" :
1786                        if not B.isEmpty():           return self.getCoefficient("omega")
1787                           b_sub,f=self.__getUpdateVector(B[:,k],hover2,alphaByU)       elif name == "X" :
1788                           for j in range(self.getDim()):           return escript.Data()
1789                              for l in range(self.getDim()):       elif name == "Y" :
1790                                     A[j,k,l]+=f*b_sub[j]*b_sub[l]           return self.getCoefficient("f")
1791                        if not C.isEmpty():       elif name == "d" :
1792                           c_sub,f=self.__getUpdateVector(C[k,:],hover2,alphaByU)           return self.getCoefficient("alpha")
1793                           for j in range(self.getDim()):       elif name == "y" :
1794                              for l in range(self.getDim()):           return self.getCoefficient("g")
1795                                 A[j,k,l]+=f*c_sub[j]*c_sub[l]       elif name == "d_contact" :
1796                  else:             return escript.Data()
                    alphaByU=self.__getAlphaByU(A[:,:],hover2)  
                    if not B.isEmpty():  
                        b_sub,f=self.__getUpdateVector(B[:],hover2,alphaByU)  
                        for j in range(self.getDim()):  
                           for l in range(self.getDim()):  
                              A[j,l]+=f*b_sub[j]*b_sub[l]  
                    if not C.isEmpty():  
                       c_sub,f=self.__getUpdateVector(C[:],hover2,alphaByU)  
                       for j in range(self.getDim()):  
                           for l in range(self.getDim()):  
                              A[j,l]+=f*c_sub[j]*c_sub[l]  
          return A  
      elif name == "B" :  
          return self.getCoefficient("B")  
      elif name == "C" :  
          return self.getCoefficient("C")  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          return self.getCoefficient("X")  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
1797       elif name == "y_contact" :       elif name == "y_contact" :
1798           return self.getCoefficient("y_contact")           return escript.Data()
1799       elif name == "r" :       elif name == "r" :
1800           return self.getCoefficient("r")           return self.getCoefficient("r")
1801       elif name == "q" :       elif name == "q" :
1802           return self.getCoefficient("q")           return self.getCoefficient("q")
1803       else:       else:
1804           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1805    
1806    class LameEquation(LinearPDE):
 class Poisson(LinearPDE):  
1807     """     """
1808     @brief Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
1809                                                                                                                                                                
1810     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] }
1811                                                                                                                                                                
1812          -u_{,jj} = f     with natural boundary conditons:
1813                                                                                                                                                                
1814       with boundary conditons:     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] }
1815                                                                                                                                                                
1816          n_j*u_{,j} = 0     and constraints:
1817                                                                                                                                                                
1818      and constraints:     M{u[i]=r[i]} where M{q[i]>0}
1819                                                                                                                                                                
          u=0 where q>0  
                                                                                                                                                               
1820     """     """
1821    
1822     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
1823         LinearPDE.__init__(self,domain,1,1)        super(LameEquation, self).__init__(domain,\
1824         self.COEFFICIENTS={                                           domain.getDim(),domain.getDim(),debug)
1825         "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),        self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1826         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1827         self.setSymmetryOn()                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1828         self.setValue(f,q)                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1829                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1830     def setValue(self,f=escript.Data(),q=escript.Data()):                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1831         self._setValue(f=f,q=q)                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1832          self.setSymmetryOn()
1833     def getCoefficientOfPDE(self,name):  
1834       """     def setValues(self,**coefficients):
1835       @brief return the value of the coefficient name of the general PDE       """
1836       @param name       sets new values to coefficients
1837       """  
1838       if name == "A" :       @param coefficients: new values assigned to coefficients
1839           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @keyword lame_mu: value for coefficient M{S{mu}}
1840       elif name == "B" :       @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1841         @keyword lame_lambda: value for coefficient M{S{lambda}}
1842         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1843         @keyword F: value for internal force M{F}
1844         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1845         @keyword sigma: value for initial stress M{S{sigma}}
1846         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1847         @keyword f: value for extrenal force M{f}
1848         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1849         @keyword r: prescribed values M{r} for the solution in constraints.
1850         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1851                   depending of reduced order is used for the representation of the equation.
1852         @keyword q: mask for location of constraints
1853         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1854                   depending of reduced order is used for the representation of the equation.
1855         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1856         """
1857         super(LameEquation, self).setValues(**coefficients)
1858    
1859       def getCoefficientOfGeneralPDE(self,name):
1860         """
1861         return the value of the coefficient name of the general PDE
1862    
1863         @param name: name of the coefficient requested.
1864         @type name: C{string}
1865         @return: the value of the coefficient  name
1866         @rtype: L{Data<escript.Data>}
1867         @raise IllegalCoefficient: if name is not one of coefficients
1868                      "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}.
1869         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1870         """
1871         if name == "A" :
1872             out =self.createCoefficientOfGeneralPDE("A")
1873             for i in range(self.getDim()):
1874               for j in range(self.getDim()):
1875                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1876                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1877                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1878             return out
1879         elif name == "B" :
1880           return escript.Data()           return escript.Data()
1881       elif name == "C" :       elif name == "C" :
1882           return escript.Data()           return escript.Data()
1883       elif name == "D" :       elif name == "D" :
1884           return escript.Data()           return escript.Data()
1885       elif name == "X" :       elif name == "X" :
1886             return self.getCoefficient("sigma")
1887         elif name == "Y" :
1888             return self.getCoefficient("F")
1889         elif name == "d" :
1890           return escript.Data()           return escript.Data()
1891       elif name == "Y" :       elif name == "y" :
1892           return self.getCoefficient("f")           return self.getCoefficient("f")
1893       elif name == "d" :       elif name == "d_contact" :
          return escript.Data()  
      elif name == "y" :  
          return escript.Data()  
      elif name == "d_contact" :  
1894           return escript.Data()           return escript.Data()
1895       elif name == "y_contact" :       elif name == "y_contact" :
1896           return escript.Data()           return escript.Data()
1897       elif name == "r" :       elif name == "r" :
1898           return escript.Data()           return self.getCoefficient("r")
1899       elif name == "q" :       elif name == "q" :
1900           return self.getCoefficient("q")           return self.getCoefficient("q")
1901       else:       else:
1902           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1903    
1904    class AdvectivePDE(LinearPDE):
1905       """
1906       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1907       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1908    
1909       In the following we set
1910    
1911       M{Z[j]=C[j]-B[j]}
1912    
1913       or
1914    
1915       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1916    
1917       To measure the dominance of the advective terms over the diffusive term M{A} the
1918       X{Pelclet number} M{P} is used. It is defined as
1919    
1920       M{P=h|Z|/(2|A|)}
1921    
1922       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1923       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1924    
1925       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1926    
1927       M{S{Xi}=S{xi}(P) h/|Z|}
1928    
1929       where M{S{xi}} is a suitable function of the Peclet number.
1930    
1931       In the case of a single PDE the coefficient are up-dated in the following way:
1932             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1933             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1934             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1935             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1936    
1937       Similar for the case of a systems of PDEs:
1938             - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}
1939             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1940             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1941             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1942    
1943       where M{S{delta}} is L{kronecker}.
1944       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1945       but with the intension to stabilize the solution.
1946    
1947       """
1948       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1949          """
1950          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1951    
1952          @param domain: domain of the PDE
1953          @type domain: L{Domain<escript.Domain>}
1954          @param numEquations: number of equations. If numEquations==None the number of equations
1955                               is exracted from the PDE coefficients.
1956          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1957                               is exracted from the PDE coefficients.
1958          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1959                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1960          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1961          @param debug: if True debug informations are printed.
1962          """
1963          super(AdvectivePDE, self).__init__(domain,\
1964                                             numEquations,numSolutions,debug)
1965          if xi==None:
1966             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1967          else:
1968             self.__xi=xi
1969          self.__Xi=escript.Data()
1970    
1971       def setValue(self,**coefficients):
1972          """
1973          sets new values to coefficients
1974    
1975          @param coefficients: new values assigned to coefficients
1976          @keyword A: value for coefficient A.
1977          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1978          @keyword B: value for coefficient B
1979          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1980          @keyword C: value for coefficient C
1981          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1982          @keyword D: value for coefficient D
1983          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1984          @keyword X: value for coefficient X
1985          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1986          @keyword Y: value for coefficient Y
1987          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1988          @keyword d: value for coefficient d
1989          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1990          @keyword y: value for coefficient y
1991          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1992          @keyword d_contact: value for coefficient d_contact
1993          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1994                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1995          @keyword y_contact: value for coefficient y_contact
1996          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1997                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1998          @keyword r: values prescribed to the solution at the locations of constraints
1999          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2000                   depending of reduced order is used for the solution.
2001          @keyword q: mask for location of constraints
2002          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2003                   depending of reduced order is used for the representation of the equation.
2004          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2005    
2006          """
2007          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2008          super(AdvectivePDE, self).setValue(**coefficients)
2009    
2010       def ELMAN_RAMAGE(self,P):
2011         """
2012         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2013         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2014              - M{S{xi}(P)=0} for M{P<1}
2015              - M{S{xi}(P)=(1-1/P)/2} otherwise
2016    
2017         @param P: Preclet number
2018         @type P: L{Scalar<escript.Scalar>}
2019         @return: up-wind weightimg factor
2020         @rtype: L{Scalar<escript.Scalar>}
2021         """
2022         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2023    
2024       def SIMPLIFIED_BROOK_HUGHES(self,P):
2025         """
2026         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2027         The original methods is
2028    
2029         M{S{xi}(P)=coth(P)-1/P}
2030    
2031         As the evaluation of M{coth} is expensive we are using the approximation:
2032    
2033             - M{S{xi}(P)=P/3} where M{P<3}
2034             - M{S{xi}(P)=1/2} otherwise
2035    
2036         @param P: Preclet number
2037         @type P: L{Scalar<escript.Scalar>}
2038         @return: up-wind weightimg factor
2039         @rtype: L{Scalar<escript.Scalar>}
2040         """
2041         c=util.whereNegative(P-3.)
2042         return P/6.*c+1./2.*(1.-c)
2043    
2044       def HALF(self,P):
2045         """
2046         Predefined function to set value M{1/2} for M{S{xi}}
2047    
2048         @param P: Preclet number
2049         @type P: L{Scalar<escript.Scalar>}
2050         @return: up-wind weightimg factor
2051         @rtype: L{Scalar<escript.Scalar>}
2052         """
2053         return escript.Scalar(0.5,P.getFunctionSpace())
2054    
2055       def __getXi(self):
2056          if self.__Xi.isEmpty():
2057             B=self.getCoefficient("B")
2058             C=self.getCoefficient("C")
2059             A=self.getCoefficient("A")
2060             h=self.getDomain().getSize()
2061             self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2062             if not C.isEmpty() or not B.isEmpty():
2063                if not C.isEmpty() and not B.isEmpty():
2064                    if self.getNumEquations()>1:
2065                       if self.getNumSolutions()>1:
2066                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2067                          for i in range(self.getNumEquations()):
2068                             for k in range(self.getNumSolutions()):
2069                                for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2070                          length_of_flux=util.sqrt(flux2)
2071                          # flux=C-util.reorderComponents(B,[0,2,1])
2072                       else:
2073                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2074                          for i in range(self.getNumEquations()):
2075                             for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2076                          length_of_flux=util.sqrt(flux2)
2077                          # flux=C-B
2078                    else:
2079                       if self.getNumSolutions()>1:
2080                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2081                          for k in range(self.getNumSolutions()):
2082                             for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2083                          # flux=C-util.reorderComponents(B,[1,0])
2084                          length_of_flux=util.sqrt(flux2)
2085                       else:
2086                          length_of_flux=util.length(C-B)
2087                elif C.isEmpty():
2088                  length_of_flux=util.length(B)
2089                else:
2090                  length_of_flux=util.length(C)
2091                flux_max=util.Lsup(length_of_flux)
2092                if flux_max>0.:
2093                  if A.isEmpty():
2094                      inv_A=1./self.SMALL_TOLERANCE
2095                      peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())
2096                      xi=self.__xi(self,peclet_number)
2097                  else:
2098                      # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2099                      length_of_A=util.length(A)
2100                      A_max=util.Lsup(length_of_A)
2101                      if A_max>0:
2102                           inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)
2103                      else:
2104                           inv_A=1./self.SMALL_TOLERANCE
2105                      peclet_number=length_of_flux*h/2*inv_A
2106                      xi=self.__xi(self,peclet_number)
2107                  self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)
2108                  self.trace("preclet number = %e"%util.Lsup(peclet_number))
2109                else:
2110                  self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())
2111          return self.__Xi
2112    
2113    
2114       def getCoefficientOfGeneralPDE(self,name):
2115         """
2116         return the value of the coefficient name of the general PDE
2117    
2118         @param name: name of the coefficient requested.
2119         @type name: C{string}
2120         @return: the value of the coefficient name
2121         @rtype: L{Data<escript.Data>}
2122         @raise IllegalCoefficient: if name is not one of coefficients
2123                      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}.
2124         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2125         """
2126         if not self.getNumEquations() == self.getNumSolutions():
2127              raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2128    
2129         if name == "A" :
2130             A=self.getCoefficient("A")
2131             B=self.getCoefficient("B")
2132             C=self.getCoefficient("C")
2133             if B.isEmpty() and C.isEmpty():
2134                Aout=A
2135             else:
2136                if A.isEmpty():
2137                   Aout=self.createCoefficientOfGeneralPDE("A")
2138                else:
2139                   Aout=A[:]
2140                Xi=self.__getXi()
2141                if self.getNumEquations()>1:
2142                    for i in range(self.getNumEquations()):
2143                       for j in range(self.getDim()):
2144                          for k in range(self.getNumSolutions()):
2145                             for l in range(self.getDim()):
2146                                if not C.isEmpty() and not B.isEmpty():
2147                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2148                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2149                                   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])
2150                                elif C.isEmpty():
2151                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2152                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2153                                else:
2154                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2155                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2156                else:
2157                   if not C.isEmpty() and not B.isEmpty():
2158                       delta=(C-B)
2159                       Aout+=util.outer(Xi*delta,delta)
2160                   elif not B.isEmpty():
2161                       Aout+=util.outer(Xi*B,B)
2162                   elif not C.isEmpty():
2163                       Aout+=util.outer(Xi*C,C)
2164             return Aout
2165         elif name == "B" :
2166             # return self.getCoefficient("B")
2167             B=self.getCoefficient("B")
2168             C=self.getCoefficient("C")
2169             D=self.getCoefficient("D")
2170             if C.isEmpty() or D.isEmpty():
2171                Bout=B
2172             else:
2173                Xi=self.__getXi()
2174                if B.isEmpty():
2175                    Bout=self.createCoefficientOfGeneralPDE("B")
2176                else:
2177                    Bout=B[:]
2178                if self.getNumEquations()>1:
2179                   for k in range(self.getNumSolutions()):
2180                      for p in range(self.getNumEquations()):
2181                         tmp=Xi*D[p,k]
2182                         for i in range(self.getNumEquations()):
2183                            for j in range(self.getDim()):
2184                               Bout[i,j,k]+=tmp*C[p,i,j]
2185                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2186                else:
2187                   Bout+=(Xi*D)*C
2188             return Bout
2189         elif name == "C" :
2190             # return self.getCoefficient("C")
2191             B=self.getCoefficient("B")
2192             C=self.getCoefficient("C")
2193             D=self.getCoefficient("D")
2194             if B.isEmpty() or D.isEmpty():
2195                Cout=C
2196             else:
2197                Xi=self.__getXi()
2198                if C.isEmpty():
2199                    Cout=self.createCoefficientOfGeneralPDE("C")
2200                else:
2201                    Cout=C[:]
2202                if self.getNumEquations()>1:
2203                   for k in range(self.getNumSolutions()):
2204                       for p in range(self.getNumEquations()):
2205                          tmp=Xi*D[p,k]
2206                          for i in range(self.getNumEquations()):
2207                            for l in range(self.getDim()):
2208                                     Cout[i,k,l]+=tmp*B[p,l,i]
2209                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2210                else:
2211                   Cout+=(Xi*D)*B
2212             return Cout
2213         elif name == "D" :
2214             return self.getCoefficient("D")
2215         elif name == "X" :
2216             # return self.getCoefficient("X")
2217             X=self.getCoefficient("X")
2218             Y=self.getCoefficient("Y")
2219             B=self.getCoefficient("B")
2220             C=self.getCoefficient("C")
2221             if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2222                Xout=X
2223             else:
2224                if X.isEmpty():
2225                    Xout=self.createCoefficientOfGeneralPDE("X")
2226                else:
2227                    Xout=X[:]
2228                Xi=self.__getXi()
2229                if self.getNumEquations()>1:
2230                     for p in range(self.getNumEquations()):
2231                        tmp=Xi*Y[p]
2232                        for i in range(self.getNumEquations()):
2233                           for j in range(self.getDim()):
2234                              if not C.isEmpty() and not B.isEmpty():
2235                                 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2236                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2237                              elif C.isEmpty():
2238                                 Xout[i,j]-=tmp*B[p,j,i]
2239                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2240                              else:
2241                                 Xout[i,j]+=tmp*C[p,i,j]
2242                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2243                else:
2244                  if not C.isEmpty() and not B.isEmpty():
2245                    Xout+=(Xi*Y)*(C-B)
2246                  elif C.isEmpty():
2247                    Xout-=(Xi*Y)*B
2248                  else:
2249                    Xout+=(Xi*Y)*C
2250             return Xout
2251         elif name == "Y" :
2252             return self.getCoefficient("Y")
2253         elif name == "d" :
2254             return self.getCoefficient("d")
2255         elif name == "y" :
2256             return self.getCoefficient("y")
2257         elif name == "d_contact" :
2258             return self.getCoefficient("d_contact")
2259         elif name == "y_contact" :
2260             return self.getCoefficient("y_contact")
2261         elif name == "r" :
2262             return self.getCoefficient("r")
2263         elif name == "q" :
2264             return self.getCoefficient("q")
2265         else:
2266            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2267    
2268    # $Log$
2269    # Revision 1.14  2005/09/22 01:54:57  jgs
2270    # Merge of development branch dev-02 back to main trunk on 2005-09-22
2271    #
2272    # Revision 1.13  2005/09/15 03:44:19  jgs
2273    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2274    #
2275    # Revision 1.12  2005/09/01 03:31:28  jgs
2276    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2277    #
2278    # Revision 1.11  2005/08/23 01:24:28  jgs
2279    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2280    #
2281    # Revision 1.10  2005/08/12 01:45:36  jgs
2282    # erge of development branch dev-02 back to main trunk on 2005-08-12
2283    #
2284    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2285    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2286    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2287    # modified to instead use portable/cooperative "super" calls to extend base
2288    # class methods.
2289    #
2290    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2291    # Removed redundant if-loop.
2292    #
2293    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2294    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2295    #
2296    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2297    # the solver from finley are put into the standalone package paso now
2298    #
2299    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2300    # in the case of lumping no new system is allocated if the constraint is changed.
2301    #
2302    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2303    # test for Lumping added
2304    #
2305    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2306    # bug in format fixed.
2307    #
2308    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2309    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2310    #
2311    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2312    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2313    #
2314    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2315    # gneric unit testing for linearPDE
2316    #
2317    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2318    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2319    #
2320    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2321    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2322    #
2323    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2324    # epydoc mark up partially fixed
2325    #
2326    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2327    # some problems with LinearPDEs fixed.
2328    #
2329    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2330    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2331    #
2332    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2333    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2334    #
2335    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2336    # new functions in util and a new pde type in linearPDEs
2337    #
2338    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2339    # Lame equation: (linear elastic, isotropic) added
2340    #
2341    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2342    # some extensions to modellib and linearPDEs
2343    #
2344    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2345    # Fixed up some docstrings.  Moved module-level functions to top of file so
2346    # that epydoc and doxygen can pick them up properly.
2347    #
2348    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2349    # some basic Models have been added
2350    #
2351    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2352    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2353    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2354    # reformatting of docstrings.  Addition of code to make equations come out
2355    # as proper LaTeX.
2356    #
2357    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2358    # some problems with functionspace and linearPDEs fixed.
2359    #
2360    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2361    # bug in SystemPattern fixed.
2362    #
2363    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2364    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2365    #
2366    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2367    # Reference Number handling added
2368    #
2369    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2370    # some function exposed to python to make mesh merging running
2371    #
2372    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2373    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2374    #
2375    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2376    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2377    #
2378    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2379    # updates in the documentation
2380    #
2381    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2382    # Added createCoefficient method for linearPDEs.
2383    #
2384    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2385    # a problem in linearPDE class fixed
2386    #
2387    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2388    # some bugs in linearPDE fixed
2389    #
2390    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2391    # some bugs in slicing fixed
2392    #
2393    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2394    # FunctionSpace checking/matchig in slicing added
2395    #
2396    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2397    # bug in setValue fixed
2398    #
2399    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2400    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2401    #
2402    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2403    # AdvectivePDE added
2404    #
2405    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2406    # some changes in linearPDEs to add AdevectivePDE
2407    #
2408    # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2409    # __init__ of LinearPDE does not accept any coefficient anymore
2410    #
2411    # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2412    # *** empty log message ***
2413    #
2414    # Revision 1.1.2.1  2004/12/12 22:53:47  gross
2415    # linearPDE has been renamed LinearPDE
2416    #
2417    # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross
2418    # GMRES added
2419    #
2420    # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross
2421    # options for GMRES and PRES20 added
2422    #
2423    # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross
2424    # some small changes
2425    #
2426    # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross
2427    # Finley solves 4M unknowns now
2428    #
2429    # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross
2430    # poisson solver added
2431    #
2432    # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross
2433    # 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
2434    #
2435    # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross
2436    # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed
2437    #
2438    # Revision 1.1.1.1  2004/10/26 06:53:56  jgs
2439    # initial import of project esys2
2440    #
2441    # Revision 1.3.2.3  2004/10/26 06:43:48  jgs
2442    # committing Lutz's and Paul's changes to brach jgs
2443    #
2444    # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane
2445    # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.
2446    #
2447    # Revision 1.3  2004/09/23 00:53:23  jgs
2448    # minor fixes
2449    #
2450    # Revision 1.1  2004/08/28 12:58:06  gross
2451    # SimpleSolve is not running yet: problem with == of functionsspace
2452    #

Legend:
Removed from v.108  
changed lines
  Added in v.720

  ViewVC Help
Powered by ViewVC 1.1.26