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trunk/esys2/escript/py_src/linearPDEs.py revision 147 by jgs, Fri Aug 12 01:45:47 2005 UTC trunk/escript/py_src/linearPDEs.py revision 328 by gross, Wed Dec 7 04:41:53 2005 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  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}
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    
 def _CompTuple2(t1,t2):  
    """  
    Compare two tuples  
41    
42     \param t1 The first tuple  class IllegalCoefficient(ValueError):
43     \param t2 The second tuple     """
44       raised if an illegal coefficient of the general ar particular PDE is requested.
45     """     """
46    
47     dif=t1[0]+t1[1]-(t2[0]+t2[1])  class IllegalCoefficientValue(ValueError):
48     if dif<0: return 1     """
49     elif dif>0: return -1     raised if an incorrect value for a coefficient is used.
50     else: return 0     """
   
 def ELMAN_RAMAGE(P):  
     return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
   
 def SIMPLIFIED_BROOK_HUGHES(P):  
     c=(P-3.).whereNegative()  
     return P/6.*c+1./2.*(1.-c)  
51    
52  def HALF(P):  class UndefinedPDEError(ValueError):
53      return escript.Scalar(0.5,P.getFunctionSpace())     """
54       raised if a PDE is not fully defined yet.
55       """
56    
57  class PDECoefficient:  class PDECoefficient(object):
58      """      """
59      A class for PDE coefficients      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         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 68  class PDECoefficient: Line 113  class PDECoefficient:
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         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         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):
        """  
        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      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 102  class PDECoefficient: Line 196  class PDECoefficient:
196    
197      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
198          """          """
199      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         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      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     Class to handle 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     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
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     \f[     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
324     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
325     \f]     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     \f[     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
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    
    \f[  
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
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}
      """  
      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]}
357         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
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       self.COEFFICIENTS=self.__COEFFICIENTS     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    
423       """
424       DEFAULT= 0
425       DIRECT= 1
426       CHOLEVSKY= 2
427       PCG= 3
428       CR= 4
429       CGS= 5
430       BICGSTAB= 6
431       SSOR= 7
432       ILU0= 8
433       ILUT= 9
434       JACOBI= 10
435       GMRES= 11
436       PRES20= 12
437       LUMPING= 13
438       NO_REORDERING= 17
439       MINIMUM_FILL_IN= 18
440       NESTED_DISSECTION= 19
441       SCSL= 14
442       MKL= 15
443       UMFPACK= 16
444       ITERATIVE= 20
445       PASO= 21
446    
447       __TOL=1.e-13
448       __PACKAGE_KEY="package"
449       __METHOD_KEY="method"
450       __SYMMETRY_KEY="symmetric"
451       __TOLERANCE_KEY="tolerance"
452    
453    
454       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
455         """
456         initializes a new linear PDE
457    
458         @param domain: domain of the PDE
459         @type domain: L{Domain<escript.Domain>}
460         @param numEquations: number of equations. If numEquations==None the number of equations
461                              is exracted from the PDE coefficients.
462         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
463                              is exracted from the PDE coefficients.
464         @param debug: if True debug informations are printed.
465    
466         """
467         super(LinearPDE, self).__init__()
468         #
469         #   the coefficients of the general PDE:
470         #
471         self.__COEFFICIENTS_OF_GENEARL_PDE={
472           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
473           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
474           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
475           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
476           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
477           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
478           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
480           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
482           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
483           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
484    
485         # COEFFICIENTS can be overwritten by subclasses:
486         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
487         self.__altered_coefficients=False
488       # initialize attributes       # initialize attributes
489       self.__debug=None       self.__debug=debug
490       self.__domain=domain       self.__domain=domain
491       self.__numEquations=numEquations       self.__numEquations=numEquations
492       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
493       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
494    
495       # set some default values:       # set some default values:
496       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
497       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
498       self.__tolerance=1.e-8       self.__tolerance=1.e-8
499       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
500       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
501         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
502       self.__sym=False       self.__sym=False
      self.__lumping=False  
503    
504     def createCoefficient(self, name):       self.resetCoefficients()
505         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
506       # =============================================================================
507       #    general stuff:
508       # =============================================================================
509       def __str__(self):
510         """
511         returns string representation of the PDE
512    
513         @return: a simple representation of the PDE
514         @rtype: C{str}
515         """
516         return "<LinearPDE %d>"%id(self)
517       # =============================================================================
518       #    debug :
519       # =============================================================================
520       def setDebugOn(self):
521       """       """
522       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
523       """       """
524       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
   
    def __del__(self):  
      pass  
525    
526     def getCoefficient(self,name):     def setDebugOff(self):
527       """       """
528       return the value of the parameter name       switches off debugging
   
      @param name:  
529       """       """
530       return self.COEFFICIENTS[name].getValue()       self.__debug=None
531    
532     def getCoefficientOfPDE(self,name):     def trace(self,text):
533       """       """
534       return the value of the coefficient name of the general PDE.       print the text message if debugging is swiched on.
535       This method is called by the assembling routine it can be       @param text: message
536       overwritten to map coefficients of a particualr PDE to the general PDE.       @type text: C{string}
   
      @param name:  
537       """       """
538       return self.getCoefficient(name)       if self.__debug: print "%s: %s"%(str(self),text)
539    
540     def hasCoefficient(self,name):     # =============================================================================
541        """     # some service functions:
542        return true if name is the name of a coefficient     # =============================================================================
543       def getDomain(self):
       @param name:  
       """  
       return self.COEFFICIENTS.has_key(name)  
   
    def hasPDECoefficient(self,name):  
       """  
       return true if name is the name of a coefficient  
   
       @param name:  
       """  
       return self.__COEFFICIENTS.has_key(name)  
   
    def getFunctionSpaceForEquation(self):  
544       """       """
545       return true if the test functions should use reduced order       returns the domain of the PDE
546    
547         @return: the domain of the PDE
548         @rtype: L{Domain<escript.Domain>}
549       """       """
550       return self.__row_function_space       return self.__domain
551    
552     def getFunctionSpaceForSolution(self):     def getDim(self):
553       """       """
554       return true if the interpolation of the solution should use reduced order       returns the spatial dimension of the PDE
555    
556         @return: the spatial dimension of the PDE domain
557         @rtype: C{int}
558       """       """
559       return self.__column_function_space       return self.getDomain().getDim()
560    
561     def setValue(self,**coefficients):     def getNumEquations(self):
562        """       """
563        sets new values to coefficients       returns the number of equations
564    
565        @param coefficients:       @return: the number of equations
566        """       @rtype: C{int}
567        self.__setValue(**coefficients)       @raise UndefinedPDEError: if the number of equations is not be specified yet.
568               """
569         if self.__numEquations==None:
570             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
571         else:
572             return self.__numEquations
573    
574     def cleanCoefficients(self):     def getNumSolutions(self):
575       """       """
576       resets all coefficients to default values.       returns the number of unknowns
577    
578         @return: the number of unknowns
579         @rtype: C{int}
580         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
581       """       """
582       for i in self.COEFFICIENTS.iterkeys():       if self.__numSolutions==None:
583           self.COEFFICIENTS[i].resetValue()          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
584         else:
585            return self.__numSolutions
586    
587     def createNewCoefficient(self,name):     def reduceEquationOrder(self):
588       """       """
589       returns a new coefficient appropriate for coefficient name:       return status for order reduction for equation
590    
591         @return: return True is reduced interpolation order is used for the represenation of the equation
592         @rtype: L{bool}
593       """       """
594       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       return self.__reduce_equation_order
595          
596     def createNewCoefficientOfPDE(self,name):     def reduceSolutionOrder(self):
597       """       """
598       returns a new coefficient appropriate for coefficient name:       return status for order reduction for the solution
599    
600         @return: return True is reduced interpolation order is used for the represenation of the solution
601         @rtype: L{bool}
602       """       """
603       return escript.Data(0,self.getShapeOfCoefficientOfPDE(name),self.getFunctionSpaceForCoefficientOfPDE(name))       return self.__reduce_solution_order
604          
605     def getShapeOfCoefficientOfPDE(self,name):     def getFunctionSpaceForEquation(self):
606       """       """
607       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
608    
609       @param name:       @return: representation space of equation
610         @rtype: L{FunctionSpace<escript.FunctionSpace>}
611       """       """
612       if self.hasPDECoefficient(name):       if self.reduceEquationOrder():
613          return self.__COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
614       else:       else:
615          raise ValueError,"Unknown coefficient %s requested"%name           return escript.Solution(self.getDomain())
616    
617     def getFunctionSpaceForCoefficientOfPDE(self,name):     def getFunctionSpaceForSolution(self):
618       """       """
619       return the atoms of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
620    
621       @param name:       @return: representation space of solution
622         @rtype: L{FunctionSpace<escript.FunctionSpace>}
623       """       """
624       if self.hasPDECoefficient(name):       if self.reduceSolutionOrder():
625          return self.__COEFFICIENTS[name].getFunctionSpace(self.getDomain())           return escript.ReducedSolution(self.getDomain())
626       else:       else:
627          raise ValueError,"unknown coefficient %s requested"%name           return escript.Solution(self.getDomain())
628    
629     def getShapeOfCoefficient(self,name):  
630       def getOperator(self):
631       """       """
632       return the shape of the coefficient name       provides access to the operator of the PDE
633    
634       @param name:       @return: the operator of the PDE
635         @rtype: L{Operator<escript.Operator>}
636       """       """
637       if self.hasCoefficient(name):       m=self.getSystem()[0]
638          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())       if self.isUsingLumping():
639             return self.copyConstraint(1./m)
640       else:       else:
641          raise ValueError,"Unknown coefficient %s requested"%name           return m
642    
643     def getFunctionSpaceForCoefficient(self,name):     def getRightHandSide(self):
644       """       """
645       return the atoms of the coefficient name       provides access to the right hand side of the PDE
646         @return: the right hand side of the PDE
647         @rtype: L{Data<escript.Data>}
648         """
649         r=self.getSystem()[1]
650         if self.isUsingLumping():
651             return self.copyConstraint(r)
652         else:
653             return r
654    
655       @param name:     def applyOperator(self,u=None):
656       """       """
657       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
658          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())  
659         @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
660                   the current solution is used.
661         @type u: L{Data<escript.Data>} or None
662         @return: image of u
663         @rtype: L{Data<escript.Data>}
664         """
665         if u==None:
666              return self.getOperator()*self.getSolution()
667       else:       else:
668          raise ValueError,"unknown coefficient %s requested"%name          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
669    
670     def alteredCoefficient(self,name):     def getResidual(self,u=None):
671       """       """
672       announce that coefficient name has been changed       return the residual of u or the current solution if u is not present.
673    
674       @param name:       @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
675                   the current solution is used.
676         @type u: L{Data<escript.Data>} or None
677         @return: residual of u
678         @rtype: L{Data<escript.Data>}
679       """       """
680       if self.hasCoefficient(name):       return self.applyOperator(u)-self.getRightHandSide()
         if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
         if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()  
      else:  
         raise ValueError,"unknown coefficient %s requested"%name  
681    
682     # ===== debug ==============================================================     def checkSymmetry(self,verbose=True):
683     def setDebugOn(self):        """
684         """        test the PDE for symmetry.
        """  
        self.__debug=not None  
685    
686     def setDebugOff(self):        @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
687         """        @type verbose: C{bool}
688         """        @return:  True if the PDE is symmetric.
689         self.__debug=None        @rtype: L{Data<escript.Data>}
690          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
691          """
692          verbose=verbose or self.__debug
693          out=True
694          if self.getNumSolutions()!=self.getNumEquations():
695             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
696             out=False
697          else:
698             A=self.getCoefficientOfGeneralPDE("A")
699             if not A.isEmpty():
700                tol=util.Lsup(A)*self.__TOL
701                if self.getNumSolutions()>1:
702                   for i in range(self.getNumEquations()):
703                      for j in range(self.getDim()):
704                         for k in range(self.getNumSolutions()):
705                            for l in range(self.getDim()):
706                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
707                                   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)
708                                   out=False
709                else:
710                   for j in range(self.getDim()):
711                      for l in range(self.getDim()):
712                         if util.Lsup(A[j,l]-A[l,j])>tol:
713                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
714                            out=False
715             B=self.getCoefficientOfGeneralPDE("B")
716             C=self.getCoefficientOfGeneralPDE("C")
717             if B.isEmpty() and not C.isEmpty():
718                if verbose: print "non-symmetric PDE because B is not present but C is"
719                out=False
720             elif not B.isEmpty() and C.isEmpty():
721                if verbose: print "non-symmetric PDE because C is not present but B is"
722                out=False
723             elif not B.isEmpty() and not C.isEmpty():
724                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
725                if self.getNumSolutions()>1:
726                   for i in range(self.getNumEquations()):
727                       for j in range(self.getDim()):
728                          for k in range(self.getNumSolutions()):
729                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
730                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
731                                  out=False
732                else:
733                   for j in range(self.getDim()):
734                      if util.Lsup(B[j]-C[j])>tol:
735                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
736                         out=False
737             if self.getNumSolutions()>1:
738               D=self.getCoefficientOfGeneralPDE("D")
739               if not D.isEmpty():
740                 tol=util.Lsup(D)*self.__TOL
741                 for i in range(self.getNumEquations()):
742                    for k in range(self.getNumSolutions()):
743                      if util.Lsup(D[i,k]-D[k,i])>tol:
744                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
745                          out=False
746               d=self.getCoefficientOfGeneralPDE("d")
747               if not d.isEmpty():
748                 tol=util.Lsup(d)*self.__TOL
749                 for i in range(self.getNumEquations()):
750                    for k in range(self.getNumSolutions()):
751                      if util.Lsup(d[i,k]-d[k,i])>tol:
752                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
753                          out=False
754               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
755               if not d_contact.isEmpty():
756                 tol=util.Lsup(d_contact)*self.__TOL
757                 for i in range(self.getNumEquations()):
758                    for k in range(self.getNumSolutions()):
759                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
760                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
761                          out=False
762          return out
763    
764     def debug(self):     def getSolution(self,**options):
765         """         """
766         returns true if the PDE is in the debug mode         returns the solution of the PDE. If the solution is not valid the PDE is solved.
767    
768           @return: the solution
769           @rtype: L{Data<escript.Data>}
770           @param options: solver options
771           @keyword verbose: True to get some information during PDE solution
772           @type verbose: C{bool}
773           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
774                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
775           @keyword preconditioner: preconditioner method to be used. Allowed values are
776                                    L{SSOR}, L{ILU0}, L{ILUT}, L{JACOBI}
777           @keyword iter_max: maximum number of iteration steps allowed.
778           @keyword drop_tolerance: threshold for drupping in L{ILUT}
779           @keyword drop_storage: maximum of allowed memory in L{ILUT}
780           @keyword truncation: maximum number of residuals in L{GMRES}
781           @keyword restart: restart cycle length in L{GMRES}
782         """         """
783         return self.__debug         if not self.__solution_isValid:
784              mat,f=self.getSystem()
785              if self.isUsingLumping():
786                 self.__solution=self.copyConstraint(f*mat)
787              else:
788                 options[self.__TOLERANCE_KEY]=self.getTolerance()
789                 options[self.__METHOD_KEY]=self.getSolverMethod()
790                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
791                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
792                 self.trace("PDE is resolved.")
793                 self.trace("solver options: %s"%str(options))
794                 self.__solution=mat.solve(f,options)
795              self.__solution_isValid=True
796           return self.__solution
797    
798     #===== Lumping ===========================     def getFlux(self,u=None):
799     def setLumpingOn(self):       """
800        """       returns the flux M{J} for a given M{u}
       indicates to use matrix lumping  
       """  
       if not self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set on"  
          self.__rebuildOperator()  
          self.__lumping=True  
801    
802     def setLumpingOff(self):       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
       """  
       switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
803    
804     def setLumping(self,flag=False):       or
       """  
       set the matrix lumping flag to flag  
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
805    
806     def isUsingLumping(self):       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
       """  
         
       """  
       return self.__lumping  
807    
808     #============ method business =========================================================       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
809     def setSolverMethod(self,solver=util.DEFAULT_METHOD):       @type u: L{Data<escript.Data>} or None
810         @return: flux
811         @rtype: L{Data<escript.Data>}
812         """
813         if u==None: u=self.getSolution()
814         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
815       # =============================================================================
816       #   solver settings:
817       # =============================================================================
818       def setSolverMethod(self,solver=None):
819         """         """
820         sets a new solver         sets a new solver
821    
822           @param solver: sets a new solver method.
823           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.
824         """         """
825           if solver==None: solve=self.DEFAULT
826         if not solver==self.getSolverMethod():         if not solver==self.getSolverMethod():
827             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
828             self.__checkMatrixType()             self.__checkMatrixType()
829               self.trace("New solver is %s"%self.getSolverMethodName())
830    
831       def getSolverMethodName(self):
832           """
833           returns the name of the solver currently used
834    
835           @return: the name of the solver currently used.
836           @rtype: C{string}
837           """
838    
839           m=self.getSolverMethod()
840           p=self.getSolverPackage()
841           if m==self.DEFAULT: method="DEFAULT"
842           elif m==self.DIRECT: method= "DIRECT"
843           elif m==self.ITERATIVE: method= "ITERATIVE"
844           elif m==self.CHOLEVSKY: method= "CHOLEVSKY"
845           elif m==self.PCG: method= "PCG"
846           elif m==self.CR: method= "CR"
847           elif m==self.CGS: method= "CGS"
848           elif m==self.BICGSTAB: method= "BICGSTAB"
849           elif m==self.SSOR: method= "SSOR"
850           elif m==self.GMRES: method= "GMRES"
851           elif m==self.PRES20: method= "PRES20"
852           elif m==self.LUMPING: method= "LUMPING"
853           else : method="unknown"
854           if p==self.DEFAULT: package="DEFAULT"
855           elif p==self.PASO: package= "PASO"
856           elif p==self.MKL: package= "MKL"
857           elif p==self.SCSL: package= "SCSL"
858           elif p==self.UMFPACK: package= "UMFPACK"
859           else : method="unknown"
860           return "%s solver of %s package"%(method,package)
861    
862    
863     def getSolverMethod(self):     def getSolverMethod(self):
864         """         """
865         returns the solver method         returns the solver method
866    
867           @return: the solver method currently be used.
868           @rtype: C{int}
869         """         """
870         return self.__solver_method         return self.__solver_method
871    
872     #============ tolerance business =========================================================     def setSolverPackage(self,package=None):
873           """
874           sets a new solver package
875    
876           @param solver: sets a new solver method.
877           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
878           """
879           if package==None: package=self.DEFAULT
880           if not package==self.getSolverPackage():
881               self.__solver_method=solver
882               self.__checkMatrixType()
883               self.trace("New solver is %s"%self.getSolverMethodName())
884    
885       def getSolverPackage(self):
886           """
887           returns the package of the solver
888    
889           @return: the solver package currently being used.
890           @rtype: C{int}
891           """
892           return self.__solver_package
893    
894       def isUsingLumping(self):
895          """
896          checks if matrix lumping is used a solver method
897    
898          @return: True is lumping is currently used a solver method.
899          @rtype: C{bool}
900          """
901          return self.getSolverMethod()==self.LUMPING
902    
903     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
904         """         """
905         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
906    
907           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
908    
909           defines the stopping criterion.
910    
911           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
912                       the system will be resolved.
913           @type tol: positive C{float}
914           @raise ValueException: if tolerance is not positive.
915         """         """
916         if not tol>0:         if not tol>0:
917             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
918         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
919         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
920         self.__tolerance=tol         self.__tolerance=tol
921         return         return
922    
923     def getTolerance(self):     def getTolerance(self):
924         """         """
925         returns the tolerance set for the solution         returns the tolerance set for the solution
926    
927           @return: tolerance currently used.
928           @rtype: C{float}
929         """         """
930         return self.__tolerance         return self.__tolerance
931    
932     #===== symmetry  flag ==========================     # =============================================================================
933       #    symmetry  flag:
934       # =============================================================================
935     def isSymmetric(self):     def isSymmetric(self):
936        """        """
937        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
938    
939          @return: True is a symmetric PDE is indicated, otherwise False is returned
940          @rtype: C{bool}
941        """        """
942        return self.__sym        return self.__sym
943    
944     def setSymmetryOn(self):     def setSymmetryOn(self):
945        """        """
946        sets the symmetry flag to true        sets the symmetry flag.
947        """        """
948        if not self.isSymmetric():        if not self.isSymmetric():
949           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
950           self.__sym=True           self.__sym=True
951           self.__checkMatrixType()           self.__checkMatrixType()
952    
953     def setSymmetryOff(self):     def setSymmetryOff(self):
954        """        """
955        sets the symmetry flag to false        removes the symmetry flag.
956        """        """
957        if self.isSymmetric():        if self.isSymmetric():
958           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
959           self.__sym=False           self.__sym=False
960           self.__checkMatrixType()           self.__checkMatrixType()
961    
962     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
963       """        """
964       sets the symmetry flag to flag        sets the symmetry flag to flag
965    
966       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
967       """        @type flag: C{bool}
968       if flag:        """
969          self.setSymmetryOn()        if flag:
970       else:           self.setSymmetryOn()
971          self.setSymmetryOff()        else:
972             self.setSymmetryOff()
973    
974     #===== order reduction ==========================     # =============================================================================
975       # function space handling for the equation as well as the solution
976       # =============================================================================
977     def setReducedOrderOn(self):     def setReducedOrderOn(self):
978       """       """
979       switches to on reduced order       switches on reduced order for solution and equation representation
980    
981         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
982       """       """
983       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
984       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
985    
986     def setReducedOrderOff(self):     def setReducedOrderOff(self):
987       """       """
988       switches to full order       switches off reduced order for solution and equation representation
989    
990         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
991       """       """
992       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
993       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
994    
995     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
996       """       """
997       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
998         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
999       @param flag:                    if flag is not present order reduction is switched off
1000         @type flag: C{bool}
1001         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1002       """       """
1003       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1004       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1005    
1006     #===== order reduction solution ==========================  
1007     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1008       """       """
1009       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1010    
1011         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1012       """       """
1013       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1014       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1015           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1016           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1017           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1018             self.__resetSystem()
1019    
1020     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1021       """       """
1022       switches to full order to interpolate solution       switches off reduced order for solution representation
1023    
1024         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1025       """       """
1026       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1027       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1028           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1029           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1030           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1031             self.__resetSystem()
1032    
1033     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1034       """       """
1035       sets order for test functions according to flag       sets order for test functions according to flag
1036    
1037       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1038                      if flag is not present order reduction is switched off
1039         @type flag: C{bool}
1040         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1041       """       """
1042       if flag:       if flag:
1043          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1044       else:       else:
1045          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1046                                                                                                                                                              
    #===== order reduction equation ==========================  
1047     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1048       """       """
1049       switches to reduced order for test functions       switches on reduced order for equation representation
1050    
1051         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1052       """       """
1053       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1054       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1055           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1056           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1057           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1058             self.__resetSystem()
1059    
1060     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1061       """       """
1062       switches to full order for test functions       switches off reduced order for equation representation
1063    
1064         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1065       """       """
1066       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1067       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1068           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1069           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1070           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1071             self.__resetSystem()
1072    
1073     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1074       """       """
1075       sets order for test functions according to flag       sets order for test functions according to flag
1076    
1077       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1078                      if flag is not present order reduction is switched off
1079         @type flag: C{bool}
1080         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1081       """       """
1082       if flag:       if flag:
1083          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1084       else:       else:
1085          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1086                                                                                                                                                              
1087     # ==== initialization =====================================================================     # =============================================================================
1088       # private method:
1089       # =============================================================================
1090       def __checkMatrixType(self):
1091         """
1092         reassess the matrix type and, if a new matrix is needed, resets the system.
1093         """
1094         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.getSolverPackage(),self.isSymmetric())
1095         if not new_matrix_type==self.__matrix_type:
1096             self.trace("Matrix type is now %d."%new_matrix_type)
1097             self.__matrix_type=new_matrix_type
1098             self.__resetSystem()
1099       #
1100       #   rebuild switches :
1101       #
1102       def __invalidateSolution(self):
1103           """
1104           indicates the PDE has to be resolved if the solution is requested
1105           """
1106           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1107           self.__solution_isValid=False
1108    
1109       def __invalidateOperator(self):
1110           """
1111           indicates the operator has to be rebuilt next time it is used
1112           """
1113           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1114           self.__invalidateSolution()
1115           self.__operator_is_Valid=False
1116    
1117       def __invalidateRightHandSide(self):
1118           """
1119           indicates the right hand side has to be rebuild next time it is used
1120           """
1121           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1122           self.__invalidateSolution()
1123           self.__righthandside_isValid=False
1124    
1125       def __invalidateSystem(self):
1126           """
1127           annonced that everthing has to be rebuild:
1128           """
1129           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1130           self.__invalidateSolution()
1131           self.__invalidateOperator()
1132           self.__invalidateRightHandSide()
1133    
1134       def __resetSystem(self):
1135           """
1136           annonced that everthing has to be rebuild:
1137           """
1138           self.trace("New System is built from scratch.")
1139           self.__operator=escript.Operator()
1140           self.__operator_is_Valid=False
1141           self.__righthandside=escript.Data()
1142           self.__righthandside_isValid=False
1143           self.__solution=escript.Data()
1144           self.__solution_isValid=False
1145       #
1146       #    system initialization:
1147       #
1148     def __getNewOperator(self):     def __getNewOperator(self):
1149         """         """
1150           returns an instance of a new operator
1151         """         """
1152           self.trace("New operator is allocated.")
1153         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1154                             self.getNumEquations(), \                             self.getNumEquations(), \
1155                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 601  class LinearPDE: Line 1157  class LinearPDE:
1157                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1158                             self.__matrix_type)                             self.__matrix_type)
1159    
1160     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1161         """         """
1162           returns an instance of a new right hand side
1163         """         """
1164         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1165         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1166             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1167         else:         else:
1168             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1169    
1170     def __getNewSolution(self):     def __getNewSolution(self):
1171         """         """
1172           returns an instance of a new solution
1173         """         """
1174         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1175         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1176             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1177         else:         else:
1178             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1179    
1180       def __makeFreshSolution(self):
1181           """
1182           makes sure that the solution is instantiated and returns it initialized by zeros
1183           """
1184           if self.__solution.isEmpty():
1185               self.__solution=self.__getNewSolution()
1186           else:
1187               self.__solution*=0
1188               self.trace("Solution is reset to zero.")
1189           return self.__solution
1190    
1191       def __makeFreshRightHandSide(self):
1192           """
1193           makes sure that the right hand side is instantiated and returns it initialized by zeros
1194           """
1195           if self.__righthandside.isEmpty():
1196               self.__righthandside=self.__getNewRightHandSide()
1197           else:
1198               self.__righthandside*=0
1199               self.trace("Right hand side is reset to zero.")
1200           return self.__righthandside
1201    
1202     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1203         """         """
1204           makes sure that the operator is instantiated and returns it initialized by zeros
1205         """         """
1206         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1207             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1208         else:         else:
1209             self.__operator.setValue(0.)             self.__operator.resetValues()
1210             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1211         return self.__operator         return self.__operator
1212    
1213     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1214     def getDomain(self):         """
1215           applies the constraints defined by q and r to the system
1216           """
1217           if not self.isUsingLumping():
1218              q=self.getCoefficientOfGeneralPDE("q")
1219              r=self.getCoefficientOfGeneralPDE("r")
1220              if not q.isEmpty() and not self.__operator.isEmpty():
1221                 # q is the row and column mask to indicate where constraints are set:
1222                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1223                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1224                 u=self.__getNewSolution()
1225                 if r.isEmpty():
1226                    r_s=self.__getNewSolution()
1227                 else:
1228                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1229                 u.copyWithMask(r_s,col_q)
1230                 if not self.__righthandside.isEmpty():
1231                    self.__righthandside-=self.__operator*u
1232                    self.__righthandside=self.copyConstraint(self.__righthandside)
1233                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1234       # =============================================================================
1235       # function giving access to coefficients of the general PDE:
1236       # =============================================================================
1237       def getCoefficientOfGeneralPDE(self,name):
1238         """
1239         return the value of the coefficient name of the general PDE.
1240    
1241         @note: This method is called by the assembling routine it can be overwritten
1242               to map coefficients of a particular PDE to the general PDE.
1243         @param name: name of the coefficient requested.
1244         @type name: C{string}
1245         @return: the value of the coefficient  name
1246         @rtype: L{Data<escript.Data>}
1247         @raise IllegalCoefficient: if name is not one of coefficients
1248                      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}.
1249       """       """
1250       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1251            return self.getCoefficient(name)
1252         else:
1253            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1254    
1255       def hasCoefficientOfGeneralPDE(self,name):
1256       """       """
1257       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1258    
1259         @param name: name of the coefficient enquired.
1260         @type name: C{string}
1261         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1262         @rtype: C{bool}
1263    
    def getDim(self):  
1264       """       """
1265       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1266    
1267       def createCoefficientOfGeneralPDE(self,name):
1268       """       """
1269       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1270    
1271     def getNumEquations(self):       @param name: name of the coefficient requested.
1272         @type name: C{string}
1273         @return: a coefficient name initialized to 0.
1274         @rtype: L{Data<escript.Data>}
1275         @raise IllegalCoefficient: if name is not one of coefficients
1276                      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}.
1277       """       """
1278       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1279            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1280         else:
1281            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1282    
1283       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1284       """       """
1285       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1286           return self.__numEquations  
1287         @param name: name of the coefficient enquired.
1288         @type name: C{string}
1289         @return: the function space to be used for coefficient name
1290         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1291         @raise IllegalCoefficient: if name is not one of coefficients
1292                      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}.
1293         """
1294         if self.hasCoefficientOfGeneralPDE(name):
1295            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1296       else:       else:
1297           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1298    
1299     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1300       """       """
1301       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1302    
1303         @param name: name of the coefficient enquired.
1304         @type name: C{string}
1305         @return: the shape of the coefficient name
1306         @rtype: C{tuple} of C{int}
1307         @raise IllegalCoefficient: if name is not one of coefficients
1308                      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}.
1309       """       """
1310       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1311          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1312       else:       else:
1313          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1314    
1315       # =============================================================================
1316       # functions giving access to coefficients of a particular PDE implementation:
1317       # =============================================================================
1318       def getCoefficient(self,name):
1319         """
1320         returns the value of the coefficient name
1321    
1322     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1323        """       @type name: C{string}
1324        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
1325        """       @rtype: L{Data<escript.Data>}
1326        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1327        out=True       """
1328        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1329           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1330           out=False       else:
1331        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  
1332    
1333     def getFlux(self,u):     def hasCoefficient(self,name):
1334         """       """
1335         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1336    
1337         \f[       @param name: name of the coefficient enquired.
1338         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1339         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1340         @rtype: C{bool}
1341         """
1342         return self.COEFFICIENTS.has_key(name)
1343    
1344         @param u: argument of the operator     def createCoefficient(self, name):
1345         """       """
1346         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1347    
1348     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1349         """       @rtype: L{Data<escript.Data>}
1350         applies the operator of the PDE to a given solution u in weak from       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1351         """
1352         if self.hasCoefficient(name):
1353            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1354         else:
1355            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1356    
1357         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1358         """       """
1359         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        return the residual of u in the weak from  
1360    
1361         @param u:       @param name: name of the coefficient enquired.
1362         """       @type name: C{string}
1363         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1364         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1365         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1366         """
1367         if self.hasCoefficient(name):
1368            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1369         else:
1370            raise ValueError,"unknown coefficient %s requested"%name
1371       def getShapeOfCoefficient(self,name):
1372         """
1373         return the shape of the coefficient name
1374    
1375         @param name: name of the coefficient enquired.
1376         @type name: C{string}
1377         @return: the shape of the coefficient name
1378         @rtype: C{tuple} of C{int}
1379         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1380         """
1381         if self.hasCoefficient(name):
1382            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1383         else:
1384            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1385    
1386       def resetCoefficients(self):
1387         """
1388         resets all coefficients to there default values.
1389         """
1390         for i in self.COEFFICIENTS.iterkeys():
1391             self.COEFFICIENTS[i].resetValue()
1392    
1393       def alteredCoefficient(self,name):
1394         """
1395         announce that coefficient name has been changed
1396    
1397     def __setValue(self,**coefficients):       @param name: name of the coefficient enquired.
1398         @type name: C{string}
1399         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1400         @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.
1401         """
1402         if self.hasCoefficient(name):
1403            self.trace("Coefficient %s has been altered."%name)
1404            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1405               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1406               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1407         else:
1408            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1409    
1410       def copyConstraint(self,u):
1411        """        """
1412        sets new values to coefficient        copies the constraint into u and returns u.
1413    
1414          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1415          @type u: L{Data<escript.Data>}
1416          @return: the input u modified by the constraints.
1417          @rtype: L{Data<escript.Data>}
1418          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1419          """
1420          q=self.getCoefficientOfGeneralPDE("q")
1421          r=self.getCoefficientOfGeneralPDE("r")
1422          if not q.isEmpty():
1423             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1424             if r.isEmpty():
1425                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1426             else:
1427                 r=escript.Data(r,u.getFunctionSpace())
1428             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1429          return u
1430    
1431        @param coefficients:     def setValue(self,**coefficients):
1432          """
1433          sets new values to coefficients
1434    
1435          @param coefficients: new values assigned to coefficients
1436          @keyword A: value for coefficient A.
1437          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1438          @keyword B: value for coefficient B
1439          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1440          @keyword C: value for coefficient C
1441          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1442          @keyword D: value for coefficient D
1443          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1444          @keyword X: value for coefficient X
1445          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1446          @keyword Y: value for coefficient Y
1447          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1448          @keyword d: value for coefficient d
1449          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1450          @keyword y: value for coefficient y
1451          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1452          @keyword d_contact: value for coefficient d_contact
1453          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1454                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1455          @keyword y_contact: value for coefficient y_contact
1456          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1457                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1458          @keyword r: values prescribed to the solution at the locations of constraints
1459          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1460                   depending of reduced order is used for the solution.
1461          @keyword q: mask for location of constraints
1462          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1463                   depending of reduced order is used for the representation of the equation.
1464          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1465        """        """
1466        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1467        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1468           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1469              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1470        # 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:
1471        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1472           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1473              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1474                  s=d.shape                  s=d.shape
# Line 775  class LinearPDE: Line 1478  class LinearPDE:
1478                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1479              if s!=None:              if s!=None:
1480                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1481                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1482                  if res==None:                  if res==None:
1483                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1484                  else:                  else:
1485                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1486                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1487        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1488        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1489        # 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:
1490        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1491          if d==None:          try:
1492               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1493          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1494               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)  
1495          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):  
       """  
       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):  
        """  
        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):  
        """  
        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):  
        """  
        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):  
        """  
        annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      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):  
       """  
       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()))  
1496    
1497     def __applyConstraint(self):        self.__altered_coefficients=True
1498         """        # check if the systrem is inhomogeneous:
1499         applies the constraints defined by q and r to the system        if len(coefficients)>0 and not self.isUsingLumping():
1500         """           q=self.getCoefficientOfGeneralPDE("q")
1501         q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1502         r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1503         if not q.isEmpty() and not self.__operator.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1504            # q is the row and column mask to indicate where constraints are set:               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1505            row_q=escript.Data(q,self.getFunctionSpaceForEquation())                 self.trace("Inhomogeneous constraint detected.")
1506            col_q=escript.Data(q,self.getFunctionSpaceForSolution())                 self.__invalidateSystem()
           u=self.__getNewSolution()  
           if r.isEmpty():  
              r_s=self.__getNewSolution()  
           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.)  
1507    
1508     def getSystem(self):     def getSystem(self):
1509         """         """
1510         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1511    
1512           @return: the discrete version of the PDE
1513           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1514         """         """
1515         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1516            if self.isUsingLumping():            if self.isUsingLumping():
1517                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1518                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1519                         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"
1520                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1521                            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"
                  if not self.getCoefficientOfPDE("B").isEmpty():  
                           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."  
1522                   mat=self.__getNewOperator()                   mat=self.__getNewOperator()
1523                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   self.getDomain().addPDEToSystem(mat,escript.Data(), \
1524                             self.getCoefficientOfPDE("A"), \                             self.getCoefficientOfGeneralPDE("A"), \
1525                             self.getCoefficientOfPDE("B"), \                             self.getCoefficientOfGeneralPDE("B"), \
1526                             self.getCoefficientOfPDE("C"), \                             self.getCoefficientOfGeneralPDE("C"), \
1527                             self.getCoefficientOfPDE("D"), \                             self.getCoefficientOfGeneralPDE("D"), \
1528                             escript.Data(), \                             escript.Data(), \
1529                             escript.Data(), \                             escript.Data(), \
1530                             self.getCoefficientOfPDE("d"), \                             self.getCoefficientOfGeneralPDE("d"), \
1531                             escript.Data(),\                             escript.Data(),\
1532                             self.getCoefficientOfPDE("d_contact"), \                             self.getCoefficientOfGeneralPDE("d_contact"), \
1533                             escript.Data())                             escript.Data())
1534                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1535                   self.__applyConstraint()                   del mat
1536                   self.__operator_isValid=True                   self.trace("New lumped operator has been built.")
1537                     self.__operator_is_Valid=True
1538                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1539                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1540                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1541                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1542                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1543                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1544                   self.__copyConstraint()                   self.trace("New right hand side as been built.")
1545                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1546            else:            else:
1547               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New system is built."  
1548                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1549                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1550                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1551                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1552                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1553                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1554                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1555                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1556                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1557                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1558                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1559                   self.__applyConstraint()                   self.__applyConstraint()
1560                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1561                   self.__operator_isValid=True                   self.trace("New system has been built.")
1562                     self.__operator_is_Valid=True
1563                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1564               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1565                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1566                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1567                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1568                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1569                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1570                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1571                     self.trace("New right hand side has been built.")
1572                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1573               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1574                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1575                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1576                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1577                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1578                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1579                              escript.Data(), \                              escript.Data(), \
1580                              escript.Data(), \                              escript.Data(), \
1581                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1582                              escript.Data(),\                              escript.Data(),\
1583                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1584                              escript.Data())                              escript.Data())
1585                   self.__applyConstraint()                   self.__applyConstraint()
1586                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1587                     self.__operator_is_Valid=True
1588         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1589    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1590    
1591     def solve(self,**options):  class Poisson(LinearPDE):
1592        """     """
1593        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1594    
1595        @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  
1596    
1597     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
1598    
1599         @param options:     M{n[j]*grad(u)[j] = 0 }
        """  
        if not self.__solution_isValid:  
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
1600    
1601       and constraints:
1602    
1603       M{u=0} where M{q>0}
1604    
1605  def ELMAN_RAMAGE(P):     """
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
 def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
1606    
1607  def HALF(P):     def __init__(self,domain,debug=False):
1608      """ """       """
1609      return escript.Scalar(0.5,P.getFunctionSpace())       initializes a new Poisson equation
1610    
1611  class AdvectivePDE(LinearPDE):       @param domain: domain of the PDE
1612         @type domain: L{Domain<escript.Domain>}
1613         @param debug: if True debug informations are printed.
1614    
1615         """
1616         super(Poisson, self).__init__(domain,1,1,debug)
1617         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1618                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1619         self.setSymmetryOn()
1620    
1621       def setValue(self,**coefficients):
1622         """
1623         sets new values to coefficients
1624    
1625         @param coefficients: new values assigned to coefficients
1626         @keyword f: value for right hand side M{f}
1627         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1628         @keyword q: mask for location of constraints
1629         @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>}
1630                   depending of reduced order is used for the representation of the equation.
1631         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1632         """
1633         super(Poisson, self).setValue(**coefficients)
1634    
1635       def getCoefficientOfGeneralPDE(self,name):
1636         """
1637         return the value of the coefficient name of the general PDE
1638         @param name: name of the coefficient requested.
1639         @type name: C{string}
1640         @return: the value of the coefficient  name
1641         @rtype: L{Data<escript.Data>}
1642         @raise IllegalCoefficient: if name is not one of coefficients
1643                      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}.
1644         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1645         """
1646         if name == "A" :
1647             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1648         elif name == "B" :
1649             return escript.Data()
1650         elif name == "C" :
1651             return escript.Data()
1652         elif name == "D" :
1653             return escript.Data()
1654         elif name == "X" :
1655             return escript.Data()
1656         elif name == "Y" :
1657             return self.getCoefficient("f")
1658         elif name == "d" :
1659             return escript.Data()
1660         elif name == "y" :
1661             return escript.Data()
1662         elif name == "d_contact" :
1663             return escript.Data()
1664         elif name == "y_contact" :
1665             return escript.Data()
1666         elif name == "r" :
1667             return escript.Data()
1668         elif name == "q" :
1669             return self.getCoefficient("q")
1670         else:
1671            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1672    
1673    class Helmholtz(LinearPDE):
1674     """     """
1675     Class to handle a linear PDE dominated by advective terms:     Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1676      
1677     class to define a linear PDE of the form     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1678    
1679       with natural boundary conditons
1680    
1681       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1682    
1683       and constraints:
1684    
1685     \f[     M{u=r} where M{q>0}
    -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
1686    
1687     with boundary conditons:     """
1688    
1689       def __init__(self,domain,debug=False):
1690         """
1691         initializes a new Poisson equation
1692    
1693     \f[       @param domain: domain of the PDE
1694     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       @type domain: L{Domain<escript.Domain>}
1695     \f]       @param debug: if True debug informations are printed.
1696    
1697         """
1698         super(Helmholtz, self).__init__(domain,1,1,debug)
1699         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1700                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1701                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1702                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1703                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1704                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1705                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1706         self.setSymmetryOn()
1707    
1708     and contact conditions     def setValue(self,**coefficients):
1709         """
1710         sets new values to coefficients
1711    
1712     \f[       @param coefficients: new values assigned to coefficients
1713     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}       @keyword omega: value for coefficient M{S{omega}}
1714     \f]       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1715         @keyword k: value for coefficeint M{k}
1716         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1717         @keyword f: value for right hand side M{f}
1718         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1719         @keyword alpha: value for right hand side M{S{alpha}}
1720         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1721         @keyword g: value for right hand side M{g}
1722         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1723         @keyword r: prescribed values M{r} for the solution in constraints.
1724         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1725                   depending of reduced order is used for the representation of the equation.
1726         @keyword q: mask for location of constraints
1727         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1728                   depending of reduced order is used for the representation of the equation.
1729         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1730         """
1731         super(Helmholtz, self).setValue(**coefficients)
1732    
1733       def getCoefficientOfGeneralPDE(self,name):
1734         """
1735         return the value of the coefficient name of the general PDE
1736    
1737         @param name: name of the coefficient requested.
1738         @type name: C{string}
1739         @return: the value of the coefficient  name
1740         @rtype: L{Data<escript.Data>}
1741         @raise IllegalCoefficient: if name is not one of coefficients
1742                      "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}.
1743         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1744         """
1745         if name == "A" :
1746             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1747         elif name == "B" :
1748             return escript.Data()
1749         elif name == "C" :
1750             return escript.Data()
1751         elif name == "D" :
1752             return self.getCoefficient("omega")
1753         elif name == "X" :
1754             return escript.Data()
1755         elif name == "Y" :
1756             return self.getCoefficient("f")
1757         elif name == "d" :
1758             return self.getCoefficient("alpha")
1759         elif name == "y" :
1760             return self.getCoefficient("g")
1761         elif name == "d_contact" :
1762             return escript.Data()
1763         elif name == "y_contact" :
1764             return escript.Data()
1765         elif name == "r" :
1766             return self.getCoefficient("r")
1767         elif name == "q" :
1768             return self.getCoefficient("q")
1769         else:
1770            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1771    
1772    class LameEquation(LinearPDE):
1773       """
1774       Class to define a Lame equation problem:
1775    
1776       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] }
1777    
1778       with natural boundary conditons:
1779    
1780       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] }
1781    
1782     and constraints:     and constraints:
1783    
1784     \f[     M{u[i]=r[i]} where M{q[i]>0}
1785     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1786     """     """
1787     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
1788        LinearPDE.__init__(self,domain,numEquations,numSolutions)     def __init__(self,domain,debug=False):
1789        self.__xi=xi        super(LameEquation, self).__init__(domain,\
1790                                             domain.getDim(),domain.getDim(),debug)
1791          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1792                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1793                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1794                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1795                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1796                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1797                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1798          self.setSymmetryOn()
1799    
1800       def setValue(self,**coefficients):
1801         """
1802         sets new values to coefficients
1803    
1804         @param coefficients: new values assigned to coefficients
1805         @keyword lame_mu: value for coefficient M{S{mu}}
1806         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1807         @keyword lame_lambda: value for coefficient M{S{lambda}}
1808         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1809         @keyword F: value for internal force M{F}
1810         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1811         @keyword sigma: value for initial stress M{S{sigma}}
1812         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1813         @keyword f: value for extrenal force M{f}
1814         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1815         @keyword r: prescribed values M{r} for the solution in constraints.
1816         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1817                   depending of reduced order is used for the representation of the equation.
1818         @keyword q: mask for location of constraints
1819         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1820                   depending of reduced order is used for the representation of the equation.
1821         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1822         """
1823         super(LameEquation, self).setValue(**coefficients)
1824    
1825       def getCoefficientOfGeneralPDE(self,name):
1826         """
1827         return the value of the coefficient name of the general PDE
1828    
1829         @param name: name of the coefficient requested.
1830         @type name: C{string}
1831         @return: the value of the coefficient  name
1832         @rtype: L{Data<escript.Data>}
1833         @raise IllegalCoefficient: if name is not one of coefficients
1834                      "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}.
1835         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1836         """
1837         if name == "A" :
1838             out =self.createCoefficientOfGeneralPDE("A")
1839             for i in range(self.getDim()):
1840               for j in range(self.getDim()):
1841                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1842                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1843                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1844             return out
1845         elif name == "B" :
1846             return escript.Data()
1847         elif name == "C" :
1848             return escript.Data()
1849         elif name == "D" :
1850             return escript.Data()
1851         elif name == "X" :
1852             return self.getCoefficient("sigma")
1853         elif name == "Y" :
1854             return self.getCoefficient("F")
1855         elif name == "d" :
1856             return escript.Data()
1857         elif name == "y" :
1858             return self.getCoefficient("f")
1859         elif name == "d_contact" :
1860             return escript.Data()
1861         elif name == "y_contact" :
1862             return escript.Data()
1863         elif name == "r" :
1864             return self.getCoefficient("r")
1865         elif name == "q" :
1866             return self.getCoefficient("q")
1867         else:
1868            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1869    
1870    class AdvectivePDE(LinearPDE):
1871       """
1872       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1873       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1874    
1875       In the following we set
1876    
1877       M{Z[j]=C[j]-B[j]}
1878    
1879       or
1880    
1881       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1882    
1883       To measure the dominance of the advective terms over the diffusive term M{A} the
1884       X{Pelclet number} M{P} is used. It is defined as
1885    
1886       M{P=h|Z|/(2|A|)}
1887    
1888       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1889       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1890    
1891       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1892    
1893       M{S{Xi}=S{xi}(P) h/|Z|}
1894    
1895       where M{S{xi}} is a suitable function of the Peclet number.
1896    
1897       In the case of a single PDE the coefficient are up-dated in the following way:
1898             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1899             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1900             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1901             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1902    
1903       Similar for the case of a systems of PDEs:
1904             - 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]}
1905             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1906             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1907             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1908    
1909       where M{S{delta}} is L{kronecker}.
1910       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1911       but with the intension to stabilize the solution.
1912    
1913       """
1914       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1915          """
1916          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1917    
1918          @param domain: domain of the PDE
1919          @type domain: L{Domain<escript.Domain>}
1920          @param numEquations: number of equations. If numEquations==None the number of equations
1921                               is exracted from the PDE coefficients.
1922          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1923                               is exracted from the PDE coefficients.
1924          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1925                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1926          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1927          @param debug: if True debug informations are printed.
1928          """
1929          super(AdvectivePDE, self).__init__(domain,\
1930                                             numEquations,numSolutions,debug)
1931          if xi==None:
1932             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1933          else:
1934             self.__xi=xi
1935        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1936    
1937     def __calculateXi(self,peclet_factor,Z,h):     def setValue(**coefficients):
1938         Z_max=util.Lsup(Z)        """
1939         if Z_max>0.:        sets new values to coefficients
1940            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1941          @param coefficients: new values assigned to coefficients
1942          @keyword A: value for coefficient A.
1943          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1944          @keyword B: value for coefficient B
1945          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1946          @keyword C: value for coefficient C
1947          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1948          @keyword D: value for coefficient D
1949          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1950          @keyword X: value for coefficient X
1951          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1952          @keyword Y: value for coefficient Y
1953          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1954          @keyword d: value for coefficient d
1955          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1956          @keyword y: value for coefficient y
1957          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1958          @keyword d_contact: value for coefficient d_contact
1959          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1960                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1961          @keyword y_contact: value for coefficient y_contact
1962          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1963                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1964          @keyword r: values prescribed to the solution at the locations of constraints
1965          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1966                   depending of reduced order is used for the solution.
1967          @keyword q: mask for location of constraints
1968          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1969                   depending of reduced order is used for the representation of the equation.
1970          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1971    
1972          """
1973          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1974          super(AdvectivePDE, self).setValue(**coefficients)
1975    
1976       def ELMAN_RAMAGE(self,P):
1977         """
1978         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1979         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1980              - M{S{xi}(P)=0} for M{P<1}
1981              - M{S{xi}(P)=(1-1/P)/2} otherwise
1982    
1983         @param P: Preclet number
1984         @type P: L{Scalar<escript.Scalar>}
1985         @return: up-wind weightimg factor
1986         @rtype: L{Scalar<escript.Scalar>}
1987         """
1988         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
1989    
1990       def SIMPLIFIED_BROOK_HUGHES(self,P):
1991         """
1992         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1993         The original methods is
1994    
1995         M{S{xi}(P)=coth(P)-1/P}
1996    
1997         As the evaluation of M{coth} is expensive we are using the approximation:
1998    
1999             - M{S{xi}(P)=P/3} where M{P<3}
2000             - M{S{xi}(P)=1/2} otherwise
2001    
2002         @param P: Preclet number
2003         @type P: L{Scalar<escript.Scalar>}
2004         @return: up-wind weightimg factor
2005         @rtype: L{Scalar<escript.Scalar>}
2006         """
2007         c=util.whereNegative(P-3.)
2008         return P/6.*c+1./2.*(1.-c)
2009    
2010       def HALF(self,P):
2011         """
2012         Predefined function to set value M{1/2} for M{S{xi}}
2013    
2014         @param P: Preclet number
2015         @type P: L{Scalar<escript.Scalar>}
2016         @return: up-wind weightimg factor
2017         @rtype: L{Scalar<escript.Scalar>}
2018         """
2019         return escript.Scalar(0.5,P.getFunctionSpace())
2020    
2021       def __calculateXi(self,peclet_factor,flux,h):
2022           flux=util.Lsup(flux)
2023           if flux_max>0.:
2024              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2025         else:         else:
2026            return 0.            return 0.
2027    
2028     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._LinearPDE__setValue(**args)  
             
    def getXi(self):  
2029        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2030           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2031           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1096  class AdvectivePDE(LinearPDE): Line 2034  class AdvectivePDE(LinearPDE):
2034           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2035           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2036              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
2037                  Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))                  flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2038                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2039                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2040                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2041                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2042                              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
2043                          # flux=C-util.reorderComponents(B,[0,2,1])
2044                     else:                     else:
2045                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2046                           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
2047                          # flux=C-B
2048                  else:                  else:
2049                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2050                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2051                           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
2052                          # flux=C-util.reorderComponents(B,[1,0])
2053                     else:                     else:
2054                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2055                  length_of_Z=util.sqrt(Z2)                        #flux=C-B
2056                    length_of_flux=util.sqrt(flux2)
2057              elif C.isEmpty():              elif C.isEmpty():
2058                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2059                  #flux=B
2060              else:              else:
2061                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2062                  #flux=C
2063    
2064              Z_max=util.Lsup(length_of_Z)              #length_of_flux=util.length(flux)
2065              if Z_max>0.:              flux_max=util.Lsup(length_of_flux)
2066                if flux_max>0.:
2067                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2068                 length_of_A=util.length(A)                 length_of_A=util.length(A)
2069                 A_max=util.Lsup(length_of_A)                 A_max=util.Lsup(length_of_A)
2070                 if A_max>0:                 if A_max>0:
2071                      inv_A=1./(length_of_A+A_max*self.TOL)                      inv_A=1./(length_of_A+A_max*self.__TOL)
2072                 else:                 else:
2073                      inv_A=1./self.TOL                      inv_A=1./self.__TOL
2074                 peclet_number=length_of_Z*h/2*inv_A                 peclet_number=length_of_flux*h/2*inv_A
2075                 xi=self.__xi(peclet_number)                 xi=self.__xi(peclet_number)
2076                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2077                 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))
2078        return self.__Xi        return self.__Xi
         
2079    
2080     def getCoefficientOfPDE(self,name):  
2081       def getCoefficientOfGeneralPDE(self,name):
2082       """       """
2083       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2084    
2085       @param name:       @param name: name of the coefficient requested.
2086         @type name: C{string}
2087         @return: the value of the coefficient name
2088         @rtype: L{Data<escript.Data>}
2089         @raise IllegalCoefficient: if name is not one of coefficients
2090                      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}.
2091         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2092       """       """
2093       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2094            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."
2095    
2096       if name == "A" :       if name == "A" :
2097           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2098           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2099           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2100           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2101              Aout=A              Aout=A
2102           else:           else:
2103              if A.isEmpty():              if A.isEmpty():
2104                 Aout=self.createNewCoefficient("A")                 Aout=self.createNewCoefficient("A")
2105              else:              else:
2106                 Aout=A[:]                 Aout=A[:]
2107              Xi=self.getXi()              Xi=self.__getXi()
2108              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2109                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2110                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2111                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2112                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2113                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2114                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2115                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2116                                 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])
2117                              elif C.isEmpty():                              elif C.isEmpty():
2118                                 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]
2119                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2120                              else:                              else:
2121                                 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]
2122                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2123              else:              else:
2124                  for j in range(self.getDim()):                  for j in range(self.getDim()):
2125                     for l in range(self.getDim()):                     for l in range(self.getDim()):
# Line 1173  class AdvectivePDE(LinearPDE): Line 2129  class AdvectivePDE(LinearPDE):
2129                            Aout[j,l]+=Xi*B[j]*B[l]                            Aout[j,l]+=Xi*B[j]*B[l]
2130                        else:                        else:
2131                            Aout[j,l]+=Xi*C[j]*C[l]                            Aout[j,l]+=Xi*C[j]*C[l]
2132                     # if not C.isEmpty() and not B.isEmpty():
2133                     #    tmp=C-B
2134                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2135                     # elif C.isEmpty():
2136                     #    Aout=Aout+Xi*util.outer(B,B)
2137                     # else:
2138                     # Aout=Aout+Xi*util.outer(C,C)
2139           return Aout           return Aout
2140       elif name == "B" :       elif name == "B" :
2141           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2142           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2143           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2144           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2145              Bout=B              Bout=B
2146           else:           else:
2147              Xi=self.getXi()              Xi=self.__getXi()
2148              if B.isEmpty():              if B.isEmpty():
2149                  Bout=self.createNewCoefficient("B")                  Bout=self.createNewCoefficient("B")
2150              else:              else:
2151                  Bout=B[:]                  Bout=B[:]
2152              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2153                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2154                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2155                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2156                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2157                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2158                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2159                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2160              else:              else:
2161                 tmp=Xi*D                 tmp=Xi*D
2162                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2163                   # Bout=Bout+Xi*D*C
2164           return Bout           return Bout
2165       elif name == "C" :       elif name == "C" :
2166           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2167           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2168           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2169           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2170              Cout=C              Cout=C
2171           else:           else:
2172              Xi=self.getXi()              Xi=self.__getXi()
2173              if C.isEmpty():              if C.isEmpty():
2174                  Cout=self.createNewCoefficient("C")                  Cout=self.createNewCoefficient("C")
2175              else:              else:
2176                  Cout=C[:]                  Cout=C[:]
# Line 1216  class AdvectivePDE(LinearPDE): Line 2181  class AdvectivePDE(LinearPDE):
2181                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2182                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2183                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2184                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2185              else:              else:
2186                 tmp=Xi*D                 tmp=Xi*D
2187                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2188                   # Cout=Cout+tmp*D*B
2189           return Cout           return Cout
2190       elif name == "D" :       elif name == "D" :
2191           return self.getCoefficient("D")           return self.getCoefficient("D")
2192       elif name == "X" :       elif name == "X" :
2193           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2194           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2195           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1234  class AdvectivePDE(LinearPDE): Line 2201  class AdvectivePDE(LinearPDE):
2201                  Xout=self.createNewCoefficient("X")                  Xout=self.createNewCoefficient("X")
2202              else:              else:
2203                  Xout=X[:]                  Xout=X[:]
2204              Xi=self.getXi()              Xi=self.__getXi()
2205              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2206                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2207                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2208                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2209                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2210                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2211                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2212                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2213                            elif C.isEmpty():                            elif C.isEmpty():
2214                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2215                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2216                            else:                            else:
2217                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2218                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2219              else:              else:
2220                   tmp=Xi*Y                   tmp=Xi*Y
2221                   for j in range(self.getDim()):                   for j in range(self.getDim()):
2222                      if not C.isEmpty() and not B.isEmpty():                      if not C.isEmpty() and not B.isEmpty():
2223                         Xout[j]+=tmp*(C[j]-B[j])                         Xout[j]+=tmp*(C[j]-B[j])
2224                           # Xout=Xout+Xi*Y*(C-B)
2225                      elif C.isEmpty():                      elif C.isEmpty():
2226                         Xout[j]-=tmp*B[j]                         Xout[j]-=tmp*B[j]
2227                           # Xout=Xout-Xi*Y*B
2228                      else:                      else:
2229                         Xout[j]+=tmp*C[j]                         Xout[j]+=tmp*C[j]
2230                           # Xout=Xout+Xi*Y*C
2231           return Xout           return Xout
2232       elif name == "Y" :       elif name == "Y" :
2233           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2234       elif name == "d" :       elif name == "d" :
2235           return self.getCoefficient("d")           return self.getCoefficient("d")
2236       elif name == "y" :       elif name == "y" :
2237           return self.getCoefficient("y")           return self.getCoefficient("y")
2238       elif name == "d_contact" :       elif name == "d_contact" :
2239           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2240       elif name == "y_contact" :       elif name == "y_contact" :
2241           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2242       elif name == "r" :       elif name == "r" :
2243           return self.getCoefficient("r")           return self.getCoefficient("r")
2244       elif name == "q" :       elif name == "q" :
          return self.getCoefficient("q")  
      else:  
          raise SystemError,"unknown PDE coefficient %s",name  
   
   
 class Poisson(LinearPDE):  
    """  
    Class to define a Poisson equation problem:  
   
    class to define a linear PDE of the form  
    \f[  
    -u_{,jj} = f  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
   
    and constraints:  
   
    \f[  
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
   
    def __init__(self,domain,f=escript.Data(),q=escript.Data()):  
        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)  
   
    def setValue(self,f=escript.Data(),q=escript.Data()):  
        """set value of PDE parameters f and q"""  
        self._LinearPDE__setValue(f=f,q=q)  
   
    def getCoefficientOfPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name:  
      """  
      if name == "A" :  
          return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
      elif name == "B" :  
          return escript.Data()  
      elif name == "C" :  
          return escript.Data()  
      elif name == "D" :  
          return escript.Data()  
      elif name == "X" :  
          return escript.Data()  
      elif name == "Y" :  
          return self.getCoefficient("f")  
      elif name == "d" :  
          return escript.Data()  
      elif name == "y" :  
          return escript.Data()  
      elif name == "d_contact" :  
          return escript.Data()  
      elif name == "y_contact" :  
          return escript.Data()  
      elif name == "r" :  
          return escript.Data()  
      elif name == "q" :  
2245           return self.getCoefficient("q")           return self.getCoefficient("q")
2246       else:       else:
2247           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
 class LameEquation(LinearPDE):  
    """  
    Class to define a Lame equation problem:  
   
    class to define a linear PDE of the form  
    \f[  
    -(\mu (u_{i,j}+u_{j,i}))_{,j} - \lambda u_{j,ji}} = F_i -\sigma_{ij,j}  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j(\mu (u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\lambda u_{j,j} = f_i  
    \f]  
   
    and constraints:  
   
    \f[  
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
    """  
2248    
    def __init__(self,domain,f=escript.Data(),q=escript.Data()):  
        LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim())  
        self.COEFFICIENTS={  
        "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),  
        "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),  
        "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
        "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),  
        "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
   
    def setValue(self,lame_lambda=escript.Data(),lame_mu=escript.Data(),F=escript.Data(),sigma=escript.Data(),f=escript.Data(),r=escript.Data(),q=escript.Data()):  
        """set value of PDE parameters"""  
        self._LinearPDE__setValue(lame_lambda=lame_lambda, \  
                                  lame_mu=lame_mu, \  
                                  F=F, \  
                                  sigma=sigma, \  
                                  f=f, \  
                                  r=r, \  
                                  q=q)  
    def getCoefficientOfPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name:  
      """  
      if name == "A" :  
          out =self.createNewCoefficientOfPDE("A")  
          for i in range(self.getDim()):  
            for j in range(self.getDim()):  
              out[i,i,j,j] += self.getCoefficient("lame_lambda")  
              out[i,j,j,i] += self.getCoefficient("lame_mu")  
              out[i,j,i,j] += self.getCoefficient("lame_mu")  
          return out  
      elif name == "B" :  
          return escript.Data()  
      elif name == "C" :  
          return escript.Data()  
      elif name == "D" :  
          return escript.Data()  
      elif name == "X" :  
          return self.getCoefficient("sigma")  
      elif name == "Y" :  
          return self.getCoefficient("F")  
      elif name == "d" :  
          return escript.Data()  
      elif name == "y" :  
          return self.getCoefficient("f")  
      elif name == "d_contact" :  
          return escript.Data()  
      elif name == "y_contact" :  
          return escript.Data()  
      elif name == "r" :  
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
          raise SystemError,"unknown PDE coefficient %s",name  
2249    
2250  # $Log$  # $Log$
2251    # Revision 1.14  2005/09/22 01:54:57  jgs
2252    # Merge of development branch dev-02 back to main trunk on 2005-09-22
2253    #
2254    # Revision 1.13  2005/09/15 03:44:19  jgs
2255    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2256    #
2257    # Revision 1.12  2005/09/01 03:31:28  jgs
2258    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2259    #
2260    # Revision 1.11  2005/08/23 01:24:28  jgs
2261    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2262    #
2263  # Revision 1.10  2005/08/12 01:45:36  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2264  # erge of development branch dev-02 back to main trunk on 2005-08-12  # erge of development branch dev-02 back to main trunk on 2005-08-12
2265  #  #
2266    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2267    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2268    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2269    # modified to instead use portable/cooperative "super" calls to extend base
2270    # class methods.
2271    #
2272    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2273    # Removed redundant if-loop.
2274    #
2275    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2276    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2277    #
2278    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2279    # the solver from finley are put into the standalone package paso now
2280    #
2281    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2282    # in the case of lumping no new system is allocated if the constraint is changed.
2283    #
2284    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2285    # test for Lumping added
2286    #
2287    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2288    # bug in format fixed.
2289    #
2290    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2291    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2292    #
2293    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2294    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2295    #
2296    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2297    # gneric unit testing for linearPDE
2298    #
2299    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2300    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2301    #
2302    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2303    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2304    #
2305    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2306    # epydoc mark up partially fixed
2307    #
2308    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2309    # some problems with LinearPDEs fixed.
2310    #
2311    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2312    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2313    #
2314    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2315    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2316    #
2317  # Revision 1.9.2.1  2005/07/29 07:10:27  gross  # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2318  # new functions in util and a new pde type in linearPDEs  # new functions in util and a new pde type in linearPDEs
2319  #  #
# Line 1545  class LameEquation(LinearPDE): Line 2432  class LameEquation(LinearPDE):
2432  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2433  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2434  #  #
 #  

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