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trunk/esys2/escript/py_src/linearPDEs.py revision 114 by jgs, Fri Mar 4 07:12:37 2005 UTC trunk/escript/py_src/linearPDEs.py revision 430 by gross, Wed Jan 11 06:40:50 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
2    
3  ## @file linearPDEs.py  #
4    #      COPYRIGHT ACcESS 2004 -  All Rights Reserved
5    #
6    #   This software is the property of ACcESS.  No part of this code
7    #   may be copied in any form or by any means without the expressed written
8    #   consent of ACcESS.  Copying, use or modification of this software
9    #   by any unauthorised person is illegal unless that
10    #   person has a software license agreement with ACcESS.
11    #
12  """  """
13  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
14    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
15    solver capabilities in itself but hands the PDE over to
16    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
17    The general interface is provided through the L{LinearPDE} class. The
18    L{AdvectivePDE} which is derived from the L{LinearPDE} class
19    provides an interface to PDE dominated by its advective terms. The L{Poisson},
20    L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}
21    classs which are also derived form the L{LinearPDE} class should be used
22    to define of solve these sepecial PDEs.
23    
24    @var __author__: name of author
25    @var __licence__: licence agreement
26    @var __url__: url entry point on documentation
27    @var __version__: version
28    @var __date__: date of the version
29  """  """
30    
31  import escript  import escript
32  import util  import util
33  import numarray  import numarray
34    
35    __author__="Lutz Gross, l.gross@uq.edu.au"
36    __licence__="contact: esys@access.uq.edu.au"
37    __url__="http://www.iservo.edu.au/esys/escript"
38    __version__="$Revision$"
39    __date__="$Date$"
40    
41    
42  def _CompTuple2(t1,t2):  class IllegalCoefficient(ValueError):
43       """
44       raised if an illegal coefficient of the general ar particular PDE is requested.
45     """     """
    @brief  
46    
47     @param t1  class IllegalCoefficientValue(ValueError):
48     @param t2     """
49       raised if an incorrect value for a coefficient is used.
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 UndefinedPDEError(ValueError):
53       """
54       raised if a PDE is not fully defined yet.
55       """
56    
57    class PDECoefficient(object):
58      """      """
59      @brief      A class for describing a PDE coefficient
60    
61        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
62        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
63        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
64        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
65        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
66        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
67        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
68        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
69        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
70        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
71        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
72    
73      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
74      INTERIOR=0      INTERIOR=0
75      BOUNDARY=1      BOUNDARY=1
76      CONTACT=2      CONTACT=2
77      CONTINUOUS=3      SOLUTION=3
78      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
79      # 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
80      # number of unknowns.      BY_SOLUTION=6
81      EQUATION=3      BY_DIM=7
82      SOLUTION=4      OPERATOR=10
83      DIM=5      RIGHTHANDSIDE=11
84      # indicator for what is altered if the coefficient is altered:      BOTH=12
85      OPERATOR=5  
     RIGHTHANDSIDE=6  
     BOTH=7  
86      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
87         """         """
88         @brief Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
89    
90           @param where: describes where the coefficient lives
91           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
92           @param pattern: describes the shape of the coefficient and how the shape is build for a given
93                  spatial dimension and numbers of equation and solution in then PDE. For instance,
94                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
95                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
96                  on a 2-dimensional domain. In the case of single equation and a single solution component
97                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
98                  the example would be read as (2,).
99           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
100           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
101           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
102    
103         """         """
104           super(PDECoefficient, self).__init__()
105         self.what=where         self.what=where
106         self.pattern=pattern         self.pattern=pattern
107         self.altering=altering         self.altering=altering
# Line 53  class PDECoefficient: Line 109  class PDECoefficient:
109    
110      def resetValue(self):      def resetValue(self):
111         """         """
112         @brief resets coefficient value to default         resets coefficient value to default
113         """         """
114         self.value=escript.Data()         self.value=escript.Data()
115    
116      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
117         """         """
118         @brief defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
119    
120         @param domain         @param domain: domain on which the PDE uses the coefficient
121         """         @type domain: L{Domain<escript.Domain>}
122         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
123         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type domain: C{bool}
124         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
125         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type domain: C{bool}
126           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
127           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
128           """
129           if self.what==self.INTERIOR:
130                return escript.Function(domain)
131           elif self.what==self.BOUNDARY:
132                return escript.FunctionOnBoundary(domain)
133           elif self.what==self.CONTACT:
134                return escript.FunctionOnContactZero(domain)
135           elif self.what==self.SOLUTION:
136                if reducedEquationOrder and reducedSolutionOrder:
137                    return escript.ReducedSolution(domain)
138                else:
139                    return escript.Solution(domain)
140           elif self.what==self.REDUCED:
141                return escript.ReducedSolution(domain)
142    
143      def getValue(self):      def getValue(self):
144         """         """
145         @brief returns the value of the coefficient:         returns the value of the coefficient
146    
147           @return:  value of the coefficient
148           @rtype:  L{Data<escript.Data>}
149         """         """
150         return self.value         return self.value
151        
152      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  
153         """         """
154           set the value of the coefficient to a new value
155    
156           @param domain: domain on which the PDE uses the coefficient
157           @type domain: L{Domain<escript.Domain>}
158           @param numEquations: number of equations of the PDE
159           @type numEquations: C{int}
160           @param numSolutions: number of components of the PDE solution
161           @type numSolutions: C{int}
162           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
163           @type domain: C{bool}
164           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
165           @type domain: C{bool}
166           @param newValue: number of components of the PDE solution
167           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
168           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
169           """
170           if newValue==None:
171               newValue=escript.Data()
172           elif isinstance(newValue,escript.Data):
173               if not newValue.isEmpty():
174                  try:
175                     newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
176                  except:
177                     raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
178           else:
179               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
180           if not newValue.isEmpty():
181               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
182                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
183         self.value=newValue         self.value=newValue
184        
185      def isAlteringOperator(self):      def isAlteringOperator(self):
186          """          """
187      @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
188    
189            @return:  True if the operator of the PDE is changed when the coefficient is changed
190            @rtype:  C{bool}
191      """      """
192          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
193              return not None              return not None
# Line 91  class PDECoefficient: Line 196  class PDECoefficient:
196    
197      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
198          """          """
199      @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
200    
201        @rtype:  C{bool}
202            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
203      """      """
204          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
205              return not None              return not None
206          else:          else:
207              return None              return None
208    
209      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
210         """         """
211         @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
212    
213         @param shape         @param domain: domain on which the PDE uses the coefficient
214         @param dim         @type domain: L{Domain<escript.Domain>}
215           @param shape: suggested shape of the coefficient
216           @type shape: C{tuple} of C{int} values
217           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
218                     If no appropriate numbers could be identified, C{None} is returned
219           @rtype: C{tuple} of two C{int} values or C{None}
220         """         """
221           dim=domain.getDim()
222         if len(shape)>0:         if len(shape)>0:
223             num=max(shape)+1             num=max(shape)+1
224         else:         else:
225             num=1             num=1
226         search=[]         search=[]
227         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
228            for e in range(num):            for u in range(num):
229               search.append((e,u))               for e in range(num):
230         search.sort(_CompTuple2)                  search.append((e,u))
231         for item in search:            search.sort(self.__CompTuple2)
232               s=self.buildShape(item[0],item[1],dim)            for item in search:
233                 s=self.getShape(domain,item[0],item[1])
234               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
235                   return (1,1)                   return (1,1)
236               else:               else:
237                   if s==shape: return item                   if s==shape: return item
238           elif self.definesNumEquation():
239              for e in range(num,0,-1):
240                 s=self.getShape(domain,e,0)
241                 if len(s)==0 and len(shape)==0:
242                     return (1,None)
243                 else:
244                     if s==shape: return (e,None)
245    
246           elif self.definesNumSolutions():
247              for u in range(num,0,-1):
248                 s=self.getShape(domain,0,u)
249                 if len(s)==0 and len(shape)==0:
250                     return (None,1)
251                 else:
252                     if s==shape: return (None,u)
253         return None         return None
254        def definesNumSolutions(self):
255           """
256           checks if the coefficient allows to estimate the number of solution components
257    
258      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
259          """         @rtype: C{bool}
260      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
261           for i in self.pattern:
262                 if i==self.BY_SOLUTION: return True
263           return False
264    
265      @param e      def definesNumEquation(self):
266      @param u         """
267      @param dim         checks if the coefficient allows to estimate the number of equations
268      """  
269          s=()         @return: True if the coefficient allows an estimate of the number of equations
270          for i in self.pattern:         @rtype: C{bool}
271               if i==self.EQUATION:         """
272                  if e>1: s=s+(e,)         for i in self.pattern:
273               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
274                  if u>1: s=s+(u,)         return False
275    
276        def __CompTuple2(self,t1,t2):
277          """
278          Compare two tuples of possible number of equations and number of solutions
279    
280          @param t1: The first tuple
281          @param t2: The second tuple
282    
283          """
284    
285          dif=t1[0]+t1[1]-(t2[0]+t2[1])
286          if dif<0: return 1
287          elif dif>0: return -1
288          else: return 0
289    
290        def getShape(self,domain,numEquations=1,numSolutions=1):
291           """
292           builds the required shape of the coefficient
293    
294           @param domain: domain on which the PDE uses the coefficient
295           @type domain: L{Domain<escript.Domain>}
296           @param numEquations: number of equations of the PDE
297           @type numEquations: C{int}
298           @param numSolutions: number of components of the PDE solution
299           @type numSolutions: C{int}
300           @return: shape of the coefficient
301           @rtype: C{tuple} of C{int} values
302           """
303           dim=domain.getDim()
304           s=()
305           for i in self.pattern:
306                 if i==self.BY_EQUATION:
307                    if numEquations>1: s=s+(numEquations,)
308                 elif i==self.BY_SOLUTION:
309                    if numSolutions>1: s=s+(numSolutions,)
310               else:               else:
311                  s=s+(dim,)                  s=s+(dim,)
312          return s         return s
313    
314  class LinearPDE:  class LinearPDE(object):
315     """     """
316     @brief Class to handel a linear PDE     This class is used to define a general linear, steady, second order PDE
317         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  
318    
319       -(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:
320    
321       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}
322    
323          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,
324       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
325       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
326       L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
327       M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
328    
329      and contact conditions     The following natural boundary conditions are considered:
330    
331          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}
332    
333      and constraints:     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
334       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
335       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
336    
          u_i=r_i where q_i>0  
337    
338     """     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  
    ILU0=util.ILU0  
    JACOBI=util.JACOBI  
339    
340     def __init__(self,domain,numEquations=0,numSolutions=0):     M{u=r}  where M{q>0}
      """  
      @brief initializes a new linear PDE.  
341    
342       @param args     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
343       """     The constraints override any other condition set by the PDE or the boundary condition.
344       # COEFFICIENTS can be overwritten by subclasses:  
345       self.COEFFICIENTS={     The PDE is symmetrical if
346         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
347         "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]}
348         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
349         "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
350         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
351         "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] }
352         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
353         "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.
354         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The natural boundary conditions take the form:
355         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
356         "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]}
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
357    
358    
359       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
360    
361    
362       M{u[i]=r[i]}  where  M{q[i]>0}
363    
364       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
365    
366       The system of PDEs is symmetrical if
367    
368            - M{A[i,j,k,l]=A[k,l,i,j]}
369            - M{B[i,j,k]=C[k,i,j]}
370            - M{D[i,k]=D[i,k]}
371            - M{d[i,k]=d[k,i]}
372    
373       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
374       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
375       defined as
376    
377       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
378    
379       For the case of single solution component and single PDE M{J} is defined
380    
381       M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
382    
383       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
384       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
385       the contact condition takes the form
386    
387       M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
388    
389       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
390       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
391       L{jump<util.jump>}.
392       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>}.
393       In case of a single PDE and a single component solution the contact condition takes the form
394    
395       M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
396    
397       In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
398       both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
399    
400       @cvar DEFAULT: The default method used to solve the system of linear equations
401       @cvar DIRECT: The direct solver based on LDU factorization
402       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
403       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
404       @cvar CR: The conjugate residual method
405       @cvar CGS: The conjugate gardient square method
406       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
407       @cvar SSOR: The symmetric overrealaxtion method
408       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
409       @cvar ILUT: The incomplete LU factorization preconditioner with will in
410       @cvar JACOBI: The Jacobi preconditioner
411       @cvar GMRES: The Gram-Schmidt minimum residual method
412       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
413       @cvar LUMPING: Matrix lumping.
414       @cvar NO_REORDERING: No matrix reordering allowed
415       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
416       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
417       @cvar PASO: PASO solver package
418       @cvar SCSL: SGI SCSL solver library
419       @cvar MKL: Intel's MKL solver library
420       @cvar UMFPACK: the UMFPACK library
421       @cvar ITERATIVE: The default iterative solver
422       @cvar AMG: algebraic multi grid
423       @cvar RILU: recursive ILU
424    
425       """
426       DEFAULT= 0
427       DIRECT= 1
428       CHOLEVSKY= 2
429       PCG= 3
430       CR= 4
431       CGS= 5
432       BICGSTAB= 6
433       SSOR= 7
434       ILU0= 8
435       ILUT= 9
436       JACOBI= 10
437       GMRES= 11
438       PRES20= 12
439       LUMPING= 13
440       NO_REORDERING= 17
441       MINIMUM_FILL_IN= 18
442       NESTED_DISSECTION= 19
443       SCSL= 14
444       MKL= 15
445       UMFPACK= 16
446       ITERATIVE= 20
447       PASO= 21
448       AMG= 22
449       RILU = 23
450    
451       __TOL=1.e-13
452       __PACKAGE_KEY="package"
453       __METHOD_KEY="method"
454       __SYMMETRY_KEY="symmetric"
455       __TOLERANCE_KEY="tolerance"
456       __PRECONDITIONER_KEY="preconditioner"
457    
458    
459       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
460         """
461         initializes a new linear PDE
462    
463         @param domain: domain of the PDE
464         @type domain: L{Domain<escript.Domain>}
465         @param numEquations: number of equations. If numEquations==None the number of equations
466                              is exracted from the PDE coefficients.
467         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
468                              is exracted from the PDE coefficients.
469         @param debug: if True debug informations are printed.
470    
471         """
472         super(LinearPDE, self).__init__()
473         #
474         #   the coefficients of the general PDE:
475         #
476         self.__COEFFICIENTS_OF_GENEARL_PDE={
477           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
478           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
480           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
482           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
484           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
485           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
486           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
487           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
488           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
489    
490         # COEFFICIENTS can be overwritten by subclasses:
491         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
492         self.__altered_coefficients=False
493       # initialize attributes       # initialize attributes
494       self.__debug=None       self.__debug=debug
495       self.__domain=domain       self.__domain=domain
496       self.__numEquations=numEquations       self.__numEquations=numEquations
497       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
498       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  
499    
500       # set some default values:       # set some default values:
501       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
502       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
503       self.__tolerance=1.e-8       self.__tolerance=1.e-8
504       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
505       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
506         self.__preconditioner=self.DEFAULT
507         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
508       self.__sym=False       self.__sym=False
      self.__lumping=False  
509    
510     def createCoefficient(self, name):       self.resetCoefficients()
511         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
512       # =============================================================================
513       #    general stuff:
514       # =============================================================================
515       def __str__(self):
516         """
517         returns string representation of the PDE
518    
519         @return: a simple representation of the PDE
520         @rtype: C{str}
521         """
522         return "<LinearPDE %d>"%id(self)
523       # =============================================================================
524       #    debug :
525       # =============================================================================
526       def setDebugOn(self):
527       """       """
528       @brief create a data object corresponding to coefficient name       switches on debugging
      @param name  
529       """       """
530       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
   
    def __del__(self):  
      pass  
531    
532     def getCoefficient(self,name):     def setDebugOff(self):
533       """       """
534       @brief return the value of the parameter name       switches off debugging
535         """
536         self.__debug=None
537    
538       @param name     def trace(self,text):
539         """
540         print the text message if debugging is swiched on.
541         @param text: message
542         @type text: C{string}
543       """       """
544       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
545    
546     def getCoefficientOfPDE(self,name):     # =============================================================================
547       # some service functions:
548       # =============================================================================
549       def getDomain(self):
550       """       """
551       @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
552              it can be overwritten to map coefficients of a particualr PDE to the general PDE.  
553       @param name       @return: the domain of the PDE
554         @rtype: L{Domain<escript.Domain>}
555       """       """
556       return self.getCoefficient(name)       return self.__domain
557    
558     def hasCoefficient(self,name):     def getDim(self):
559        """       """
560        @brief return true if name is the name of a coefficient       returns the spatial dimension of the PDE
561    
562        @param name       @return: the spatial dimension of the PDE domain
563        """       @rtype: C{int}
564        return self.COEFFICIENTS.has_key(name)       """
565         return self.getDomain().getDim()
566    
567     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
568       """       """
569       @brief return true if the test functions should use reduced order       returns the number of equations
570    
571         @return: the number of equations
572         @rtype: C{int}
573         @raise UndefinedPDEError: if the number of equations is not be specified yet.
574       """       """
575       return self.__row_function_space       if self.__numEquations==None:
576             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
577         else:
578             return self.__numEquations
579    
580     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
581       """       """
582       @brief return true if the interpolation of the solution should use reduced order       returns the number of unknowns
583    
584         @return: the number of unknowns
585         @rtype: C{int}
586         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
587       """       """
588       return self.__column_function_space       if self.__numSolutions==None:
589            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
590         else:
591            return self.__numSolutions
592    
593     def setValue(self,**coefficients):     def reduceEquationOrder(self):
594        """       """
595        @brief sets new values to coefficients       return status for order reduction for equation
596    
597        @param coefficients       @return: return True is reduced interpolation order is used for the represenation of the equation
598        """       @rtype: L{bool}
599        self._setValue(**coefficients)       """
600               return self.__reduce_equation_order
601    
602     def cleanCoefficients(self):     def reduceSolutionOrder(self):
603       """       """
604       @brief resets all coefficients to default values.       return status for order reduction for the solution
605    
606         @return: return True is reduced interpolation order is used for the represenation of the solution
607         @rtype: L{bool}
608       """       """
609       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
610    
611     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
612       """       """
613       @brief returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
614    
615         @return: representation space of equation
616         @rtype: L{FunctionSpace<escript.FunctionSpace>}
617       """       """
618       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
619                   return escript.ReducedSolution(self.getDomain())
620         else:
621             return escript.Solution(self.getDomain())
622    
623     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
624       """       """
625       @brief return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
626    
627       @param name       @return: representation space of solution
628         @rtype: L{FunctionSpace<escript.FunctionSpace>}
629       """       """
630       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
631          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
632       else:       else:
633          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
634    
635     def getFunctionSpaceForCoefficient(self,name):  
636       def getOperator(self):
637       """       """
638       @brief return the atoms of the coefficient name       provides access to the operator of the PDE
639    
640       @param name       @return: the operator of the PDE
641         @rtype: L{Operator<escript.Operator>}
642       """       """
643       if self.hasCoefficient(name):       m=self.getSystem()[0]
644          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
645             return self.copyConstraint(1./m)
646       else:       else:
647          raise ValueError,"Solution coefficient %s requested"%name           return m
648    
649     def alteredCoefficient(self,name):     def getRightHandSide(self):
650       """       """
651       @brief annonced that coefficient name has been changed       provides access to the right hand side of the PDE
652         @return: the right hand side of the PDE
653         @rtype: L{Data<escript.Data>}
654         """
655         r=self.getSystem()[1]
656         if self.isUsingLumping():
657             return self.copyConstraint(r)
658         else:
659             return r
660    
661       @param name     def applyOperator(self,u=None):
662       """       """
663       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
664          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
665          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}
666                   the current solution is used.
667         @type u: L{Data<escript.Data>} or None
668         @return: image of u
669         @rtype: L{Data<escript.Data>}
670         """
671         if u==None:
672              return self.getOperator()*self.getSolution()
673       else:       else:
674          raise ValueError,"unknown coefficient %s requested"%name          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
675    
676     # ===== debug ==============================================================     def getResidual(self,u=None):
677     def setDebugOn(self):       """
678         return the residual of u or the current solution if u is not present.
679    
680         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
681                   the current solution is used.
682         @type u: L{Data<escript.Data>} or None
683         @return: residual of u
684         @rtype: L{Data<escript.Data>}
685         """
686         return self.applyOperator(u)-self.getRightHandSide()
687    
688       def checkSymmetry(self,verbose=True):
689          """
690          test the PDE for symmetry.
691    
692          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
693          @type verbose: C{bool}
694          @return:  True if the PDE is symmetric.
695          @rtype: L{Data<escript.Data>}
696          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
697          """
698          verbose=verbose or self.__debug
699          out=True
700          if self.getNumSolutions()!=self.getNumEquations():
701             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
702             out=False
703          else:
704             A=self.getCoefficientOfGeneralPDE("A")
705             if not A.isEmpty():
706                tol=util.Lsup(A)*self.__TOL
707                if self.getNumSolutions()>1:
708                   for i in range(self.getNumEquations()):
709                      for j in range(self.getDim()):
710                         for k in range(self.getNumSolutions()):
711                            for l in range(self.getDim()):
712                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
713                                   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)
714                                   out=False
715                else:
716                   for j in range(self.getDim()):
717                      for l in range(self.getDim()):
718                         if util.Lsup(A[j,l]-A[l,j])>tol:
719                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
720                            out=False
721             B=self.getCoefficientOfGeneralPDE("B")
722             C=self.getCoefficientOfGeneralPDE("C")
723             if B.isEmpty() and not C.isEmpty():
724                if verbose: print "non-symmetric PDE because B is not present but C is"
725                out=False
726             elif not B.isEmpty() and C.isEmpty():
727                if verbose: print "non-symmetric PDE because C is not present but B is"
728                out=False
729             elif not B.isEmpty() and not C.isEmpty():
730                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
731                if self.getNumSolutions()>1:
732                   for i in range(self.getNumEquations()):
733                       for j in range(self.getDim()):
734                          for k in range(self.getNumSolutions()):
735                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
736                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
737                                  out=False
738                else:
739                   for j in range(self.getDim()):
740                      if util.Lsup(B[j]-C[j])>tol:
741                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
742                         out=False
743             if self.getNumSolutions()>1:
744               D=self.getCoefficientOfGeneralPDE("D")
745               if not D.isEmpty():
746                 tol=util.Lsup(D)*self.__TOL
747                 for i in range(self.getNumEquations()):
748                    for k in range(self.getNumSolutions()):
749                      if util.Lsup(D[i,k]-D[k,i])>tol:
750                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
751                          out=False
752               d=self.getCoefficientOfGeneralPDE("d")
753               if not d.isEmpty():
754                 tol=util.Lsup(d)*self.__TOL
755                 for i in range(self.getNumEquations()):
756                    for k in range(self.getNumSolutions()):
757                      if util.Lsup(d[i,k]-d[k,i])>tol:
758                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
759                          out=False
760               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
761               if not d_contact.isEmpty():
762                 tol=util.Lsup(d_contact)*self.__TOL
763                 for i in range(self.getNumEquations()):
764                    for k in range(self.getNumSolutions()):
765                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
766                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
767                          out=False
768          return out
769    
770       def getSolution(self,**options):
771         """         """
772         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
773    
774           @return: the solution
775           @rtype: L{Data<escript.Data>}
776           @param options: solver options
777           @keyword verbose: True to get some information during PDE solution
778           @type verbose: C{bool}
779           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
780                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
781           @keyword iter_max: maximum number of iteration steps allowed.
782           @keyword drop_tolerance: threshold for drupping in L{ILUT}
783           @keyword drop_storage: maximum of allowed memory in L{ILUT}
784           @keyword truncation: maximum number of residuals in L{GMRES}
785           @keyword restart: restart cycle length in L{GMRES}
786         """         """
787         self.__debug=not None         if not self.__solution_isValid:
788              mat,f=self.getSystem()
789              if self.isUsingLumping():
790                 self.__solution=self.copyConstraint(f*mat)
791              else:
792                 options[self.__TOLERANCE_KEY]=self.getTolerance()
793                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
794                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
795                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
796                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
797                 self.trace("PDE is resolved.")
798                 self.trace("solver options: %s"%str(options))
799                 self.__solution=mat.solve(f,options)
800              self.__solution_isValid=True
801           return self.__solution
802    
803     def setDebugOff(self):     def getFlux(self,u=None):
804         """
805         returns the flux M{J} for a given M{u}
806    
807         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
808    
809         or
810    
811         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
812    
813         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
814         @type u: L{Data<escript.Data>} or None
815         @return: flux
816         @rtype: L{Data<escript.Data>}
817         """
818         if u==None: u=self.getSolution()
819         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
820       # =============================================================================
821       #   solver settings:
822       # =============================================================================
823       def setSolverMethod(self,solver=None,preconditioner=None):
824         """         """
825         @brief         sets a new solver
826    
827           @param solver: sets a new solver method.
828           @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}.
829           @param preconditioner: sets a new solver method.
830           @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}
831         """         """
832         self.__debug=None         if solver==None: solve=self.DEFAULT
833           if preconditioner==None: preconditioner=self.DEFAULT
834           if not (solver,preconditioner)==self.getSolverMethod():
835               self.__solver_method=solver
836               self.__preconditioner=preconditioner
837               self.__checkMatrixType()
838               self.trace("New solver is %s"%self.getSolverMethodName())
839    
840     def debug(self):     def getSolverMethodName(self):
841         """         """
842         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
843    
844           @return: the name of the solver currently used.
845           @rtype: C{string}
846         """         """
        return self.__debug  
847    
848     #===== Lumping ===========================         m=self.getSolverMethod()
849     def setLumpingOn(self):         p=self.getSolverPackage()
850        """         method=""
851        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
852        """         elif m[0]==self.DIRECT: method= "DIRECT"
853        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
854           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
855           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
856           self.__lumping=True         elif m[0]==self.CR: method= "CR"
857           elif m[0]==self.CGS: method= "CGS"
858           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
859           elif m[0]==self.SSOR: method= "SSOR"
860           elif m[0]==self.GMRES: method= "GMRES"
861           elif m[0]==self.PRES20: method= "PRES20"
862           elif m[0]==self.LUMPING: method= "LUMPING"
863           if m[1]==self.DEFAULT: method+="+DEFAULT"
864           elif m[1]==self.JACOBI: method+= "+JACOBI"
865           elif m[1]==self.ILU0: method+= "+ILU0"
866           elif m[1]==self.ILUT: method+= "+ILUT"
867           elif m[1]==self.SSOR: method+= "+SSOR"
868           if p==self.DEFAULT: package="DEFAULT"
869           elif p==self.PASO: package= "PASO"
870           elif p==self.MKL: package= "MKL"
871           elif p==self.SCSL: package= "SCSL"
872           elif p==self.UMFPACK: package= "UMFPACK"
873           else : method="unknown"
874           return "%s solver of %s package"%(method,package)
875    
    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  
876    
877     def setLumping(self,flag=False):     def getSolverMethod(self):
878        """         """
879        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
880    
881     def isUsingLumping(self):         @return: the solver method currently be used.
882        """         @rtype: C{int}
883        @brief         """
884        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
885    
886     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
887         """         """
888         @brief sets a new solver         sets a new solver package
889    
890           @param solver: sets a new solver method.
891           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
892         """         """
893         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
894           if not package==self.getSolverPackage():
895             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
896             self.__checkMatrixType()             self.__checkMatrixType()
897               self.trace("New solver is %s"%self.getSolverMethodName())
898    
899     def getSolverMethod(self):     def getSolverPackage(self):
900         """         """
901         @brief returns the solver method         returns the package of the solver
902    
903           @return: the solver package currently being used.
904           @rtype: C{int}
905         """         """
906         return self.__solver_method         return self.__solver_package
907    
908       def isUsingLumping(self):
909          """
910          checks if matrix lumping is used a solver method
911    
912          @return: True is lumping is currently used a solver method.
913          @rtype: C{bool}
914          """
915          return self.getSolverMethod()[0]==self.LUMPING
916    
    #============ tolerance business =========================================================  
917     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
918         """         """
919         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
920    
921           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
922    
923           defines the stopping criterion.
924    
925           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
926                       the system will be resolved.
927           @type tol: positive C{float}
928           @raise ValueException: if tolerance is not positive.
929         """         """
930         if not tol>0:         if not tol>0:
931             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
932         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
933         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
934         self.__tolerance=tol         self.__tolerance=tol
935         return         return
936    
937     def getTolerance(self):     def getTolerance(self):
938         """         """
939         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
940    
941           @return: tolerance currently used.
942           @rtype: C{float}
943         """         """
944         return self.__tolerance         return self.__tolerance
945    
946     #===== symmetry  flag ==========================     # =============================================================================
947       #    symmetry  flag:
948       # =============================================================================
949     def isSymmetric(self):     def isSymmetric(self):
950        """        """
951        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
952    
953          @return: True is a symmetric PDE is indicated, otherwise False is returned
954          @rtype: C{bool}
955        """        """
956        return self.__sym        return self.__sym
957    
958     def setSymmetryOn(self):     def setSymmetryOn(self):
959        """        """
960        @brief sets the symmetry flag to true        sets the symmetry flag.
961        """        """
962        if not self.isSymmetric():        if not self.isSymmetric():
963           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
964           self.__sym=True           self.__sym=True
965           self.__checkMatrixType()           self.__checkMatrixType()
966    
967     def setSymmetryOff(self):     def setSymmetryOff(self):
968        """        """
969        @brief sets the symmetry flag to false        removes the symmetry flag.
970        """        """
971        if self.isSymmetric():        if self.isSymmetric():
972           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
973           self.__sym=False           self.__sym=False
974           self.__checkMatrixType()           self.__checkMatrixType()
975    
976     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
977       """        """
978       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
979    
980       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
981       """        @type flag: C{bool}
982       if flag:        """
983          self.setSymmetryOn()        if flag:
984       else:           self.setSymmetryOn()
985          self.setSymmetryOff()        else:
986             self.setSymmetryOff()
987    
988     #===== order reduction ==========================     # =============================================================================
989       # function space handling for the equation as well as the solution
990       # =============================================================================
991     def setReducedOrderOn(self):     def setReducedOrderOn(self):
992       """       """
993       @brief switches to on reduced order       switches on reduced order for solution and equation representation
994    
995         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
996       """       """
997       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
998       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
999    
1000     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1001       """       """
1002       @brief switches to full order       switches off reduced order for solution and equation representation
1003    
1004         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1005       """       """
1006       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1007       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1008    
1009     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1010       """       """
1011       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1012         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1013       @param flag                    if flag is not present order reduction is switched off
1014         @type flag: C{bool}
1015         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1016       """       """
1017       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1018       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1019    
1020     #===== order reduction solution ==========================  
1021     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1022       """       """
1023       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1024    
1025         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1026       """       """
1027       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1028       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1029           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1030           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1031           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1032             self.__resetSystem()
1033    
1034     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1035       """       """
1036       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1037    
1038         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1039       """       """
1040       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1041       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1042           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1043           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1044           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1045             self.__resetSystem()
1046    
1047     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1048       """       """
1049       @brief sets order for test functions according to flag       sets order for test functions according to flag
1050    
1051       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1052                      if flag is not present order reduction is switched off
1053         @type flag: C{bool}
1054         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1055       """       """
1056       if flag:       if flag:
1057          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1058       else:       else:
1059          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1060                                                                                                                                                              
    #===== order reduction equation ==========================  
1061     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1062       """       """
1063       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1064    
1065         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1066       """       """
1067       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1068       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1069           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1070           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1071           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1072             self.__resetSystem()
1073    
1074     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1075       """       """
1076       @brief switches to full order for test functions       switches off reduced order for equation representation
1077    
1078         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1079       """       """
1080       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1081       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1082           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1083           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1084           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1085             self.__resetSystem()
1086    
1087     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1088       """       """
1089       @brief sets order for test functions according to flag       sets order for test functions according to flag
1090    
1091       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1092                      if flag is not present order reduction is switched off
1093         @type flag: C{bool}
1094         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1095       """       """
1096       if flag:       if flag:
1097          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1098       else:       else:
1099          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1100                                                                                                                                                              
1101     # ==== initialization =====================================================================     # =============================================================================
1102     def __makeNewOperator(self):     # private method:
1103       # =============================================================================
1104       def __checkMatrixType(self):
1105         """
1106         reassess the matrix type and, if a new matrix is needed, resets the system.
1107         """
1108         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1109         if not new_matrix_type==self.__matrix_type:
1110             self.trace("Matrix type is now %d."%new_matrix_type)
1111             self.__matrix_type=new_matrix_type
1112             self.__resetSystem()
1113       #
1114       #   rebuild switches :
1115       #
1116       def __invalidateSolution(self):
1117           """
1118           indicates the PDE has to be resolved if the solution is requested
1119           """
1120           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1121           self.__solution_isValid=False
1122    
1123       def __invalidateOperator(self):
1124         """         """
1125         @brief         indicates the operator has to be rebuilt next time it is used
1126         """         """
1127           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1128           self.__invalidateSolution()
1129           self.__operator_is_Valid=False
1130    
1131       def __invalidateRightHandSide(self):
1132           """
1133           indicates the right hand side has to be rebuild next time it is used
1134           """
1135           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1136           self.__invalidateSolution()
1137           self.__righthandside_isValid=False
1138    
1139       def __invalidateSystem(self):
1140           """
1141           annonced that everthing has to be rebuild:
1142           """
1143           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1144           self.__invalidateSolution()
1145           self.__invalidateOperator()
1146           self.__invalidateRightHandSide()
1147    
1148       def __resetSystem(self):
1149           """
1150           annonced that everthing has to be rebuild:
1151           """
1152           self.trace("New System is built from scratch.")
1153           self.__operator=escript.Operator()
1154           self.__operator_is_Valid=False
1155           self.__righthandside=escript.Data()
1156           self.__righthandside_isValid=False
1157           self.__solution=escript.Data()
1158           self.__solution_isValid=False
1159       #
1160       #    system initialization:
1161       #
1162       def __getNewOperator(self):
1163           """
1164           returns an instance of a new operator
1165           """
1166           self.trace("New operator is allocated.")
1167         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1168                             self.getNumEquations(), \                             self.getNumEquations(), \
1169                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 547  class LinearPDE: Line 1171  class LinearPDE:
1171                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1172                             self.__matrix_type)                             self.__matrix_type)
1173    
1174     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1175         """         """
1176         @brief         returns an instance of a new right hand side
1177         """         """
1178         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1179           if self.getNumEquations()>1:
1180               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1181           else:
1182               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1183    
1184     def __makeNewSolution(self):     def __getNewSolution(self):
1185         """         """
1186         @brief         returns an instance of a new solution
1187         """         """
1188         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1189           if self.getNumSolutions()>1:
1190               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1191           else:
1192               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1193    
1194     def __getFreshOperator(self):     def __makeFreshSolution(self):
1195         """         """
1196         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1197         """         """
1198         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1199             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1200         else:         else:
1201             self.__operator.setValue(0.)             self.__solution*=0
1202             self.__operator.resetSolver()             self.trace("Solution is reset to zero.")
1203             if self.debug() : print "PDE Debug: Operator reset to zero"         return self.__solution
        return self.__operator  
1204    
1205     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1206         """         """
1207         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1208         """         """
1209         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1210             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1211         else:         else:
1212             print "fix self.__righthandside*=0"             self.__righthandside*=0
1213             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1214             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1215    
1216     #============ some serivice functions  =====================================================     def __makeFreshOperator(self):
1217     def getDomain(self):         """
1218           makes sure that the operator is instantiated and returns it initialized by zeros
1219           """
1220           if self.__operator.isEmpty():
1221               self.__operator=self.__getNewOperator()
1222           else:
1223               self.__operator.resetValues()
1224               self.trace("Operator reset to zero")
1225           return self.__operator
1226    
1227       def __applyConstraint(self):
1228           """
1229           applies the constraints defined by q and r to the system
1230           """
1231           if not self.isUsingLumping():
1232              q=self.getCoefficientOfGeneralPDE("q")
1233              r=self.getCoefficientOfGeneralPDE("r")
1234              if not q.isEmpty() and not self.__operator.isEmpty():
1235                 # q is the row and column mask to indicate where constraints are set:
1236                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1237                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1238                 u=self.__getNewSolution()
1239                 if r.isEmpty():
1240                    r_s=self.__getNewSolution()
1241                 else:
1242                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1243                 u.copyWithMask(r_s,col_q)
1244                 if not self.__righthandside.isEmpty():
1245                    self.__righthandside-=self.__operator*u
1246                    self.__righthandside=self.copyConstraint(self.__righthandside)
1247                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1248       # =============================================================================
1249       # function giving access to coefficients of the general PDE:
1250       # =============================================================================
1251       def getCoefficientOfGeneralPDE(self,name):
1252         """
1253         return the value of the coefficient name of the general PDE.
1254    
1255         @note: This method is called by the assembling routine it can be overwritten
1256               to map coefficients of a particular PDE to the general PDE.
1257         @param name: name of the coefficient requested.
1258         @type name: C{string}
1259         @return: the value of the coefficient  name
1260         @rtype: L{Data<escript.Data>}
1261         @raise IllegalCoefficient: if name is not one of coefficients
1262                      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}.
1263       """       """
1264       @brief returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1265            return self.getCoefficient(name)
1266         else:
1267            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1268    
1269       def hasCoefficientOfGeneralPDE(self,name):
1270       """       """
1271       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1272    
1273         @param name: name of the coefficient enquired.
1274         @type name: C{string}
1275         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1276         @rtype: C{bool}
1277    
    def getDim(self):  
1278       """       """
1279       @brief returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1280    
1281       def createCoefficientOfGeneralPDE(self,name):
1282       """       """
1283       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1284    
1285     def getNumEquations(self):       @param name: name of the coefficient requested.
1286         @type name: C{string}
1287         @return: a coefficient name initialized to 0.
1288         @rtype: L{Data<escript.Data>}
1289         @raise IllegalCoefficient: if name is not one of coefficients
1290                      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}.
1291       """       """
1292       @brief returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1293            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1294         else:
1295            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1296    
1297       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1298       """       """
1299       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1300           return self.__numEquations  
1301         @param name: name of the coefficient enquired.
1302         @type name: C{string}
1303         @return: the function space to be used for coefficient name
1304         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1305         @raise IllegalCoefficient: if name is not one of coefficients
1306                      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}.
1307         """
1308         if self.hasCoefficientOfGeneralPDE(name):
1309            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1310       else:       else:
1311           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1312    
1313     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1314       """       """
1315       @brief returns the number of unknowns       return the shape of the coefficient name of the general PDE
1316    
1317         @param name: name of the coefficient enquired.
1318         @type name: C{string}
1319         @return: the shape of the coefficient name
1320         @rtype: C{tuple} of C{int}
1321         @raise IllegalCoefficient: if name is not one of coefficients
1322                      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}.
1323       """       """
1324       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1325          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1326       else:       else:
1327          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1328    
1329       # =============================================================================
1330       # functions giving access to coefficients of a particular PDE implementation:
1331       # =============================================================================
1332       def getCoefficient(self,name):
1333         """
1334         returns the value of the coefficient name
1335    
1336     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1337        """       @type name: C{string}
1338        @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
1339        """       @rtype: L{Data<escript.Data>}
1340        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1341        out=True       """
1342        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1343           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1344           out=False       else:
1345        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[k,i,j])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)  
                               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  
1346    
1347     def getFlux(self,u):     def hasCoefficient(self,name):
1348         """       """
1349         @brief returns the flux J_ij for a given u       return True if name is the name of a coefficient
1350    
1351              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @param name: name of the coefficient enquired.
1352         @type name: C{string}
1353         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1354         @rtype: C{bool}
1355         """
1356         return self.COEFFICIENTS.has_key(name)
1357    
1358         @param u argument of the operator     def createCoefficient(self, name):
1359         """
1360         create a L{Data<escript.Data>} object corresponding to coefficient name
1361    
1362         """       @return: a coefficient name initialized to 0.
1363         raise SystemError,"getFlux is not implemented yet"       @rtype: L{Data<escript.Data>}
1364         return None       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1365         """
1366         if self.hasCoefficient(name):
1367            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1368         else:
1369            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1370    
1371     def applyOperator(self,u):     def getFunctionSpaceForCoefficient(self,name):
1372         """       """
1373         @brief applies the operator of the PDE to a given solution u in weak from       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1374    
1375         @param u argument of the operator       @param name: name of the coefficient enquired.
1376         @type name: C{string}
1377         @return: the function space to be used for coefficient name
1378         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1379         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1380         """
1381         if self.hasCoefficient(name):
1382            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1383         else:
1384            raise ValueError,"unknown coefficient %s requested"%name
1385       def getShapeOfCoefficient(self,name):
1386         """
1387         return the shape of the coefficient name
1388    
1389         """       @param name: name of the coefficient enquired.
1390         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       @type name: C{string}
1391                                                                                                                                                                   @return: the shape of the coefficient name
1392     def getResidual(self,u):       @rtype: C{tuple} of C{int}
1393         """       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1394         @brief return the residual of u in the weak from       """
1395         if self.hasCoefficient(name):
1396            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1397         else:
1398            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1399    
1400         @param u     def resetCoefficients(self):
1401         """       """
1402         return self.applyOperator(u)-self.getRightHandSide()       resets all coefficients to there default values.
1403         """
1404         for i in self.COEFFICIENTS.iterkeys():
1405             self.COEFFICIENTS[i].resetValue()
1406    
1407       def alteredCoefficient(self,name):
1408         """
1409         announce that coefficient name has been changed
1410    
1411         @param name: name of the coefficient enquired.
1412         @type name: C{string}
1413         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1414         @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.
1415         """
1416         if self.hasCoefficient(name):
1417            self.trace("Coefficient %s has been altered."%name)
1418            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1419               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1420               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1421         else:
1422            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1423    
1424     def _setValue(self,**coefficients):     def copyConstraint(self,u):
1425        """        """
1426        @brief sets new values to coefficient        copies the constraint into u and returns u.
1427    
1428          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1429          @type u: L{Data<escript.Data>}
1430          @return: the input u modified by the constraints.
1431          @rtype: L{Data<escript.Data>}
1432          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1433          """
1434          q=self.getCoefficientOfGeneralPDE("q")
1435          r=self.getCoefficientOfGeneralPDE("r")
1436          if not q.isEmpty():
1437             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1438             if r.isEmpty():
1439                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1440             else:
1441                 r=escript.Data(r,u.getFunctionSpace())
1442             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1443          return u
1444    
1445        @param coefficients     def setValue(self,**coefficients):
1446          """
1447          sets new values to coefficients
1448    
1449          @param coefficients: new values assigned to coefficients
1450          @keyword A: value for coefficient A.
1451          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452          @keyword B: value for coefficient B
1453          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454          @keyword C: value for coefficient C
1455          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1456          @keyword D: value for coefficient D
1457          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458          @keyword X: value for coefficient X
1459          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1460          @keyword Y: value for coefficient Y
1461          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1462          @keyword d: value for coefficient d
1463          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1464          @keyword y: value for coefficient y
1465          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1466          @keyword d_contact: value for coefficient d_contact
1467          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1468                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1469          @keyword y_contact: value for coefficient y_contact
1470          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1471                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1472          @keyword r: values prescribed to the solution at the locations of constraints
1473          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1474                   depending of reduced order is used for the solution.
1475          @keyword q: mask for location of constraints
1476          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1477                   depending of reduced order is used for the representation of the equation.
1478          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1479        """        """
1480        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1481        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1482           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1483              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1484        # 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:
1485        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1486           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1487              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1488                  s=d.shape                  s=d.shape
# Line 728  class LinearPDE: Line 1492  class LinearPDE:
1492                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1493              if s!=None:              if s!=None:
1494                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1495                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1496                  if res==None:                  if res==None:
1497                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1498                  else:                  else:
1499                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1500                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1501        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1502        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1503        # 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:
1504        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1505          if d==None:          try:
1506               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1507          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1508               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)  
1509          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()  
   
   
    def __rebuildOperator(self,deep=False):  
        """  
        @brief indicates the operator has to be rebuilt next time it is used  
        """  
        if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__operator_isValid=False  
        if deep: self.__operator=escript.Operator()  
   
    def __rebuildRightHandSide(self,deep=False):  
        """  
        @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()))  
1510    
1511     def __applyConstraint(self):        self.__altered_coefficients=True
1512         """        # check if the systrem is inhomogeneous:
1513         @brief applies the constraints defined by q and r to the system        if len(coefficients)>0 and not self.isUsingLumping():
1514         """           q=self.getCoefficientOfGeneralPDE("q")
1515         q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1516         r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1517         if not q.isEmpty() and not self.__operator.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1518            # q is the row and column mask to indicate where constraints are set:               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1519            row_q=escript.Data(q,self.getFunctionSpaceForEquation())                 self.trace("Inhomogeneous constraint detected.")
1520            col_q=escript.Data(q,self.getFunctionSpaceForSolution())                 self.__invalidateSystem()
           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.)  
1521    
1522     def getSystem(self):     def getSystem(self):
1523         """         """
1524         @brief return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1525    
1526           @return: the discrete version of the PDE
1527           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1528         """         """
1529         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1530            if self.isUsingLumping():            if self.isUsingLumping():
1531                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1532                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1533                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"
1534                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1535                            raise Warning,"Lumped matrix does not allow coefficient A"                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"
1536                   if not self.getCoefficientOfPDE("B").isEmpty():                   mat=self.__getNewOperator()
                           raise Warning,"Lumped matrix does not allow coefficient B"  
                  if not self.getCoefficientOfPDE("C").isEmpty():  
                           raise Warning,"Lumped matrix does not allow coefficient C"  
                  if self.debug() : print "PDE Debug: New lumped operator is built."  
                  mat=self.__makeNewOperator()  
1537                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   self.getDomain().addPDEToSystem(mat,escript.Data(), \
1538                             self.getCoefficientOfPDE("A"), \                             self.getCoefficientOfGeneralPDE("A"), \
1539                             self.getCoefficientOfPDE("B"), \                             self.getCoefficientOfGeneralPDE("B"), \
1540                             self.getCoefficientOfPDE("C"), \                             self.getCoefficientOfGeneralPDE("C"), \
1541                             self.getCoefficientOfPDE("D"), \                             self.getCoefficientOfGeneralPDE("D"), \
1542                             escript.Data(), \                             escript.Data(), \
1543                             escript.Data(), \                             escript.Data(), \
1544                             self.getCoefficientOfPDE("d"), \                             self.getCoefficientOfGeneralPDE("d"), \
1545                             escript.Data(),\                             escript.Data(),\
1546                             self.getCoefficientOfPDE("d_contact"), \                             self.getCoefficientOfGeneralPDE("d_contact"), \
1547                             escript.Data())                             escript.Data())
1548                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1549                   self.__applyConstraint()                   del mat
1550                   self.__operator_isValid=True                   self.trace("New lumped operator has been built.")
1551                     self.__operator_is_Valid=True
1552                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
1553                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1554                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1555                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1556                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1557                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1558                                 self.getCoefficientOfPDE("y_contact"))                   self.trace("New right hand side as been built.")
                  self.__copyConstraint()  
1559                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1560            else:            else:
1561               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1562                   if self.debug() : print "PDE Debug: New system is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1563                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("A"), \
1564                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1565                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1566                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1567                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1568                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1569                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1570                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1571                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1572                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y_contact"))
                                self.getCoefficientOfPDE("y_contact"))  
1573                   self.__applyConstraint()                   self.__applyConstraint()
1574                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1575                   self.__operator_isValid=True                   self.trace("New system has been built.")
1576                     self.__operator_is_Valid=True
1577                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1578               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1579                   if self.debug() : print "PDE Debug: New right hand side is built."                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1580                   self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \                                 self.getCoefficientOfGeneralPDE("X"), \
1581                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("Y"),\
1582                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1583                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y_contact"))
1584                                 self.getCoefficientOfPDE("y_contact"))                   self.__righthandside=self.copyConstraint(self.__righthandside)
1585                   self.__copyConstraint()                   self.trace("New right hand side has been built.")
1586                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1587               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
1588                   if self.debug() : print "PDE Debug: New operator is built."                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1589                   self.getDomain().addPDEToSystem(self.__getFreshOperator(),escript.Data(), \                              self.getCoefficientOfGeneralPDE("A"), \
1590                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("B"), \
1591                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("C"), \
1592                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("D"), \
                             self.getCoefficientOfPDE("D"), \  
1593                              escript.Data(), \                              escript.Data(), \
1594                              escript.Data(), \                              escript.Data(), \
1595                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1596                              escript.Data(),\                              escript.Data(),\
1597                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1598                              escript.Data())                              escript.Data())
1599                   self.__applyConstraint()                   self.__applyConstraint()
1600                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1601                     self.__operator_is_Valid=True
1602         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        @brief returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1603    
    def getRightHandSide(self):  
        """  
        @brief returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1604    
1605     def solve(self,**options):  class Poisson(LinearPDE):
1606        """     """
1607        @brief solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1608    
1609        @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  
1610    
1611     def getSolution(self,**options):     with natural boundary conditons
        """  
        @brief returns the solution of the PDE  
1612    
1613         @param options     M{n[j]*grad(u)[j] = 0 }
1614         """  
1615         if not self.__solution_isValid:     and constraints:
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
1616    
1617       M{u=0} where M{q>0}
1618    
1619       """
1620    
1621       def __init__(self,domain,debug=False):
1622         """
1623         initializes a new Poisson equation
1624    
1625         @param domain: domain of the PDE
1626         @type domain: L{Domain<escript.Domain>}
1627         @param debug: if True debug informations are printed.
1628    
1629         """
1630         super(Poisson, self).__init__(domain,1,1,debug)
1631         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1632                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1633         self.setSymmetryOn()
1634    
1635       def setValue(self,**coefficients):
1636         """
1637         sets new values to coefficients
1638    
1639         @param coefficients: new values assigned to coefficients
1640         @keyword f: value for right hand side M{f}
1641         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1642         @keyword q: mask for location of constraints
1643         @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>}
1644                   depending of reduced order is used for the representation of the equation.
1645         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1646         """
1647         super(Poisson, self).setValue(**coefficients)
1648    
1649       def getCoefficientOfGeneralPDE(self,name):
1650         """
1651         return the value of the coefficient name of the general PDE
1652         @param name: name of the coefficient requested.
1653         @type name: C{string}
1654         @return: the value of the coefficient  name
1655         @rtype: L{Data<escript.Data>}
1656         @raise IllegalCoefficient: if name is not one of coefficients
1657                      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}.
1658         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1659         """
1660         if name == "A" :
1661             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1662         elif name == "B" :
1663             return escript.Data()
1664         elif name == "C" :
1665             return escript.Data()
1666         elif name == "D" :
1667             return escript.Data()
1668         elif name == "X" :
1669             return escript.Data()
1670         elif name == "Y" :
1671             return self.getCoefficient("f")
1672         elif name == "d" :
1673             return escript.Data()
1674         elif name == "y" :
1675             return escript.Data()
1676         elif name == "d_contact" :
1677             return escript.Data()
1678         elif name == "y_contact" :
1679             return escript.Data()
1680         elif name == "r" :
1681             return escript.Data()
1682         elif name == "q" :
1683             return self.getCoefficient("q")
1684         else:
1685            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1686    
1687    class Helmholtz(LinearPDE):
1688       """
1689       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1690    
1691       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1692    
1693       with natural boundary conditons
1694    
1695  def ELMAN_RAMAGE(P): return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
 def SIMPLIFIED_BROOK_HUGHES(P):  
          c=(P-3.).whereNegative()  
          return P/6.*c+1./2.*(1.-c)  
 def HALF(P): return escript.Scalar(0.5,P.getFunctionSpace())  
1696    
1697       and constraints:
1698    
1699       M{u=r} where M{q>0}
1700    
1701       """
1702    
1703       def __init__(self,domain,debug=False):
1704         """
1705         initializes a new Poisson equation
1706    
1707         @param domain: domain of the PDE
1708         @type domain: L{Domain<escript.Domain>}
1709         @param debug: if True debug informations are printed.
1710    
1711         """
1712         super(Helmholtz, self).__init__(domain,1,1,debug)
1713         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1714                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1715                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1716                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1717                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1718                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1719                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1720         self.setSymmetryOn()
1721    
1722       def setValue(self,**coefficients):
1723         """
1724         sets new values to coefficients
1725    
1726         @param coefficients: new values assigned to coefficients
1727         @keyword omega: value for coefficient M{S{omega}}
1728         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1729         @keyword k: value for coefficeint M{k}
1730         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1731         @keyword f: value for right hand side M{f}
1732         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1733         @keyword alpha: value for right hand side M{S{alpha}}
1734         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1735         @keyword g: value for right hand side M{g}
1736         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1737         @keyword r: prescribed values M{r} for the solution in constraints.
1738         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1739                   depending of reduced order is used for the representation of the equation.
1740         @keyword q: mask for location of constraints
1741         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1742                   depending of reduced order is used for the representation of the equation.
1743         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1744         """
1745         super(Helmholtz, self).setValue(**coefficients)
1746    
1747       def getCoefficientOfGeneralPDE(self,name):
1748         """
1749         return the value of the coefficient name of the general PDE
1750    
1751         @param name: name of the coefficient requested.
1752         @type name: C{string}
1753         @return: the value of the coefficient  name
1754         @rtype: L{Data<escript.Data>}
1755         @raise IllegalCoefficient: if name is not one of coefficients
1756                      "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}.
1757         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1758         """
1759         if name == "A" :
1760             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1761         elif name == "B" :
1762             return escript.Data()
1763         elif name == "C" :
1764             return escript.Data()
1765         elif name == "D" :
1766             return self.getCoefficient("omega")
1767         elif name == "X" :
1768             return escript.Data()
1769         elif name == "Y" :
1770             return self.getCoefficient("f")
1771         elif name == "d" :
1772             return self.getCoefficient("alpha")
1773         elif name == "y" :
1774             return self.getCoefficient("g")
1775         elif name == "d_contact" :
1776             return escript.Data()
1777         elif name == "y_contact" :
1778             return escript.Data()
1779         elif name == "r" :
1780             return self.getCoefficient("r")
1781         elif name == "q" :
1782             return self.getCoefficient("q")
1783         else:
1784            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1785    
1786    class LameEquation(LinearPDE):
1787       """
1788       Class to define a Lame equation problem:
1789    
1790       M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }
1791    
1792       with natural boundary conditons:
1793    
1794       M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }
1795    
1796       and constraints:
1797    
1798       M{u[i]=r[i]} where M{q[i]>0}
1799    
1800       """
1801    
1802       def __init__(self,domain,debug=False):
1803          super(LameEquation, self).__init__(domain,\
1804                                             domain.getDim(),domain.getDim(),debug)
1805          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1806                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1807                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1808                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1809                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1810                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1811                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1812          self.setSymmetryOn()
1813    
1814       def setValue(self,**coefficients):
1815         """
1816         sets new values to coefficients
1817    
1818         @param coefficients: new values assigned to coefficients
1819         @keyword lame_mu: value for coefficient M{S{mu}}
1820         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1821         @keyword lame_lambda: value for coefficient M{S{lambda}}
1822         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1823         @keyword F: value for internal force M{F}
1824         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1825         @keyword sigma: value for initial stress M{S{sigma}}
1826         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1827         @keyword f: value for extrenal force M{f}
1828         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1829         @keyword r: prescribed values M{r} for the solution in constraints.
1830         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1831                   depending of reduced order is used for the representation of the equation.
1832         @keyword q: mask for location of constraints
1833         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1834                   depending of reduced order is used for the representation of the equation.
1835         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1836         """
1837         super(LameEquation, self).setValue(**coefficients)
1838    
1839       def getCoefficientOfGeneralPDE(self,name):
1840         """
1841         return the value of the coefficient name of the general PDE
1842    
1843         @param name: name of the coefficient requested.
1844         @type name: C{string}
1845         @return: the value of the coefficient  name
1846         @rtype: L{Data<escript.Data>}
1847         @raise IllegalCoefficient: if name is not one of coefficients
1848                      "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}.
1849         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1850         """
1851         if name == "A" :
1852             out =self.createCoefficientOfGeneralPDE("A")
1853             for i in range(self.getDim()):
1854               for j in range(self.getDim()):
1855                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1856                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1857                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1858             return out
1859         elif name == "B" :
1860             return escript.Data()
1861         elif name == "C" :
1862             return escript.Data()
1863         elif name == "D" :
1864             return escript.Data()
1865         elif name == "X" :
1866             return self.getCoefficient("sigma")
1867         elif name == "Y" :
1868             return self.getCoefficient("F")
1869         elif name == "d" :
1870             return escript.Data()
1871         elif name == "y" :
1872             return self.getCoefficient("f")
1873         elif name == "d_contact" :
1874             return escript.Data()
1875         elif name == "y_contact" :
1876             return escript.Data()
1877         elif name == "r" :
1878             return self.getCoefficient("r")
1879         elif name == "q" :
1880             return self.getCoefficient("q")
1881         else:
1882            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1883    
1884  class AdvectivePDE(LinearPDE):  class AdvectivePDE(LinearPDE):
1885     """     """
1886     @brief Class to handel a linear PDE domineated by advective terms:     In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1887         up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
    class to define a linear PDE of the form  
1888    
1889       -(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     In the following we set
1890    
1891       with boundary conditons:     M{Z[j]=C[j]-B[j]}
1892    
1893          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     or
1894    
1895      and contact conditions     M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1896    
1897          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     To measure the dominance of the advective terms over the diffusive term M{A} the
1898       X{Pelclet number} M{P} is used. It is defined as
1899    
1900      and constraints:     M{P=h|Z|/(2|A|)}
1901    
1902           u_i=r_i where q_i>0     where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1903       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1904    
1905       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1906    
1907       M{S{Xi}=S{xi}(P) h/|Z|}
1908    
1909       where M{S{xi}} is a suitable function of the Peclet number.
1910    
1911       In the case of a single PDE the coefficient are up-dated in the following way:
1912             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1913             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1914             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1915             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1916    
1917       Similar for the case of a systems of PDEs:
1918             - 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]}
1919             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1920             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1921             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1922    
1923       where M{S{delta}} is L{kronecker}.
1924       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1925       but with the intension to stabilize the solution.
1926    
1927     """     """
1928     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1929        LinearPDE.__init__(self,domain,numEquations,numSolutions)        """
1930        self.__xi=xi        creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1931    
1932          @param domain: domain of the PDE
1933          @type domain: L{Domain<escript.Domain>}
1934          @param numEquations: number of equations. If numEquations==None the number of equations
1935                               is exracted from the PDE coefficients.
1936          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1937                               is exracted from the PDE coefficients.
1938          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1939                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1940          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1941          @param debug: if True debug informations are printed.
1942          """
1943          super(AdvectivePDE, self).__init__(domain,\
1944                                             numEquations,numSolutions,debug)
1945          if xi==None:
1946             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1947          else:
1948             self.__xi=xi
1949        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1950    
1951     def __calculateXi(self,peclet_factor,Z,h):     def setValue(**coefficients):
1952         Z_max=util.Lsup(Z)        """
1953         if Z_max>0.:        sets new values to coefficients
1954            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1955          @param coefficients: new values assigned to coefficients
1956          @keyword A: value for coefficient A.
1957          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1958          @keyword B: value for coefficient B
1959          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1960          @keyword C: value for coefficient C
1961          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1962          @keyword D: value for coefficient D
1963          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1964          @keyword X: value for coefficient X
1965          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1966          @keyword Y: value for coefficient Y
1967          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1968          @keyword d: value for coefficient d
1969          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1970          @keyword y: value for coefficient y
1971          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1972          @keyword d_contact: value for coefficient d_contact
1973          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1974                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1975          @keyword y_contact: value for coefficient y_contact
1976          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1977                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1978          @keyword r: values prescribed to the solution at the locations of constraints
1979          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1980                   depending of reduced order is used for the solution.
1981          @keyword q: mask for location of constraints
1982          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1983                   depending of reduced order is used for the representation of the equation.
1984          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1985    
1986          """
1987          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1988          super(AdvectivePDE, self).setValue(**coefficients)
1989    
1990       def ELMAN_RAMAGE(self,P):
1991         """
1992         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1993         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1994              - M{S{xi}(P)=0} for M{P<1}
1995              - M{S{xi}(P)=(1-1/P)/2} otherwise
1996    
1997         @param P: Preclet number
1998         @type P: L{Scalar<escript.Scalar>}
1999         @return: up-wind weightimg factor
2000         @rtype: L{Scalar<escript.Scalar>}
2001         """
2002         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2003    
2004       def SIMPLIFIED_BROOK_HUGHES(self,P):
2005         """
2006         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2007         The original methods is
2008    
2009         M{S{xi}(P)=coth(P)-1/P}
2010    
2011         As the evaluation of M{coth} is expensive we are using the approximation:
2012    
2013             - M{S{xi}(P)=P/3} where M{P<3}
2014             - M{S{xi}(P)=1/2} otherwise
2015    
2016         @param P: Preclet number
2017         @type P: L{Scalar<escript.Scalar>}
2018         @return: up-wind weightimg factor
2019         @rtype: L{Scalar<escript.Scalar>}
2020         """
2021         c=util.whereNegative(P-3.)
2022         return P/6.*c+1./2.*(1.-c)
2023    
2024       def HALF(self,P):
2025         """
2026         Predefined function to set value M{1/2} for M{S{xi}}
2027    
2028         @param P: Preclet number
2029         @type P: L{Scalar<escript.Scalar>}
2030         @return: up-wind weightimg factor
2031         @rtype: L{Scalar<escript.Scalar>}
2032         """
2033         return escript.Scalar(0.5,P.getFunctionSpace())
2034    
2035       def __calculateXi(self,peclet_factor,flux,h):
2036           flux=util.Lsup(flux)
2037           if flux_max>0.:
2038              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2039         else:         else:
2040            return 0.            return 0.
2041    
2042     def setValue(self,**args):     def __getXi(self):
        if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()  
        self._setValue(**args)  
             
    def getXi(self):  
2043        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2044           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2045           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1037  class AdvectivePDE(LinearPDE): Line 2048  class AdvectivePDE(LinearPDE):
2048           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2049           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2050              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
2051                  Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))                  flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2052                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2053                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2054                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2055                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2056                              for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2                              for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2057                          # flux=C-util.reorderComponents(B,[0,2,1])
2058                     else:                     else:
2059                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2060                           for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2                           for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2061                          # flux=C-B
2062                  else:                  else:
2063                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2064                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2065                           for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2                           for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2066                          # flux=C-util.reorderComponents(B,[1,0])
2067                     else:                     else:
2068                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2069                  length_of_Z=util.sqrt(Z2)                        #flux=C-B
2070                    length_of_flux=util.sqrt(flux2)
2071              elif C.isEmpty():              elif C.isEmpty():
2072                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2073                  #flux=B
2074              else:              else:
2075                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2076                  #flux=C
2077    
2078              Z_max=util.Lsup(length_of_Z)              #length_of_flux=util.length(flux)
2079              if Z_max>0.:              flux_max=util.Lsup(length_of_flux)
2080                if flux_max>0.:
2081                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2082                 length_of_A=util.length(A)                 length_of_A=util.length(A)
2083                 A_max=util.Lsup(length_of_A)                 A_max=util.Lsup(length_of_A)
2084                 if A_max>0:                 if A_max>0:
2085                      inv_A=1./(length_of_A+A_max*self.TOL)                      inv_A=1./(length_of_A+A_max*self.__TOL)
2086                 else:                 else:
2087                      inv_A=1./self.TOL                      inv_A=1./self.__TOL
2088                 peclet_number=length_of_Z*h/2*inv_A                 peclet_number=length_of_flux*h/2*inv_A
2089                 xi=self.__xi(peclet_number)                 xi=self.__xi(peclet_number)
2090                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2091                 print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)                 self.trace("preclet number = %e"%util.Lsup(peclet_number))
2092        return self.__Xi        return self.__Xi
         
2093    
2094     def getCoefficientOfPDE(self,name):  
2095       def getCoefficientOfGeneralPDE(self,name):
2096       """       """
2097       @brief return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2098       @param name  
2099         @param name: name of the coefficient requested.
2100         @type name: C{string}
2101         @return: the value of the coefficient name
2102         @rtype: L{Data<escript.Data>}
2103         @raise IllegalCoefficient: if name is not one of coefficients
2104                      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}.
2105         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2106       """       """
2107       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2108            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2109    
2110       if name == "A" :       if name == "A" :
2111           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2112           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2113           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2114           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2115              Aout=A              Aout=A
2116           else:           else:
2117              if A.isEmpty():              if A.isEmpty():
2118                 Aout=self.createNewCoefficient("A")                 Aout=self.createNewCoefficient("A")
2119              else:              else:
2120                 Aout=A[:]                 Aout=A[:]
2121              Xi=self.getXi()              Xi=self.__getXi()
2122              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2123                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2124                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2125                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2126                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2127                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2128                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2129                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2130                                 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])                                 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])
2131                              elif C.isEmpty():                              elif C.isEmpty():
2132                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2133                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2134                              else:                              else:
2135                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2136                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2137              else:              else:
2138                  for j in range(self.getDim()):                  for j in range(self.getDim()):
2139                     for l in range(self.getDim()):                     for l in range(self.getDim()):
# Line 1113  class AdvectivePDE(LinearPDE): Line 2143  class AdvectivePDE(LinearPDE):
2143                            Aout[j,l]+=Xi*B[j]*B[l]                            Aout[j,l]+=Xi*B[j]*B[l]
2144                        else:                        else:
2145                            Aout[j,l]+=Xi*C[j]*C[l]                            Aout[j,l]+=Xi*C[j]*C[l]
2146                     # if not C.isEmpty() and not B.isEmpty():
2147                     #    tmp=C-B
2148                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2149                     # elif C.isEmpty():
2150                     #    Aout=Aout+Xi*util.outer(B,B)
2151                     # else:
2152                     # Aout=Aout+Xi*util.outer(C,C)
2153           return Aout           return Aout
2154       elif name == "B" :       elif name == "B" :
2155           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2156           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2157           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2158           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2159              Bout=B              Bout=B
2160           else:           else:
2161              Xi=self.getXi()              Xi=self.__getXi()
2162              if B.isEmpty():              if B.isEmpty():
2163                  Bout=self.createNewCoefficient("B")                  Bout=self.createNewCoefficient("B")
2164              else:              else:
2165                  Bout=B[:]                  Bout=B[:]
2166              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2167                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2168                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2169                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2170                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2171                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2172                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2173                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2174              else:              else:
2175                 tmp=Xi*D                 tmp=Xi*D
2176                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2177                   # Bout=Bout+Xi*D*C
2178           return Bout           return Bout
2179       elif name == "C" :       elif name == "C" :
2180           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2181           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2182           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2183           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2184              Cout=C              Cout=C
2185           else:           else:
2186              Xi=self.getXi()              Xi=self.__getXi()
2187              if C.isEmpty():              if C.isEmpty():
2188                  Cout=self.createNewCoefficient("C")                  Cout=self.createNewCoefficient("C")
2189              else:              else:
2190                  Cout=C[:]                  Cout=C[:]
# Line 1156  class AdvectivePDE(LinearPDE): Line 2195  class AdvectivePDE(LinearPDE):
2195                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2196                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2197                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2198                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2199              else:              else:
2200                 tmp=Xi*D                 tmp=Xi*D
2201                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2202                   # Cout=Cout+tmp*D*B
2203           return Cout           return Cout
2204       elif name == "D" :       elif name == "D" :
2205           return self.getCoefficient("D")           return self.getCoefficient("D")
2206       elif name == "X" :       elif name == "X" :
2207           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2208           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2209           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1174  class AdvectivePDE(LinearPDE): Line 2215  class AdvectivePDE(LinearPDE):
2215                  Xout=self.createNewCoefficient("X")                  Xout=self.createNewCoefficient("X")
2216              else:              else:
2217                  Xout=X[:]                  Xout=X[:]
2218              Xi=self.getXi()              Xi=self.__getXi()
2219              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2220                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2221                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2222                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2223                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2224                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2225                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2226                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2227                            elif C.isEmpty():                            elif C.isEmpty():
2228                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2229                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2230                            else:                            else:
2231                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2232                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2233              else:              else:
2234                   tmp=Xi*Y                   tmp=Xi*Y
2235                   for j in range(self.getDim()):                   for j in range(self.getDim()):
2236                      if not C.isEmpty() and not B.isEmpty():                      if not C.isEmpty() and not B.isEmpty():
2237                         Xout[j]+=tmp*(C[j]-B[j])                         Xout[j]+=tmp*(C[j]-B[j])
2238                           # Xout=Xout+Xi*Y*(C-B)
2239                      elif C.isEmpty():                      elif C.isEmpty():
2240                         Xout[j]-=tmp*B[j]                         Xout[j]-=tmp*B[j]
2241                           # Xout=Xout-Xi*Y*B
2242                      else:                      else:
2243                         Xout[j]+=tmp*C[j]                         Xout[j]+=tmp*C[j]
2244                           # Xout=Xout+Xi*Y*C
2245           return Xout           return Xout
2246       elif name == "Y" :       elif name == "Y" :
2247           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2248       elif name == "d" :       elif name == "d" :
2249           return self.getCoefficient("d")           return self.getCoefficient("d")
2250       elif name == "y" :       elif name == "y" :
2251           return self.getCoefficient("y")           return self.getCoefficient("y")
2252       elif name == "d_contact" :       elif name == "d_contact" :
2253           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2254       elif name == "y_contact" :       elif name == "y_contact" :
2255           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2256       elif name == "r" :       elif name == "r" :
2257           return self.getCoefficient("r")           return self.getCoefficient("r")
2258       elif name == "q" :       elif name == "q" :
2259           return self.getCoefficient("q")           return self.getCoefficient("q")
2260       else:       else:
2261           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2262    
2263  class Poisson(LinearPDE):  class AdvectionDiffusion(LinearPDE):
    """  
    @brief Class to define a Poisson equstion problem:  
                                                                                                                                                               
    class to define a linear PDE of the form  
                                                                                                                                                               
         -u_{,jj} = f  
                                                                                                                                                               
      with boundary conditons:  
                                                                                                                                                               
         n_j*u_{,j} = 0  
                                                                                                                                                               
     and constraints:  
                                                                                                                                                               
          u=0 where q>0  
                                                                                                                                                               
2264     """     """
2265       Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2266    
2267       M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
2268    
2269       with natural boundary conditons
2270    
2271     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
        LinearPDE.__init__(self,domain,1,1)  
        self.COEFFICIENTS={  
        "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
        self.setValue(f,q)  
2272    
2273     def setValue(self,f=escript.Data(),q=escript.Data()):     and constraints:
        self._setValue(f=f,q=q)  
2274    
2275     def getCoefficientOfPDE(self,name):     M{u=r} where M{q>0}
2276    
2277       and
2278    
2279       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2280    
2281       """
2282    
2283       def __init__(self,domain,debug=False):
2284       """       """
2285       @brief return the value of the coefficient name of the general PDE       initializes a new Poisson equation
2286       @param name  
2287         @param domain: domain of the PDE
2288         @type domain: L{Domain<escript.Domain>}
2289         @param debug: if True debug informations are printed.
2290    
2291         """
2292         super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2293         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2294                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2295                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2296                            "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2297                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2298                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2299                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2300                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2301                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2302    
2303       def setValue(self,**coefficients):
2304       """       """
2305       if name == "A" :       sets new values to coefficients
2306           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
2307       elif name == "B" :       @param coefficients: new values assigned to coefficients
2308           return escript.Data()       @keyword omega: value for coefficient M{S{omega}}
2309       elif name == "C" :       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2310           return escript.Data()       @keyword k: value for coefficient M{k}
2311       elif name == "D" :       @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2312         @keyword v: value for coefficient M{v}
2313         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2314         @keyword upwind: value for upwind term M{upwind}
2315         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2316         @keyword f: value for right hand side M{f}
2317         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2318         @keyword alpha: value for right hand side M{S{alpha}}
2319         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2320         @keyword g: value for right hand side M{g}
2321         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2322         @keyword r: prescribed values M{r} for the solution in constraints.
2323         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2324                   depending of reduced order is used for the representation of the equation.
2325         @keyword q: mask for location of constraints
2326         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2327                   depending of reduced order is used for the representation of the equation.
2328         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2329         """
2330         super(AdvectionDiffusion, self).setValue(**coefficients)
2331    
2332       def getCoefficientOfGeneralPDE(self,name):
2333         """
2334         return the value of the coefficient name of the general PDE
2335    
2336         @param name: name of the coefficient requested.
2337         @type name: C{string}
2338         @return: the value of the coefficient  name
2339         @rtype: L{Data<escript.Data>}
2340         @raise IllegalCoefficient: if name is not one of coefficients
2341                      "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}.
2342         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2343         """
2344         if name == "A" :
2345             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2346         elif name == "B" :
2347           return escript.Data()           return escript.Data()
2348       elif name == "X" :       elif name == "C" :
2349             return self.getCoefficient("v")
2350         elif name == "D" :
2351             return self.getCoefficient("omega")
2352         elif name == "X" :
2353           return escript.Data()           return escript.Data()
2354       elif name == "Y" :       elif name == "Y" :
2355           return self.getCoefficient("f")           return self.getCoefficient("f")
2356       elif name == "d" :       elif name == "d" :
2357           return escript.Data()           return self.getCoefficient("alpha")
2358       elif name == "y" :       elif name == "y" :
2359           return escript.Data()           return self.getCoefficient("g")
2360       elif name == "d_contact" :       elif name == "d_contact" :
2361           return escript.Data()           return escript.Data()
2362       elif name == "y_contact" :       elif name == "y_contact" :
2363           return escript.Data()           return escript.Data()
2364       elif name == "r" :       elif name == "r" :
2365           return escript.Data()           return self.getCoefficient("r")
2366       elif name == "q" :       elif name == "q" :
2367           return self.getCoefficient("q")           return self.getCoefficient("q")
2368       else:       else:
2369           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2370    
2371    
2372    # $Log$
2373    # Revision 1.14  2005/09/22 01:54:57  jgs
2374    # Merge of development branch dev-02 back to main trunk on 2005-09-22
2375    #
2376    # Revision 1.13  2005/09/15 03:44:19  jgs
2377    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2378    #
2379    # Revision 1.12  2005/09/01 03:31:28  jgs
2380    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2381    #
2382    # Revision 1.11  2005/08/23 01:24:28  jgs
2383    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2384    #
2385    # Revision 1.10  2005/08/12 01:45:36  jgs
2386    # erge of development branch dev-02 back to main trunk on 2005-08-12
2387    #
2388    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2389    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2390    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2391    # modified to instead use portable/cooperative "super" calls to extend base
2392    # class methods.
2393    #
2394    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2395    # Removed redundant if-loop.
2396    #
2397    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2398    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2399    #
2400    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2401    # the solver from finley are put into the standalone package paso now
2402    #
2403    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2404    # in the case of lumping no new system is allocated if the constraint is changed.
2405    #
2406    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2407    # test for Lumping added
2408    #
2409    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2410    # bug in format fixed.
2411    #
2412    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2413    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2414    #
2415    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2416    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2417    #
2418    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2419    # gneric unit testing for linearPDE
2420    #
2421    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2422    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2423    #
2424    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2425    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2426    #
2427    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2428    # epydoc mark up partially fixed
2429    #
2430    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2431    # some problems with LinearPDEs fixed.
2432    #
2433    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2434    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2435    #
2436    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2437    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2438    #
2439    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2440    # new functions in util and a new pde type in linearPDEs
2441    #
2442    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2443    # Lame equation: (linear elastic, isotropic) added
2444    #
2445    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2446    # some extensions to modellib and linearPDEs
2447    #
2448    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2449    # Fixed up some docstrings.  Moved module-level functions to top of file so
2450    # that epydoc and doxygen can pick them up properly.
2451    #
2452    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2453    # some basic Models have been added
2454    #
2455    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2456    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2457    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2458    # reformatting of docstrings.  Addition of code to make equations come out
2459    # as proper LaTeX.
2460    #
2461    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2462    # some problems with functionspace and linearPDEs fixed.
2463    #
2464    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2465    # bug in SystemPattern fixed.
2466    #
2467    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2468    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2469    #
2470    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2471    # Reference Number handling added
2472    #
2473    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2474    # some function exposed to python to make mesh merging running
2475    #
2476    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2477    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2478    #
2479    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2480    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2481    #
2482    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2483    # updates in the documentation
2484    #
2485    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2486    # Added createCoefficient method for linearPDEs.
2487    #
2488    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2489    # a problem in linearPDE class fixed
2490    #
2491    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2492    # some bugs in linearPDE fixed
2493    #
2494    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2495    # some bugs in slicing fixed
2496    #
2497    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2498    # FunctionSpace checking/matchig in slicing added
2499    #
2500    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2501    # bug in setValue fixed
2502    #
2503    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2504    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2505    #
2506    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2507    # AdvectivePDE added
2508    #
2509    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2510    # some changes in linearPDEs to add AdevectivePDE
2511    #
2512    # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2513    # __init__ of LinearPDE does not accept any coefficient anymore
2514    #
2515    # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2516    # *** empty log message ***
2517    #
2518    # Revision 1.1.2.1  2004/12/12 22:53:47  gross
2519    # linearPDE has been renamed LinearPDE
2520    #
2521    # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross
2522    # GMRES added
2523    #
2524    # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross
2525    # options for GMRES and PRES20 added
2526    #
2527    # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross
2528    # some small changes
2529    #
2530    # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross
2531    # Finley solves 4M unknowns now
2532    #
2533    # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross
2534    # poisson solver added
2535    #
2536    # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross
2537    # 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
2538    #
2539    # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross
2540    # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed
2541    #
2542    # Revision 1.1.1.1  2004/10/26 06:53:56  jgs
2543    # initial import of project esys2
2544    #
2545    # Revision 1.3.2.3  2004/10/26 06:43:48  jgs
2546    # committing Lutz's and Paul's changes to brach jgs
2547    #
2548    # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane
2549    # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.
2550    #
2551    # Revision 1.3  2004/09/23 00:53:23  jgs
2552    # minor fixes
2553    #
2554    # Revision 1.1  2004/08/28 12:58:06  gross
2555    # SimpleSolve is not running yet: problem with == of functionsspace
2556    #

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