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trunk/esys2/escript/py_src/linearPDEs.py revision 122 by jgs, Thu Jun 9 05:38:05 2005 UTC trunk/escript/py_src/linearPDEs.py revision 410 by gross, Fri Dec 23 01:27:38 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}, L{AdvectionDiffusion}
21    classs which are also derived form the L{LinearPDE} class should be used
22    to define of solve these sepecial PDEs.
23    
24    @var __author__: name of author
25    @var __licence__: licence agreement
26    @var __url__: url entry point on documentation
27    @var __version__: version
28    @var __date__: date of the version
29  """  """
30    
31  import escript  import escript
32  import util  import util
33  import numarray  import numarray
34    
35    __author__="Lutz Gross, l.gross@uq.edu.au"
36    __licence__="contact: esys@access.uq.edu.au"
37    __url__="http://www.iservo.edu.au/esys/escript"
38    __version__="$Revision$"
39    __date__="$Date$"
40    
 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       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       __PRECONDITIONER_KEY="preconditioner"
453    
454    
455       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
456         """
457         initializes a new linear PDE
458    
459         @param domain: domain of the PDE
460         @type domain: L{Domain<escript.Domain>}
461         @param numEquations: number of equations. If numEquations==None the number of equations
462                              is exracted from the PDE coefficients.
463         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
464                              is exracted from the PDE coefficients.
465         @param debug: if True debug informations are printed.
466    
467         """
468         super(LinearPDE, self).__init__()
469         #
470         #   the coefficients of the general PDE:
471         #
472         self.__COEFFICIENTS_OF_GENEARL_PDE={
473           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
474           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
475           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
476           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
477           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
478           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
479           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
480           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
481           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
482           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
484           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
485    
486         # COEFFICIENTS can be overwritten by subclasses:
487         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
488         self.__altered_coefficients=False
489       # initialize attributes       # initialize attributes
490       self.__debug=None       self.__debug=debug
491       self.__domain=domain       self.__domain=domain
492       self.__numEquations=numEquations       self.__numEquations=numEquations
493       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
494       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  
495    
496       # set some default values:       # set some default values:
497       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
498       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
499       self.__tolerance=1.e-8       self.__tolerance=1.e-8
500       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
501       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
502         self.__preconditioner=self.DEFAULT
503         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
504       self.__sym=False       self.__sym=False
      self.__lumping=False  
505    
506     def createCoefficient(self, name):       self.resetCoefficients()
507         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
508       # =============================================================================
509       #    general stuff:
510       # =============================================================================
511       def __str__(self):
512         """
513         returns string representation of the PDE
514    
515         @return: a simple representation of the PDE
516         @rtype: C{str}
517         """
518         return "<LinearPDE %d>"%id(self)
519       # =============================================================================
520       #    debug :
521       # =============================================================================
522       def setDebugOn(self):
523       """       """
524       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
525       """       """
526       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
527    
528     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
529       """       """
530       return the value of the parameter name       switches off debugging
531         """
532         self.__debug=None
533    
534       @param name:     def trace(self,text):
535         """
536         print the text message if debugging is swiched on.
537         @param text: message
538         @type text: C{string}
539       """       """
540       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
541    
542     def getCoefficientOfPDE(self,name):     # =============================================================================
543       # some service functions:
544       # =============================================================================
545       def getDomain(self):
546       """       """
547       return the value of the coefficient name of the general PDE.       returns the domain of the PDE
      This method is called by the assembling routine it can be  
      overwritten to map coefficients of a particualr PDE to the general PDE.  
548    
549       @param name:       @return: the domain of the PDE
550         @rtype: L{Domain<escript.Domain>}
551       """       """
552       return self.getCoefficient(name)       return self.__domain
553    
554     def hasCoefficient(self,name):     def getDim(self):
555        """       """
556        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
557    
558        @param name:       @return: the spatial dimension of the PDE domain
559        """       @rtype: C{int}
560        return self.COEFFICIENTS.has_key(name)       """
561         return self.getDomain().getDim()
562    
563     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
564       """       """
565       return true if the test functions should use reduced order       returns the number of equations
566    
567         @return: the number of equations
568         @rtype: C{int}
569         @raise UndefinedPDEError: if the number of equations is not be specified yet.
570       """       """
571       return self.__row_function_space       if self.__numEquations==None:
572             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
573         else:
574             return self.__numEquations
575    
576     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
577       """       """
578       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
579    
580         @return: the number of unknowns
581         @rtype: C{int}
582         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
583       """       """
584       return self.__column_function_space       if self.__numSolutions==None:
585            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
586         else:
587            return self.__numSolutions
588    
589     def setValue(self,**coefficients):     def reduceEquationOrder(self):
590        """       """
591        sets new values to coefficients       return status for order reduction for equation
592    
593        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
594        """       @rtype: L{bool}
595        self.__setValue(**coefficients)       """
596               return self.__reduce_equation_order
597    
598     def cleanCoefficients(self):     def reduceSolutionOrder(self):
599       """       """
600       resets all coefficients to default values.       return status for order reduction for the solution
601    
602         @return: return True is reduced interpolation order is used for the represenation of the solution
603         @rtype: L{bool}
604       """       """
605       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
606    
607     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
608       """       """
609       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
610    
611         @return: representation space of equation
612         @rtype: L{FunctionSpace<escript.FunctionSpace>}
613       """       """
614       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
615                   return escript.ReducedSolution(self.getDomain())
616         else:
617             return escript.Solution(self.getDomain())
618    
619     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
620       """       """
621       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
622    
623       @param name:       @return: representation space of solution
624         @rtype: L{FunctionSpace<escript.FunctionSpace>}
625       """       """
626       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
627          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
628       else:       else:
629          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
630    
631     def getFunctionSpaceForCoefficient(self,name):  
632       def getOperator(self):
633       """       """
634       return the atoms of the coefficient name       provides access to the operator of the PDE
635    
636       @param name:       @return: the operator of the PDE
637         @rtype: L{Operator<escript.Operator>}
638       """       """
639       if self.hasCoefficient(name):       m=self.getSystem()[0]
640          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
641             return self.copyConstraint(1./m)
642       else:       else:
643          raise ValueError,"Solution coefficient %s requested"%name           return m
644    
645     def alteredCoefficient(self,name):     def getRightHandSide(self):
646       """       """
647       announce that coefficient name has been changed       provides access to the right hand side of the PDE
648         @return: the right hand side of the PDE
649         @rtype: L{Data<escript.Data>}
650         """
651         r=self.getSystem()[1]
652         if self.isUsingLumping():
653             return self.copyConstraint(r)
654         else:
655             return r
656    
657       @param name:     def applyOperator(self,u=None):
658       """       """
659       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
660          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
661          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
662                   the current solution is used.
663         @type u: L{Data<escript.Data>} or None
664         @return: image of u
665         @rtype: L{Data<escript.Data>}
666         """
667         if u==None:
668              return self.getOperator()*self.getSolution()
669       else:       else:
670          raise ValueError,"unknown coefficient %s requested"%name          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
671    
672     # ===== debug ==============================================================     def getResidual(self,u=None):
673     def setDebugOn(self):       """
674         """       return the residual of u or the current solution if u is not present.
675    
676         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
677                   the current solution is used.
678         @type u: L{Data<escript.Data>} or None
679         @return: residual of u
680         @rtype: L{Data<escript.Data>}
681         """
682         return self.applyOperator(u)-self.getRightHandSide()
683    
684       def checkSymmetry(self,verbose=True):
685          """
686          test the PDE for symmetry.
687    
688          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
689          @type verbose: C{bool}
690          @return:  True if the PDE is symmetric.
691          @rtype: L{Data<escript.Data>}
692          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
693          """
694          verbose=verbose or self.__debug
695          out=True
696          if self.getNumSolutions()!=self.getNumEquations():
697             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
698             out=False
699          else:
700             A=self.getCoefficientOfGeneralPDE("A")
701             if not A.isEmpty():
702                tol=util.Lsup(A)*self.__TOL
703                if self.getNumSolutions()>1:
704                   for i in range(self.getNumEquations()):
705                      for j in range(self.getDim()):
706                         for k in range(self.getNumSolutions()):
707                            for l in range(self.getDim()):
708                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
709                                   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)
710                                   out=False
711                else:
712                   for j in range(self.getDim()):
713                      for l in range(self.getDim()):
714                         if util.Lsup(A[j,l]-A[l,j])>tol:
715                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
716                            out=False
717             B=self.getCoefficientOfGeneralPDE("B")
718             C=self.getCoefficientOfGeneralPDE("C")
719             if B.isEmpty() and not C.isEmpty():
720                if verbose: print "non-symmetric PDE because B is not present but C is"
721                out=False
722             elif not B.isEmpty() and C.isEmpty():
723                if verbose: print "non-symmetric PDE because C is not present but B is"
724                out=False
725             elif not B.isEmpty() and not C.isEmpty():
726                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
727                if self.getNumSolutions()>1:
728                   for i in range(self.getNumEquations()):
729                       for j in range(self.getDim()):
730                          for k in range(self.getNumSolutions()):
731                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
732                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
733                                  out=False
734                else:
735                   for j in range(self.getDim()):
736                      if util.Lsup(B[j]-C[j])>tol:
737                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
738                         out=False
739             if self.getNumSolutions()>1:
740               D=self.getCoefficientOfGeneralPDE("D")
741               if not D.isEmpty():
742                 tol=util.Lsup(D)*self.__TOL
743                 for i in range(self.getNumEquations()):
744                    for k in range(self.getNumSolutions()):
745                      if util.Lsup(D[i,k]-D[k,i])>tol:
746                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
747                          out=False
748               d=self.getCoefficientOfGeneralPDE("d")
749               if not d.isEmpty():
750                 tol=util.Lsup(d)*self.__TOL
751                 for i in range(self.getNumEquations()):
752                    for k in range(self.getNumSolutions()):
753                      if util.Lsup(d[i,k]-d[k,i])>tol:
754                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
755                          out=False
756               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
757               if not d_contact.isEmpty():
758                 tol=util.Lsup(d_contact)*self.__TOL
759                 for i in range(self.getNumEquations()):
760                    for k in range(self.getNumSolutions()):
761                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
762                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
763                          out=False
764          return out
765    
766       def getSolution(self,**options):
767         """         """
768         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
769    
770     def setDebugOff(self):         @return: the solution
771           @rtype: L{Data<escript.Data>}
772           @param options: solver options
773           @keyword verbose: True to get some information during PDE solution
774           @type verbose: C{bool}
775           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
776                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
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           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()[0]
790                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
791                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
792                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
793                 self.trace("PDE is resolved.")
794                 self.trace("solver options: %s"%str(options))
795                 self.__solution=mat.solve(f,options)
796              self.__solution_isValid=True
797           return self.__solution
798    
799       def getFlux(self,u=None):
800         """
801         returns the flux M{J} for a given M{u}
802    
803         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
804    
805         or
806    
807         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
808    
809         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
810         @type u: L{Data<escript.Data>} or None
811         @return: flux
812         @rtype: L{Data<escript.Data>}
813         """
814         if u==None: u=self.getSolution()
815         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
816       # =============================================================================
817       #   solver settings:
818       # =============================================================================
819       def setSolverMethod(self,solver=None,preconditioner=None):
820         """         """
821         self.__debug=None         sets a new solver
822    
823           @param solver: sets a new solver method.
824           @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}.
825           @param preconditioner: sets a new solver method.
826           @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}
827           """
828           if solver==None: solve=self.DEFAULT
829           if preconditioner==None: preconditioner=self.DEFAULT
830           if not (solver,preconditioner)==self.getSolverMethod():
831               self.__solver_method=solver
832               self.__preconditioner=preconditioner
833               self.__checkMatrixType()
834               self.trace("New solver is %s"%self.getSolverMethodName())
835    
836     def debug(self):     def getSolverMethodName(self):
837         """         """
838         returns true if the PDE is in the debug mode         returns the name of the solver currently used
839    
840           @return: the name of the solver currently used.
841           @rtype: C{string}
842         """         """
        return self.__debug  
843    
844     #===== Lumping ===========================         m=self.getSolverMethod()
845     def setLumpingOn(self):         p=self.getSolverPackage()
846        """         if m[0]==self.DEFAULT: method="DEFAULT"
847        indicates to use matrix lumping         elif m[0]==self.DIRECT: method= "DIRECT"
848        """         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
849        if not self.isUsingLumping():         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
850           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.PCG: method= "PCG"
851           self.__rebuildOperator()         elif m[0]==self.CR: method= "CR"
852           self.__lumping=True         elif m[0]==self.CGS: method= "CGS"
853           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
854           elif m[0]==self.SSOR: method= "SSOR"
855           elif m[0]==self.GMRES: method= "GMRES"
856           elif m[0]==self.PRES20: method= "PRES20"
857           elif m[0]==self.LUMPING: method= "LUMPING"
858           else : method="unknown"
859           if m[1]==self.DEFAULT: method+="DEFAULT"
860           elif m[1]==self.JACOBI: method+= "JACOBI"
861           elif m[1]==self.ILU0: method+= "ILU0"
862           elif m[1]==self.ILUT: method+= "ILUT"
863           elif m[1]==self.SSOR: method+= "SSOR"
864           else : method+="unknown"
865           if p==self.DEFAULT: package="DEFAULT"
866           elif p==self.PASO: package= "PASO"
867           elif p==self.MKL: package= "MKL"
868           elif p==self.SCSL: package= "SCSL"
869           elif p==self.UMFPACK: package= "UMFPACK"
870           else : method="unknown"
871           return "%s solver of %s package"%(method,package)
872    
    def setLumpingOff(self):  
       """  
       switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
873    
874     def setLumping(self,flag=False):     def getSolverMethod(self):
875        """         """
876        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
877    
878     def isUsingLumping(self):         @return: the solver method currently be used.
879        """         @rtype: C{int}
880                 """
881        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
882    
883     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
884         """         """
885         sets a new solver         sets a new solver package
886    
887           @param solver: sets a new solver method.
888           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
889         """         """
890         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
891           if not package==self.getSolverPackage():
892             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
893             self.__checkMatrixType()             self.__checkMatrixType()
894               self.trace("New solver is %s"%self.getSolverMethodName())
895    
896     def getSolverMethod(self):     def getSolverPackage(self):
897         """         """
898         returns the solver method         returns the package of the solver
899    
900           @return: the solver package currently being used.
901           @rtype: C{int}
902         """         """
903         return self.__solver_method         return self.__solver_package
904    
905       def isUsingLumping(self):
906          """
907          checks if matrix lumping is used a solver method
908    
909          @return: True is lumping is currently used a solver method.
910          @rtype: C{bool}
911          """
912          return self.getSolverMethod()[0]==self.LUMPING
913    
    #============ tolerance business =========================================================  
914     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
915         """         """
916         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
917    
918           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
919    
920           defines the stopping criterion.
921    
922           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
923                       the system will be resolved.
924           @type tol: positive C{float}
925           @raise ValueException: if tolerance is not positive.
926         """         """
927         if not tol>0:         if not tol>0:
928             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
929         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
930         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
931         self.__tolerance=tol         self.__tolerance=tol
932         return         return
933    
934     def getTolerance(self):     def getTolerance(self):
935         """         """
936         returns the tolerance set for the solution         returns the tolerance set for the solution
937    
938           @return: tolerance currently used.
939           @rtype: C{float}
940         """         """
941         return self.__tolerance         return self.__tolerance
942    
943     #===== symmetry  flag ==========================     # =============================================================================
944       #    symmetry  flag:
945       # =============================================================================
946     def isSymmetric(self):     def isSymmetric(self):
947        """        """
948        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
949    
950          @return: True is a symmetric PDE is indicated, otherwise False is returned
951          @rtype: C{bool}
952        """        """
953        return self.__sym        return self.__sym
954    
955     def setSymmetryOn(self):     def setSymmetryOn(self):
956        """        """
957        sets the symmetry flag to true        sets the symmetry flag.
958        """        """
959        if not self.isSymmetric():        if not self.isSymmetric():
960           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
961           self.__sym=True           self.__sym=True
962           self.__checkMatrixType()           self.__checkMatrixType()
963    
964     def setSymmetryOff(self):     def setSymmetryOff(self):
965        """        """
966        sets the symmetry flag to false        removes the symmetry flag.
967        """        """
968        if self.isSymmetric():        if self.isSymmetric():
969           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
970           self.__sym=False           self.__sym=False
971           self.__checkMatrixType()           self.__checkMatrixType()
972    
973     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
974       """        """
975       sets the symmetry flag to flag        sets the symmetry flag to flag
976    
977       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
978       """        @type flag: C{bool}
979       if flag:        """
980          self.setSymmetryOn()        if flag:
981       else:           self.setSymmetryOn()
982          self.setSymmetryOff()        else:
983             self.setSymmetryOff()
984    
985     #===== order reduction ==========================     # =============================================================================
986       # function space handling for the equation as well as the solution
987       # =============================================================================
988     def setReducedOrderOn(self):     def setReducedOrderOn(self):
989       """       """
990       switches to on reduced order       switches on reduced order for solution and equation representation
991    
992         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
993       """       """
994       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
995       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
996    
997     def setReducedOrderOff(self):     def setReducedOrderOff(self):
998       """       """
999       switches to full order       switches off reduced order for solution and equation representation
1000    
1001         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1002       """       """
1003       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1004       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1005    
1006     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1007       """       """
1008       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1009         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1010       @param flag:                    if flag is not present order reduction is switched off
1011         @type flag: C{bool}
1012         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1013       """       """
1014       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1015       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1016    
1017     #===== order reduction solution ==========================  
1018     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1019       """       """
1020       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1021    
1022         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1023       """       """
1024       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1025       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1026           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1027           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1028           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1029             self.__resetSystem()
1030    
1031     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1032       """       """
1033       switches to full order to interpolate solution       switches off reduced order for solution representation
1034    
1035         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1036       """       """
1037       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1038       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1039           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1040           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1041           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1042             self.__resetSystem()
1043    
1044     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1045       """       """
1046       sets order for test functions according to flag       sets order for test functions according to flag
1047    
1048       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1049                      if flag is not present order reduction is switched off
1050         @type flag: C{bool}
1051         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1052       """       """
1053       if flag:       if flag:
1054          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1055       else:       else:
1056          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1057                                                                                                                                                              
    #===== order reduction equation ==========================  
1058     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1059       """       """
1060       switches to reduced order for test functions       switches on reduced order for equation representation
1061    
1062         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1063       """       """
1064       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1065       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1066           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1067           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1068           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1069             self.__resetSystem()
1070    
1071     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1072       """       """
1073       switches to full order for test functions       switches off reduced order for equation representation
1074    
1075         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1076       """       """
1077       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1078       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1079           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1080           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1081           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1082             self.__resetSystem()
1083    
1084     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1085       """       """
1086       sets order for test functions according to flag       sets order for test functions according to flag
1087    
1088       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1089                      if flag is not present order reduction is switched off
1090         @type flag: C{bool}
1091         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1092       """       """
1093       if flag:       if flag:
1094          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1095       else:       else:
1096          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1097                                                                                                                                                              
1098     # ==== initialization =====================================================================     # =============================================================================
1099       # private method:
1100       # =============================================================================
1101       def __checkMatrixType(self):
1102         """
1103         reassess the matrix type and, if a new matrix is needed, resets the system.
1104         """
1105         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1106         if not new_matrix_type==self.__matrix_type:
1107             self.trace("Matrix type is now %d."%new_matrix_type)
1108             self.__matrix_type=new_matrix_type
1109             self.__resetSystem()
1110       #
1111       #   rebuild switches :
1112       #
1113       def __invalidateSolution(self):
1114           """
1115           indicates the PDE has to be resolved if the solution is requested
1116           """
1117           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1118           self.__solution_isValid=False
1119    
1120       def __invalidateOperator(self):
1121           """
1122           indicates the operator has to be rebuilt next time it is used
1123           """
1124           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1125           self.__invalidateSolution()
1126           self.__operator_is_Valid=False
1127    
1128       def __invalidateRightHandSide(self):
1129           """
1130           indicates the right hand side has to be rebuild next time it is used
1131           """
1132           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1133           self.__invalidateSolution()
1134           self.__righthandside_isValid=False
1135    
1136       def __invalidateSystem(self):
1137           """
1138           annonced that everthing has to be rebuild:
1139           """
1140           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1141           self.__invalidateSolution()
1142           self.__invalidateOperator()
1143           self.__invalidateRightHandSide()
1144    
1145       def __resetSystem(self):
1146           """
1147           annonced that everthing has to be rebuild:
1148           """
1149           self.trace("New System is built from scratch.")
1150           self.__operator=escript.Operator()
1151           self.__operator_is_Valid=False
1152           self.__righthandside=escript.Data()
1153           self.__righthandside_isValid=False
1154           self.__solution=escript.Data()
1155           self.__solution_isValid=False
1156       #
1157       #    system initialization:
1158       #
1159     def __getNewOperator(self):     def __getNewOperator(self):
1160         """         """
1161           returns an instance of a new operator
1162         """         """
1163           self.trace("New operator is allocated.")
1164         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1165                             self.getNumEquations(), \                             self.getNumEquations(), \
1166                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1168  class LinearPDE:
1168                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1169                             self.__matrix_type)                             self.__matrix_type)
1170    
1171     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1172         """         """
1173           returns an instance of a new right hand side
1174         """         """
1175         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1176         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1177             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1178         else:         else:
1179             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1180    
1181     def __getNewSolution(self):     def __getNewSolution(self):
1182         """         """
1183           returns an instance of a new solution
1184         """         """
1185         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1186         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1187             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1188         else:         else:
1189             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1190    
1191       def __makeFreshSolution(self):
1192           """
1193           makes sure that the solution is instantiated and returns it initialized by zeros
1194           """
1195           if self.__solution.isEmpty():
1196               self.__solution=self.__getNewSolution()
1197           else:
1198               self.__solution*=0
1199               self.trace("Solution is reset to zero.")
1200           return self.__solution
1201    
1202       def __makeFreshRightHandSide(self):
1203           """
1204           makes sure that the right hand side is instantiated and returns it initialized by zeros
1205           """
1206           if self.__righthandside.isEmpty():
1207               self.__righthandside=self.__getNewRightHandSide()
1208           else:
1209               self.__righthandside*=0
1210               self.trace("Right hand side is reset to zero.")
1211           return self.__righthandside
1212    
1213     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1214         """         """
1215           makes sure that the operator is instantiated and returns it initialized by zeros
1216         """         """
1217         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1218             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1219         else:         else:
1220             self.__operator.setValue(0.)             self.__operator.resetValues()
1221             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1222         return self.__operator         return self.__operator
1223    
1224     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1225     def getDomain(self):         """
1226           applies the constraints defined by q and r to the system
1227           """
1228           if not self.isUsingLumping():
1229              q=self.getCoefficientOfGeneralPDE("q")
1230              r=self.getCoefficientOfGeneralPDE("r")
1231              if not q.isEmpty() and not self.__operator.isEmpty():
1232                 # q is the row and column mask to indicate where constraints are set:
1233                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1234                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1235                 u=self.__getNewSolution()
1236                 if r.isEmpty():
1237                    r_s=self.__getNewSolution()
1238                 else:
1239                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1240                 u.copyWithMask(r_s,col_q)
1241                 if not self.__righthandside.isEmpty():
1242                    self.__righthandside-=self.__operator*u
1243                    self.__righthandside=self.copyConstraint(self.__righthandside)
1244                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1245       # =============================================================================
1246       # function giving access to coefficients of the general PDE:
1247       # =============================================================================
1248       def getCoefficientOfGeneralPDE(self,name):
1249         """
1250         return the value of the coefficient name of the general PDE.
1251    
1252         @note: This method is called by the assembling routine it can be overwritten
1253               to map coefficients of a particular PDE to the general PDE.
1254         @param name: name of the coefficient requested.
1255         @type name: C{string}
1256         @return: the value of the coefficient  name
1257         @rtype: L{Data<escript.Data>}
1258         @raise IllegalCoefficient: if name is not one of coefficients
1259                      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}.
1260       """       """
1261       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1262            return self.getCoefficient(name)
1263         else:
1264            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1265    
1266       def hasCoefficientOfGeneralPDE(self,name):
1267       """       """
1268       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1269    
1270         @param name: name of the coefficient enquired.
1271         @type name: C{string}
1272         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1273         @rtype: C{bool}
1274    
    def getDim(self):  
1275       """       """
1276       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1277    
1278       def createCoefficientOfGeneralPDE(self,name):
1279       """       """
1280       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1281    
1282     def getNumEquations(self):       @param name: name of the coefficient requested.
1283         @type name: C{string}
1284         @return: a coefficient name initialized to 0.
1285         @rtype: L{Data<escript.Data>}
1286         @raise IllegalCoefficient: if name is not one of coefficients
1287                      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}.
1288       """       """
1289       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1290            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1291         else:
1292            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1293    
1294       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1295       """       """
1296       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1297           return self.__numEquations  
1298         @param name: name of the coefficient enquired.
1299         @type name: C{string}
1300         @return: the function space to be used for coefficient name
1301         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1302         @raise IllegalCoefficient: if name is not one of coefficients
1303                      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}.
1304         """
1305         if self.hasCoefficientOfGeneralPDE(name):
1306            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1307       else:       else:
1308           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1309    
1310     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1311       """       """
1312       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1313    
1314         @param name: name of the coefficient enquired.
1315         @type name: C{string}
1316         @return: the shape of the coefficient name
1317         @rtype: C{tuple} of C{int}
1318         @raise IllegalCoefficient: if name is not one of coefficients
1319                      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}.
1320       """       """
1321       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1322          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1323       else:       else:
1324          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1325    
1326       # =============================================================================
1327       # functions giving access to coefficients of a particular PDE implementation:
1328       # =============================================================================
1329       def getCoefficient(self,name):
1330         """
1331         returns the value of the coefficient name
1332    
1333     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1334        """       @type name: C{string}
1335        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
1336        """       @rtype: L{Data<escript.Data>}
1337        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1338        out=True       """
1339        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1340           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1341           out=False       else:
1342        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  
1343    
1344     def getFlux(self,u):     def hasCoefficient(self,name):
1345         """       """
1346         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1347    
1348         \f[       @param name: name of the coefficient enquired.
1349         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1350         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1351         @rtype: C{bool}
1352         """
1353         return self.COEFFICIENTS.has_key(name)
1354    
1355         @param u: argument of the operator     def createCoefficient(self, name):
1356         """       """
1357         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1358    
1359     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1360         """       @rtype: L{Data<escript.Data>}
1361         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.
1362         """
1363         if self.hasCoefficient(name):
1364            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1365         else:
1366            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1367    
1368         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1369         """       """
1370         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  
1371    
1372         @param u:       @param name: name of the coefficient enquired.
1373         """       @type name: C{string}
1374         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1375         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1376         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1377         """
1378         if self.hasCoefficient(name):
1379            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1380         else:
1381            raise ValueError,"unknown coefficient %s requested"%name
1382       def getShapeOfCoefficient(self,name):
1383         """
1384         return the shape of the coefficient name
1385    
1386         @param name: name of the coefficient enquired.
1387         @type name: C{string}
1388         @return: the shape of the coefficient name
1389         @rtype: C{tuple} of C{int}
1390         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1391         """
1392         if self.hasCoefficient(name):
1393            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1394         else:
1395            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1396    
1397       def resetCoefficients(self):
1398         """
1399         resets all coefficients to there default values.
1400         """
1401         for i in self.COEFFICIENTS.iterkeys():
1402             self.COEFFICIENTS[i].resetValue()
1403    
1404       def alteredCoefficient(self,name):
1405         """
1406         announce that coefficient name has been changed
1407    
1408     def __setValue(self,**coefficients):       @param name: name of the coefficient enquired.
1409         @type name: C{string}
1410         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1411         @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.
1412         """
1413         if self.hasCoefficient(name):
1414            self.trace("Coefficient %s has been altered."%name)
1415            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1416               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1417               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1418         else:
1419            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1420    
1421       def copyConstraint(self,u):
1422          """
1423          copies the constraint into u and returns u.
1424    
1425          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1426          @type u: L{Data<escript.Data>}
1427          @return: the input u modified by the constraints.
1428          @rtype: L{Data<escript.Data>}
1429          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1430          """
1431          q=self.getCoefficientOfGeneralPDE("q")
1432          r=self.getCoefficientOfGeneralPDE("r")
1433          if not q.isEmpty():
1434             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1435             if r.isEmpty():
1436                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1437             else:
1438                 r=escript.Data(r,u.getFunctionSpace())
1439             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1440          return u
1441    
1442       def setValue(self,**coefficients):
1443        """        """
1444        sets new values to coefficient        sets new values to coefficients
1445    
1446        @param coefficients:        @param coefficients: new values assigned to coefficients
1447          @keyword A: value for coefficient A.
1448          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1449          @keyword B: value for coefficient B
1450          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1451          @keyword C: value for coefficient C
1452          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1453          @keyword D: value for coefficient D
1454          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1455          @keyword X: value for coefficient X
1456          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1457          @keyword Y: value for coefficient Y
1458          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1459          @keyword d: value for coefficient d
1460          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1461          @keyword y: value for coefficient y
1462          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1463          @keyword d_contact: value for coefficient d_contact
1464          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1465                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1466          @keyword y_contact: value for coefficient y_contact
1467          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1468                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1469          @keyword r: values prescribed to the solution at the locations of constraints
1470          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1471                   depending of reduced order is used for the solution.
1472          @keyword q: mask for location of constraints
1473          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1474                   depending of reduced order is used for the representation of the equation.
1475          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1476        """        """
1477        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1478        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1479           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1480              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1481        # 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:
1482        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1483           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1484              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1485                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1489  class LinearPDE:
1489                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1490              if s!=None:              if s!=None:
1491                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1492                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1493                  if res==None:                  if res==None:
1494                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1495                  else:                  else:
1496                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1497                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1498        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1499        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1500        # 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:
1501        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1502          if d==None:          try:
1503               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1504          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1505               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)  
1506          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()  
   
1507    
1508     def __rebuildOperator(self,deep=False):        self.__altered_coefficients=True
1509         """        # check if the systrem is inhomogeneous:
1510         indicates the operator has to be rebuilt next time it is used        if len(coefficients)>0 and not self.isUsingLumping():
1511         """           q=self.getCoefficientOfGeneralPDE("q")
1512         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."           r=self.getCoefficientOfGeneralPDE("r")
1513         self.__rebuildSolution(deep)           homogeneous_constraint=True
1514         self.__operator_isValid=False           if not q.isEmpty() and not r.isEmpty():
1515         if deep: self.__operator=escript.Operator()               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1516                   self.trace("Inhomogeneous constraint detected.")
1517     def __rebuildRightHandSide(self,deep=False):                 self.__invalidateSystem()
        """  
        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()))  
   
    def __applyConstraint(self):  
        """  
        applies the constraints defined by q and r to the system  
        """  
        q=self.getCoefficientOfPDE("q")  
        r=self.getCoefficientOfPDE("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__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.)  
1518    
1519     def getSystem(self):     def getSystem(self):
1520         """         """
1521         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1522    
1523           @return: the discrete version of the PDE
1524           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1525         """         """
1526         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1527            if self.isUsingLumping():            if self.isUsingLumping():
1528                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1529                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1530                         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"
1531                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1532                            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."  
1533                   mat=self.__getNewOperator()                   mat=self.__getNewOperator()
1534                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   self.getDomain().addPDEToSystem(mat,escript.Data(), \
1535                             self.getCoefficientOfPDE("A"), \                             self.getCoefficientOfGeneralPDE("A"), \
1536                             self.getCoefficientOfPDE("B"), \                             self.getCoefficientOfGeneralPDE("B"), \
1537                             self.getCoefficientOfPDE("C"), \                             self.getCoefficientOfGeneralPDE("C"), \
1538                             self.getCoefficientOfPDE("D"), \                             self.getCoefficientOfGeneralPDE("D"), \
1539                             escript.Data(), \                             escript.Data(), \
1540                             escript.Data(), \                             escript.Data(), \
1541                             self.getCoefficientOfPDE("d"), \                             self.getCoefficientOfGeneralPDE("d"), \
1542                             escript.Data(),\                             escript.Data(),\
1543                             self.getCoefficientOfPDE("d_contact"), \                             self.getCoefficientOfGeneralPDE("d_contact"), \
1544                             escript.Data())                             escript.Data())
1545                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1546                   self.__applyConstraint()                   del mat
1547                   self.__operator_isValid=True                   self.trace("New lumped operator has been built.")
1548                     self.__operator_is_Valid=True
1549                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1550                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1551                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1552                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1553                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1554                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1555                   self.__copyConstraint()                   self.trace("New right hand side as been built.")
1556                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1557            else:            else:
1558               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."  
1559                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1560                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1561                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1562                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1563                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1564                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1565                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1566                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1567                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1568                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1569                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1570                   self.__applyConstraint()                   self.__applyConstraint()
1571                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1572                   self.__operator_isValid=True                   self.trace("New system has been built.")
1573                     self.__operator_is_Valid=True
1574                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1575               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1576                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1577                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1578                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1579                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1580                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1581                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1582                     self.trace("New right hand side has been built.")
1583                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1584               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1585                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1586                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1587                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1588                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1589                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1590                              escript.Data(), \                              escript.Data(), \
1591                              escript.Data(), \                              escript.Data(), \
1592                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1593                              escript.Data(),\                              escript.Data(),\
1594                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1595                              escript.Data())                              escript.Data())
1596                   self.__applyConstraint()                   self.__applyConstraint()
1597                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1598                     self.__operator_is_Valid=True
1599         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1600    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1601    
1602     def solve(self,**options):  class Poisson(LinearPDE):
1603        """     """
1604        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1605    
1606        @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  
1607    
1608     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
1609    
1610         @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  
1611    
1612       and constraints:
1613    
1614       M{u=0} where M{q>0}
1615    
1616  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)  
1617    
1618  def HALF(P):     def __init__(self,domain,debug=False):
1619      """ """       """
1620      return escript.Scalar(0.5,P.getFunctionSpace())       initializes a new Poisson equation
1621    
1622         @param domain: domain of the PDE
1623         @type domain: L{Domain<escript.Domain>}
1624         @param debug: if True debug informations are printed.
1625    
1626         """
1627         super(Poisson, self).__init__(domain,1,1,debug)
1628         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1629                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1630         self.setSymmetryOn()
1631    
1632       def setValue(self,**coefficients):
1633         """
1634         sets new values to coefficients
1635    
1636         @param coefficients: new values assigned to coefficients
1637         @keyword f: value for right hand side M{f}
1638         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1639         @keyword q: mask for location of constraints
1640         @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>}
1641                   depending of reduced order is used for the representation of the equation.
1642         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1643         """
1644         super(Poisson, self).setValue(**coefficients)
1645    
1646       def getCoefficientOfGeneralPDE(self,name):
1647         """
1648         return the value of the coefficient name of the general PDE
1649         @param name: name of the coefficient requested.
1650         @type name: C{string}
1651         @return: the value of the coefficient  name
1652         @rtype: L{Data<escript.Data>}
1653         @raise IllegalCoefficient: if name is not one of coefficients
1654                      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}.
1655         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1656         """
1657         if name == "A" :
1658             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1659         elif name == "B" :
1660             return escript.Data()
1661         elif name == "C" :
1662             return escript.Data()
1663         elif name == "D" :
1664             return escript.Data()
1665         elif name == "X" :
1666             return escript.Data()
1667         elif name == "Y" :
1668             return self.getCoefficient("f")
1669         elif name == "d" :
1670             return escript.Data()
1671         elif name == "y" :
1672             return escript.Data()
1673         elif name == "d_contact" :
1674             return escript.Data()
1675         elif name == "y_contact" :
1676             return escript.Data()
1677         elif name == "r" :
1678             return escript.Data()
1679         elif name == "q" :
1680             return self.getCoefficient("q")
1681         else:
1682            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1683    
1684    class Helmholtz(LinearPDE):
1685       """
1686       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1687    
1688       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1689    
1690       with natural boundary conditons
1691    
1692       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1693    
1694       and constraints:
1695    
1696       M{u=r} where M{q>0}
1697    
 class AdvectivePDE(LinearPDE):  
1698     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1699    
1700     \f[     def __init__(self,domain,debug=False):
1701     -(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       """
1702     \f]       initializes a new Poisson equation
1703    
1704     with boundary conditons:       @param domain: domain of the PDE
1705         @type domain: L{Domain<escript.Domain>}
1706         @param debug: if True debug informations are printed.
1707    
1708         """
1709         super(Helmholtz, self).__init__(domain,1,1,debug)
1710         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1711                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1712                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1713                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1714                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1715                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1716                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1717         self.setSymmetryOn()
1718    
1719     \f[     def setValue(self,**coefficients):
1720     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       """
1721     \f]       sets new values to coefficients
1722    
1723     and contact conditions       @param coefficients: new values assigned to coefficients
1724         @keyword omega: value for coefficient M{S{omega}}
1725         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1726         @keyword k: value for coefficeint M{k}
1727         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1728         @keyword f: value for right hand side M{f}
1729         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1730         @keyword alpha: value for right hand side M{S{alpha}}
1731         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1732         @keyword g: value for right hand side M{g}
1733         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1734         @keyword r: prescribed values M{r} for the solution in constraints.
1735         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1736                   depending of reduced order is used for the representation of the equation.
1737         @keyword q: mask for location of constraints
1738         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1739                   depending of reduced order is used for the representation of the equation.
1740         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1741         """
1742         super(Helmholtz, self).setValue(**coefficients)
1743    
1744     \f[     def getCoefficientOfGeneralPDE(self,name):
1745     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}       """
1746     \f]       return the value of the coefficient name of the general PDE
1747    
1748         @param name: name of the coefficient requested.
1749         @type name: C{string}
1750         @return: the value of the coefficient  name
1751         @rtype: L{Data<escript.Data>}
1752         @raise IllegalCoefficient: if name is not one of coefficients
1753                      "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}.
1754         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1755         """
1756         if name == "A" :
1757             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1758         elif name == "B" :
1759             return escript.Data()
1760         elif name == "C" :
1761             return escript.Data()
1762         elif name == "D" :
1763             return self.getCoefficient("omega")
1764         elif name == "X" :
1765             return escript.Data()
1766         elif name == "Y" :
1767             return self.getCoefficient("f")
1768         elif name == "d" :
1769             return self.getCoefficient("alpha")
1770         elif name == "y" :
1771             return self.getCoefficient("g")
1772         elif name == "d_contact" :
1773             return escript.Data()
1774         elif name == "y_contact" :
1775             return escript.Data()
1776         elif name == "r" :
1777             return self.getCoefficient("r")
1778         elif name == "q" :
1779             return self.getCoefficient("q")
1780         else:
1781            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1782    
1783    class LameEquation(LinearPDE):
1784       """
1785       Class to define a Lame equation problem:
1786    
1787       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] }
1788    
1789       with natural boundary conditons:
1790    
1791       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] }
1792    
1793     and constraints:     and constraints:
1794    
1795     \f[     M{u[i]=r[i]} where M{q[i]>0}
1796     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1797     """     """
1798     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
1799        LinearPDE.__init__(self,domain,numEquations,numSolutions)     def __init__(self,domain,debug=False):
1800        self.__xi=xi        super(LameEquation, self).__init__(domain,\
1801                                             domain.getDim(),domain.getDim(),debug)
1802          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1803                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1804                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1805                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1806                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1807                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1808                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1809          self.setSymmetryOn()
1810    
1811       def setValue(self,**coefficients):
1812         """
1813         sets new values to coefficients
1814    
1815         @param coefficients: new values assigned to coefficients
1816         @keyword lame_mu: value for coefficient M{S{mu}}
1817         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1818         @keyword lame_lambda: value for coefficient M{S{lambda}}
1819         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1820         @keyword F: value for internal force M{F}
1821         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1822         @keyword sigma: value for initial stress M{S{sigma}}
1823         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1824         @keyword f: value for extrenal force M{f}
1825         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1826         @keyword r: prescribed values M{r} for the solution in constraints.
1827         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1828                   depending of reduced order is used for the representation of the equation.
1829         @keyword q: mask for location of constraints
1830         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1831                   depending of reduced order is used for the representation of the equation.
1832         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1833         """
1834         super(LameEquation, self).setValue(**coefficients)
1835    
1836       def getCoefficientOfGeneralPDE(self,name):
1837         """
1838         return the value of the coefficient name of the general PDE
1839    
1840         @param name: name of the coefficient requested.
1841         @type name: C{string}
1842         @return: the value of the coefficient  name
1843         @rtype: L{Data<escript.Data>}
1844         @raise IllegalCoefficient: if name is not one of coefficients
1845                      "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}.
1846         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1847         """
1848         if name == "A" :
1849             out =self.createCoefficientOfGeneralPDE("A")
1850             for i in range(self.getDim()):
1851               for j in range(self.getDim()):
1852                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1853                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1854                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1855             return out
1856         elif name == "B" :
1857             return escript.Data()
1858         elif name == "C" :
1859             return escript.Data()
1860         elif name == "D" :
1861             return escript.Data()
1862         elif name == "X" :
1863             return self.getCoefficient("sigma")
1864         elif name == "Y" :
1865             return self.getCoefficient("F")
1866         elif name == "d" :
1867             return escript.Data()
1868         elif name == "y" :
1869             return self.getCoefficient("f")
1870         elif name == "d_contact" :
1871             return escript.Data()
1872         elif name == "y_contact" :
1873             return escript.Data()
1874         elif name == "r" :
1875             return self.getCoefficient("r")
1876         elif name == "q" :
1877             return self.getCoefficient("q")
1878         else:
1879            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1880    
1881    class AdvectivePDE(LinearPDE):
1882       """
1883       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1884       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1885    
1886       In the following we set
1887    
1888       M{Z[j]=C[j]-B[j]}
1889    
1890       or
1891    
1892       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1893    
1894       To measure the dominance of the advective terms over the diffusive term M{A} the
1895       X{Pelclet number} M{P} is used. It is defined as
1896    
1897       M{P=h|Z|/(2|A|)}
1898    
1899       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1900       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1901    
1902       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1903    
1904       M{S{Xi}=S{xi}(P) h/|Z|}
1905    
1906       where M{S{xi}} is a suitable function of the Peclet number.
1907    
1908       In the case of a single PDE the coefficient are up-dated in the following way:
1909             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1910             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1911             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1912             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1913    
1914       Similar for the case of a systems of PDEs:
1915             - 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]}
1916             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1917             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1918             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1919    
1920       where M{S{delta}} is L{kronecker}.
1921       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1922       but with the intension to stabilize the solution.
1923    
1924       """
1925       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1926          """
1927          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1928    
1929          @param domain: domain of the PDE
1930          @type domain: L{Domain<escript.Domain>}
1931          @param numEquations: number of equations. If numEquations==None the number of equations
1932                               is exracted from the PDE coefficients.
1933          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1934                               is exracted from the PDE coefficients.
1935          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1936                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1937          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1938          @param debug: if True debug informations are printed.
1939          """
1940          super(AdvectivePDE, self).__init__(domain,\
1941                                             numEquations,numSolutions,debug)
1942          if xi==None:
1943             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1944          else:
1945             self.__xi=xi
1946        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1947    
1948     def __calculateXi(self,peclet_factor,Z,h):     def setValue(**coefficients):
1949         Z_max=util.Lsup(Z)        """
1950         if Z_max>0.:        sets new values to coefficients
1951            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1952          @param coefficients: new values assigned to coefficients
1953          @keyword A: value for coefficient A.
1954          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1955          @keyword B: value for coefficient B
1956          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1957          @keyword C: value for coefficient C
1958          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1959          @keyword D: value for coefficient D
1960          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1961          @keyword X: value for coefficient X
1962          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1963          @keyword Y: value for coefficient Y
1964          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1965          @keyword d: value for coefficient d
1966          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1967          @keyword y: value for coefficient y
1968          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1969          @keyword d_contact: value for coefficient d_contact
1970          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1971                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1972          @keyword y_contact: value for coefficient y_contact
1973          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1974                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1975          @keyword r: values prescribed to the solution at the locations of constraints
1976          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1977                   depending of reduced order is used for the solution.
1978          @keyword q: mask for location of constraints
1979          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1980                   depending of reduced order is used for the representation of the equation.
1981          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1982    
1983          """
1984          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1985          super(AdvectivePDE, self).setValue(**coefficients)
1986    
1987       def ELMAN_RAMAGE(self,P):
1988         """
1989         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1990         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1991              - M{S{xi}(P)=0} for M{P<1}
1992              - M{S{xi}(P)=(1-1/P)/2} otherwise
1993    
1994         @param P: Preclet number
1995         @type P: L{Scalar<escript.Scalar>}
1996         @return: up-wind weightimg factor
1997         @rtype: L{Scalar<escript.Scalar>}
1998         """
1999         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2000    
2001       def SIMPLIFIED_BROOK_HUGHES(self,P):
2002         """
2003         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2004         The original methods is
2005    
2006         M{S{xi}(P)=coth(P)-1/P}
2007    
2008         As the evaluation of M{coth} is expensive we are using the approximation:
2009    
2010             - M{S{xi}(P)=P/3} where M{P<3}
2011             - M{S{xi}(P)=1/2} otherwise
2012    
2013         @param P: Preclet number
2014         @type P: L{Scalar<escript.Scalar>}
2015         @return: up-wind weightimg factor
2016         @rtype: L{Scalar<escript.Scalar>}
2017         """
2018         c=util.whereNegative(P-3.)
2019         return P/6.*c+1./2.*(1.-c)
2020    
2021       def HALF(self,P):
2022         """
2023         Predefined function to set value M{1/2} for M{S{xi}}
2024    
2025         @param P: Preclet number
2026         @type P: L{Scalar<escript.Scalar>}
2027         @return: up-wind weightimg factor
2028         @rtype: L{Scalar<escript.Scalar>}
2029         """
2030         return escript.Scalar(0.5,P.getFunctionSpace())
2031    
2032       def __calculateXi(self,peclet_factor,flux,h):
2033           flux=util.Lsup(flux)
2034           if flux_max>0.:
2035              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2036         else:         else:
2037            return 0.            return 0.
2038    
2039     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):  
2040        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2041           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2042           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1060  class AdvectivePDE(LinearPDE): Line 2045  class AdvectivePDE(LinearPDE):
2045           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2046           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2047              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
2048                  Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))                  flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2049                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2050                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2051                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2052                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2053                              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
2054                          # flux=C-util.reorderComponents(B,[0,2,1])
2055                     else:                     else:
2056                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2057                           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
2058                          # flux=C-B
2059                  else:                  else:
2060                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2061                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2062                           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
2063                          # flux=C-util.reorderComponents(B,[1,0])
2064                     else:                     else:
2065                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2066                  length_of_Z=util.sqrt(Z2)                        #flux=C-B
2067                    length_of_flux=util.sqrt(flux2)
2068              elif C.isEmpty():              elif C.isEmpty():
2069                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2070                  #flux=B
2071              else:              else:
2072                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2073                  #flux=C
2074    
2075              Z_max=util.Lsup(length_of_Z)              #length_of_flux=util.length(flux)
2076              if Z_max>0.:              flux_max=util.Lsup(length_of_flux)
2077                if flux_max>0.:
2078                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2079                 length_of_A=util.length(A)                 length_of_A=util.length(A)
2080                 A_max=util.Lsup(length_of_A)                 A_max=util.Lsup(length_of_A)
2081                 if A_max>0:                 if A_max>0:
2082                      inv_A=1./(length_of_A+A_max*self.TOL)                      inv_A=1./(length_of_A+A_max*self.__TOL)
2083                 else:                 else:
2084                      inv_A=1./self.TOL                      inv_A=1./self.__TOL
2085                 peclet_number=length_of_Z*h/2*inv_A                 peclet_number=length_of_flux*h/2*inv_A
2086                 xi=self.__xi(peclet_number)                 xi=self.__xi(peclet_number)
2087                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2088                 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))
2089        return self.__Xi        return self.__Xi
         
2090    
2091     def getCoefficientOfPDE(self,name):  
2092       def getCoefficientOfGeneralPDE(self,name):
2093       """       """
2094       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2095    
2096       @param name:       @param name: name of the coefficient requested.
2097         @type name: C{string}
2098         @return: the value of the coefficient name
2099         @rtype: L{Data<escript.Data>}
2100         @raise IllegalCoefficient: if name is not one of coefficients
2101                      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}.
2102         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2103       """       """
2104       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2105            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."
2106    
2107       if name == "A" :       if name == "A" :
2108           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2109           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2110           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2111           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2112              Aout=A              Aout=A
2113           else:           else:
2114              if A.isEmpty():              if A.isEmpty():
2115                 Aout=self.createNewCoefficient("A")                 Aout=self.createNewCoefficient("A")
2116              else:              else:
2117                 Aout=A[:]                 Aout=A[:]
2118              Xi=self.getXi()              Xi=self.__getXi()
2119              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2120                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2121                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2122                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2123                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2124                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2125                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2126                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2127                                 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])
2128                              elif C.isEmpty():                              elif C.isEmpty():
2129                                 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]
2130                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2131                              else:                              else:
2132                                 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]
2133                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2134              else:              else:
2135                  for j in range(self.getDim()):                  for j in range(self.getDim()):
2136                     for l in range(self.getDim()):                     for l in range(self.getDim()):
# Line 1137  class AdvectivePDE(LinearPDE): Line 2140  class AdvectivePDE(LinearPDE):
2140                            Aout[j,l]+=Xi*B[j]*B[l]                            Aout[j,l]+=Xi*B[j]*B[l]
2141                        else:                        else:
2142                            Aout[j,l]+=Xi*C[j]*C[l]                            Aout[j,l]+=Xi*C[j]*C[l]
2143                     # if not C.isEmpty() and not B.isEmpty():
2144                     #    tmp=C-B
2145                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2146                     # elif C.isEmpty():
2147                     #    Aout=Aout+Xi*util.outer(B,B)
2148                     # else:
2149                     # Aout=Aout+Xi*util.outer(C,C)
2150           return Aout           return Aout
2151       elif name == "B" :       elif name == "B" :
2152           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2153           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2154           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2155           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2156              Bout=B              Bout=B
2157           else:           else:
2158              Xi=self.getXi()              Xi=self.__getXi()
2159              if B.isEmpty():              if B.isEmpty():
2160                  Bout=self.createNewCoefficient("B")                  Bout=self.createNewCoefficient("B")
2161              else:              else:
2162                  Bout=B[:]                  Bout=B[:]
2163              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2164                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2165                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2166                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2167                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2168                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2169                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2170                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2171              else:              else:
2172                 tmp=Xi*D                 tmp=Xi*D
2173                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2174                   # Bout=Bout+Xi*D*C
2175           return Bout           return Bout
2176       elif name == "C" :       elif name == "C" :
2177           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2178           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2179           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2180           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2181              Cout=C              Cout=C
2182           else:           else:
2183              Xi=self.getXi()              Xi=self.__getXi()
2184              if C.isEmpty():              if C.isEmpty():
2185                  Cout=self.createNewCoefficient("C")                  Cout=self.createNewCoefficient("C")
2186              else:              else:
2187                  Cout=C[:]                  Cout=C[:]
# Line 1180  class AdvectivePDE(LinearPDE): Line 2192  class AdvectivePDE(LinearPDE):
2192                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2193                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2194                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2195                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2196              else:              else:
2197                 tmp=Xi*D                 tmp=Xi*D
2198                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2199                   # Cout=Cout+tmp*D*B
2200           return Cout           return Cout
2201       elif name == "D" :       elif name == "D" :
2202           return self.getCoefficient("D")           return self.getCoefficient("D")
2203       elif name == "X" :       elif name == "X" :
2204           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2205           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2206           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1198  class AdvectivePDE(LinearPDE): Line 2212  class AdvectivePDE(LinearPDE):
2212                  Xout=self.createNewCoefficient("X")                  Xout=self.createNewCoefficient("X")
2213              else:              else:
2214                  Xout=X[:]                  Xout=X[:]
2215              Xi=self.getXi()              Xi=self.__getXi()
2216              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2217                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2218                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2219                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2220                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2221                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2222                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2223                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2224                            elif C.isEmpty():                            elif C.isEmpty():
2225                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2226                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2227                            else:                            else:
2228                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2229                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2230              else:              else:
2231                   tmp=Xi*Y                   tmp=Xi*Y
2232                   for j in range(self.getDim()):                   for j in range(self.getDim()):
2233                      if not C.isEmpty() and not B.isEmpty():                      if not C.isEmpty() and not B.isEmpty():
2234                         Xout[j]+=tmp*(C[j]-B[j])                         Xout[j]+=tmp*(C[j]-B[j])
2235                           # Xout=Xout+Xi*Y*(C-B)
2236                      elif C.isEmpty():                      elif C.isEmpty():
2237                         Xout[j]-=tmp*B[j]                         Xout[j]-=tmp*B[j]
2238                           # Xout=Xout-Xi*Y*B
2239                      else:                      else:
2240                         Xout[j]+=tmp*C[j]                         Xout[j]+=tmp*C[j]
2241                           # Xout=Xout+Xi*Y*C
2242           return Xout           return Xout
2243       elif name == "Y" :       elif name == "Y" :
2244           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2245       elif name == "d" :       elif name == "d" :
2246           return self.getCoefficient("d")           return self.getCoefficient("d")
2247       elif name == "y" :       elif name == "y" :
2248           return self.getCoefficient("y")           return self.getCoefficient("y")
2249       elif name == "d_contact" :       elif name == "d_contact" :
2250           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2251       elif name == "y_contact" :       elif name == "y_contact" :
2252           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2253       elif name == "r" :       elif name == "r" :
2254           return self.getCoefficient("r")           return self.getCoefficient("r")
2255       elif name == "q" :       elif name == "q" :
2256           return self.getCoefficient("q")           return self.getCoefficient("q")
2257       else:       else:
2258           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2259    
2260  class Poisson(LinearPDE):  class AdvectionDiffusion(LinearPDE):
2261     """     """
2262     Class to define a Poisson equstion problem:     Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2263    
2264       M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
2265    
2266       with natural boundary conditons
2267    
2268     class to define a linear PDE of the form     M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
    \f[  
    -u_{,jj} = f  
    \f]  
   
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
2269    
2270     and constraints:     and constraints:
2271    
2272     \f[     M{u=r} where M{q>0}
2273     u=0 \quad \mathrm{where} \quad q>0  
2274     \f]     and
2275    
2276       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2277    
2278     """     """
2279    
2280     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2281         LinearPDE.__init__(self,domain,1,1)       """
2282         self.COEFFICIENTS={       initializes a new Poisson equation
2283         "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
2284         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}       @param domain: domain of the PDE
2285         self.setSymmetryOn()       @type domain: L{Domain<escript.Domain>}
2286         self.setValue(f,q)       @param debug: if True debug informations are printed.
2287    
2288         """
2289         super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2290         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2291                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2292                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2293                            "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2294                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2295                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2296                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2297                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2298                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2299    
2300     def setValue(self,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
2301         self._LinearPDE__setValue(f=f,q=q)       """
2302         sets new values to coefficients
2303    
2304     def getCoefficientOfPDE(self,name):       @param coefficients: new values assigned to coefficients
2305         @keyword omega: value for coefficient M{S{omega}}
2306         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2307         @keyword k: value for coefficient M{k}
2308         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2309         @keyword v: value for coefficient M{v}
2310         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2311         @keyword upwind: value for upwind term M{upwind}
2312         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2313         @keyword f: value for right hand side M{f}
2314         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2315         @keyword alpha: value for right hand side M{S{alpha}}
2316         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2317         @keyword g: value for right hand side M{g}
2318         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2319         @keyword r: prescribed values M{r} for the solution in constraints.
2320         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2321                   depending of reduced order is used for the representation of the equation.
2322         @keyword q: mask for location of constraints
2323         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2324                   depending of reduced order is used for the representation of the equation.
2325         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2326       """       """
2327       return the value of the coefficient name of the general PDE       super(AdvectionDiffusion, self).setValue(**coefficients)
2328    
2329       @param name:     def getCoefficientOfGeneralPDE(self,name):
2330       """       """
2331       if name == "A" :       return the value of the coefficient name of the general PDE
2332           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
2333       elif name == "B" :       @param name: name of the coefficient requested.
2334           return escript.Data()       @type name: C{string}
2335       elif name == "C" :       @return: the value of the coefficient  name
2336           return escript.Data()       @rtype: L{Data<escript.Data>}
2337       elif name == "D" :       @raise IllegalCoefficient: if name is not one of coefficients
2338                      "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}.
2339         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2340         """
2341         if name == "A" :
2342             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2343         elif name == "B" :
2344           return escript.Data()           return escript.Data()
2345       elif name == "X" :       elif name == "C" :
2346             return self.getCoefficient("v")
2347         elif name == "D" :
2348             return self.getCoefficient("omega")
2349         elif name == "X" :
2350           return escript.Data()           return escript.Data()
2351       elif name == "Y" :       elif name == "Y" :
2352           return self.getCoefficient("f")           return self.getCoefficient("f")
2353       elif name == "d" :       elif name == "d" :
2354           return escript.Data()           return self.getCoefficient("alpha")
2355       elif name == "y" :       elif name == "y" :
2356           return escript.Data()           return self.getCoefficient("g")
2357       elif name == "d_contact" :       elif name == "d_contact" :
2358           return escript.Data()           return escript.Data()
2359       elif name == "y_contact" :       elif name == "y_contact" :
2360           return escript.Data()           return escript.Data()
2361       elif name == "r" :       elif name == "r" :
2362           return escript.Data()           return self.getCoefficient("r")
2363       elif name == "q" :       elif name == "q" :
2364           return self.getCoefficient("q")           return self.getCoefficient("q")
2365       else:       else:
2366           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2367    
2368    
2369  # $Log$  # $Log$
2370  # Revision 1.8  2005/06/09 05:37:59  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2371  # Merge of development branch back to main trunk on 2005-06-09  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2372    #
2373    # Revision 1.13  2005/09/15 03:44:19  jgs
2374    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2375    #
2376    # Revision 1.12  2005/09/01 03:31:28  jgs
2377    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2378    #
2379    # Revision 1.11  2005/08/23 01:24:28  jgs
2380    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2381  #  #
2382  # Revision 1.7  2005/05/06 04:26:10  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2383  # Merge of development branch back to main trunk on 2005-05-06  # erge of development branch dev-02 back to main trunk on 2005-08-12
2384    #
2385    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2386    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2387    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2388    # modified to instead use portable/cooperative "super" calls to extend base
2389    # class methods.
2390    #
2391    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2392    # Removed redundant if-loop.
2393    #
2394    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2395    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2396    #
2397    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2398    # the solver from finley are put into the standalone package paso now
2399    #
2400    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2401    # in the case of lumping no new system is allocated if the constraint is changed.
2402    #
2403    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2404    # test for Lumping added
2405    #
2406    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2407    # bug in format fixed.
2408    #
2409    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2410    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2411    #
2412    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2413    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2414    #
2415    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2416    # gneric unit testing for linearPDE
2417    #
2418    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2419    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2420    #
2421    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2422    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2423    #
2424    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2425    # epydoc mark up partially fixed
2426    #
2427    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2428    # some problems with LinearPDEs fixed.
2429    #
2430    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2431    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2432    #
2433    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2434    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2435    #
2436    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2437    # new functions in util and a new pde type in linearPDEs
2438    #
2439    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2440    # Lame equation: (linear elastic, isotropic) added
2441    #
2442    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2443    # some extensions to modellib and linearPDEs
2444  #  #
2445  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2446  # Fixed up some docstrings.  Moved module-level functions to top of file so  # Fixed up some docstrings.  Moved module-level functions to top of file so
# Line 1420  class Poisson(LinearPDE): Line 2551  class Poisson(LinearPDE):
2551  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2552  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2553  #  #
 #  

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