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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 431 by gross, Fri Jan 13 05:07:10 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
2    
3  ## @file linearPDEs.py  #
4    #      COPYRIGHT ACcESS 2004 -  All Rights Reserved
5    #
6    #   This software is the property of ACcESS.  No part of this code
7    #   may be copied in any form or by any means without the expressed written
8    #   consent of ACcESS.  Copying, use or modification of this software
9    #   by any unauthorised person is illegal unless that
10    #   person has a software license agreement with ACcESS.
11    #
12  """  """
13  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       @cvar AMG: algebraic multi grid
423       @cvar RILU: recursive ILU
424    
425       """
426       DEFAULT= 0
427       DIRECT= 1
428       CHOLEVSKY= 2
429       PCG= 3
430       CR= 4
431       CGS= 5
432       BICGSTAB= 6
433       SSOR= 7
434       ILU0= 8
435       ILUT= 9
436       JACOBI= 10
437       GMRES= 11
438       PRES20= 12
439       LUMPING= 13
440       NO_REORDERING= 17
441       MINIMUM_FILL_IN= 18
442       NESTED_DISSECTION= 19
443       SCSL= 14
444       MKL= 15
445       UMFPACK= 16
446       ITERATIVE= 20
447       PASO= 21
448       AMG= 22
449       RILU = 23
450    
451       __TOL=1.e-13
452       __PACKAGE_KEY="package"
453       __METHOD_KEY="method"
454       __SYMMETRY_KEY="symmetric"
455       __TOLERANCE_KEY="tolerance"
456       __PRECONDITIONER_KEY="preconditioner"
457    
458    
459       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
460         """
461         initializes a new linear PDE
462    
463         @param domain: domain of the PDE
464         @type domain: L{Domain<escript.Domain>}
465         @param numEquations: number of equations. If numEquations==None the number of equations
466                              is exracted from the PDE coefficients.
467         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
468                              is exracted from the PDE coefficients.
469         @param debug: if True debug informations are printed.
470    
471         """
472         super(LinearPDE, self).__init__()
473         #
474         #   the coefficients of the general PDE:
475         #
476         self.__COEFFICIENTS_OF_GENEARL_PDE={
477           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
478           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
480           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
482           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
484           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
485           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
486           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
487           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
488           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
489    
490         # COEFFICIENTS can be overwritten by subclasses:
491         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
492         self.__altered_coefficients=False
493       # initialize attributes       # initialize attributes
494       self.__debug=None       self.__debug=debug
495       self.__domain=domain       self.__domain=domain
496       self.__numEquations=numEquations       self.__numEquations=numEquations
497       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
498       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
499    
500       # set some default values:       # set some default values:
501       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
502       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
503       self.__tolerance=1.e-8       self.__tolerance=1.e-8
504       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
505       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
506         self.__preconditioner=self.DEFAULT
507         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
508       self.__sym=False       self.__sym=False
      self.__lumping=False  
509    
510     def createCoefficient(self, name):       self.resetCoefficients()
511         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
512       # =============================================================================
513       #    general stuff:
514       # =============================================================================
515       def __str__(self):
516         """
517         returns string representation of the PDE
518    
519         @return: a simple representation of the PDE
520         @rtype: C{str}
521         """
522         return "<LinearPDE %d>"%id(self)
523       # =============================================================================
524       #    debug :
525       # =============================================================================
526       def setDebugOn(self):
527       """       """
528       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
529       """       """
530       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
531    
532     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
533       """       """
534       return the value of the parameter name       switches off debugging
535         """
536         self.__debug=None
537    
538       @param name:     def trace(self,text):
539         """
540         print the text message if debugging is swiched on.
541         @param text: message
542         @type text: C{string}
543       """       """
544       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
545    
546     def getCoefficientOfPDE(self,name):     # =============================================================================
547       # some service functions:
548       # =============================================================================
549       def getDomain(self):
550       """       """
551       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.  
552    
553       @param name:       @return: the domain of the PDE
554         @rtype: L{Domain<escript.Domain>}
555       """       """
556       return self.getCoefficient(name)       return self.__domain
557    
558     def hasCoefficient(self,name):     def getDim(self):
559        """       """
560        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
561    
562        @param name:       @return: the spatial dimension of the PDE domain
563        """       @rtype: C{int}
564        return self.COEFFICIENTS.has_key(name)       """
565         return self.getDomain().getDim()
566    
567     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
568       """       """
569       return true if the test functions should use reduced order       returns the number of equations
570    
571         @return: the number of equations
572         @rtype: C{int}
573         @raise UndefinedPDEError: if the number of equations is not be specified yet.
574       """       """
575       return self.__row_function_space       if self.__numEquations==None:
576             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
577         else:
578             return self.__numEquations
579    
580     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
581       """       """
582       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
583    
584         @return: the number of unknowns
585         @rtype: C{int}
586         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
587       """       """
588       return self.__column_function_space       if self.__numSolutions==None:
589            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
590         else:
591            return self.__numSolutions
592    
593     def setValue(self,**coefficients):     def reduceEquationOrder(self):
594        """       """
595        sets new values to coefficients       return status for order reduction for equation
596    
597        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
598        """       @rtype: L{bool}
599        self.__setValue(**coefficients)       """
600               return self.__reduce_equation_order
601    
602     def cleanCoefficients(self):     def reduceSolutionOrder(self):
603       """       """
604       resets all coefficients to default values.       return status for order reduction for the solution
605    
606         @return: return True is reduced interpolation order is used for the represenation of the solution
607         @rtype: L{bool}
608       """       """
609       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
610    
611     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
612       """       """
613       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
614    
615         @return: representation space of equation
616         @rtype: L{FunctionSpace<escript.FunctionSpace>}
617       """       """
618       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
619                   return escript.ReducedSolution(self.getDomain())
620         else:
621             return escript.Solution(self.getDomain())
622    
623     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
624       """       """
625       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
626    
627       @param name:       @return: representation space of solution
628         @rtype: L{FunctionSpace<escript.FunctionSpace>}
629       """       """
630       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
631          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
632       else:       else:
633          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
634    
635     def getFunctionSpaceForCoefficient(self,name):  
636       def getOperator(self):
637       """       """
638       return the atoms of the coefficient name       provides access to the operator of the PDE
639    
640       @param name:       @return: the operator of the PDE
641         @rtype: L{Operator<escript.Operator>}
642       """       """
643       if self.hasCoefficient(name):       m=self.getSystem()[0]
644          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
645             return self.copyConstraint(1./m)
646       else:       else:
647          raise ValueError,"Solution coefficient %s requested"%name           return m
648    
649     def alteredCoefficient(self,name):     def getRightHandSide(self):
650       """       """
651       announce that coefficient name has been changed       provides access to the right hand side of the PDE
652         @return: the right hand side of the PDE
653         @rtype: L{Data<escript.Data>}
654         """
655         r=self.getSystem()[1]
656         if self.isUsingLumping():
657             return self.copyConstraint(r)
658         else:
659             return r
660    
661       @param name:     def applyOperator(self,u=None):
662       """       """
663       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
664          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
665          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
666                   the current solution is used.
667         @type u: L{Data<escript.Data>} or None
668         @return: image of u
669         @rtype: L{Data<escript.Data>}
670         """
671         if u==None:
672              return self.getOperator()*self.getSolution()
673       else:       else:
674          raise ValueError,"unknown coefficient %s requested"%name          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
675    
676     # ===== debug ==============================================================     def getResidual(self,u=None):
677     def setDebugOn(self):       """
678         """       return the residual of u or the current solution if u is not present.
679    
680         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
681                   the current solution is used.
682         @type u: L{Data<escript.Data>} or None
683         @return: residual of u
684         @rtype: L{Data<escript.Data>}
685         """
686         return self.applyOperator(u)-self.getRightHandSide()
687    
688       def checkSymmetry(self,verbose=True):
689          """
690          test the PDE for symmetry.
691    
692          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
693          @type verbose: C{bool}
694          @return:  True if the PDE is symmetric.
695          @rtype: L{Data<escript.Data>}
696          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
697          """
698          verbose=verbose or self.__debug
699          out=True
700          if self.getNumSolutions()!=self.getNumEquations():
701             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
702             out=False
703          else:
704             A=self.getCoefficientOfGeneralPDE("A")
705             if not A.isEmpty():
706                tol=util.Lsup(A)*self.__TOL
707                if self.getNumSolutions()>1:
708                   for i in range(self.getNumEquations()):
709                      for j in range(self.getDim()):
710                         for k in range(self.getNumSolutions()):
711                            for l in range(self.getDim()):
712                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
713                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
714                                   out=False
715                else:
716                   for j in range(self.getDim()):
717                      for l in range(self.getDim()):
718                         if util.Lsup(A[j,l]-A[l,j])>tol:
719                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
720                            out=False
721             B=self.getCoefficientOfGeneralPDE("B")
722             C=self.getCoefficientOfGeneralPDE("C")
723             if B.isEmpty() and not C.isEmpty():
724                if verbose: print "non-symmetric PDE because B is not present but C is"
725                out=False
726             elif not B.isEmpty() and C.isEmpty():
727                if verbose: print "non-symmetric PDE because C is not present but B is"
728                out=False
729             elif not B.isEmpty() and not C.isEmpty():
730                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
731                if self.getNumSolutions()>1:
732                   for i in range(self.getNumEquations()):
733                       for j in range(self.getDim()):
734                          for k in range(self.getNumSolutions()):
735                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
736                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
737                                  out=False
738                else:
739                   for j in range(self.getDim()):
740                      if util.Lsup(B[j]-C[j])>tol:
741                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
742                         out=False
743             if self.getNumSolutions()>1:
744               D=self.getCoefficientOfGeneralPDE("D")
745               if not D.isEmpty():
746                 tol=util.Lsup(D)*self.__TOL
747                 for i in range(self.getNumEquations()):
748                    for k in range(self.getNumSolutions()):
749                      if util.Lsup(D[i,k]-D[k,i])>tol:
750                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
751                          out=False
752               d=self.getCoefficientOfGeneralPDE("d")
753               if not d.isEmpty():
754                 tol=util.Lsup(d)*self.__TOL
755                 for i in range(self.getNumEquations()):
756                    for k in range(self.getNumSolutions()):
757                      if util.Lsup(d[i,k]-d[k,i])>tol:
758                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
759                          out=False
760               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
761               if not d_contact.isEmpty():
762                 tol=util.Lsup(d_contact)*self.__TOL
763                 for i in range(self.getNumEquations()):
764                    for k in range(self.getNumSolutions()):
765                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
766                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
767                          out=False
768          return out
769    
770       def getSolution(self,**options):
771         """         """
772         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
773    
774     def setDebugOff(self):         @return: the solution
775           @rtype: L{Data<escript.Data>}
776           @param options: solver options
777           @keyword verbose: True to get some information during PDE solution
778           @type verbose: C{bool}
779           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
780                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
781           @keyword iter_max: maximum number of iteration steps allowed.
782           @keyword drop_tolerance: threshold for drupping in L{ILUT}
783           @keyword drop_storage: maximum of allowed memory in L{ILUT}
784           @keyword truncation: maximum number of residuals in L{GMRES}
785           @keyword restart: restart cycle length in L{GMRES}
786         """         """
787           if not self.__solution_isValid:
788              mat,f=self.getSystem()
789              if self.isUsingLumping():
790                 self.__solution=self.copyConstraint(f*mat)
791              else:
792                 options[self.__TOLERANCE_KEY]=self.getTolerance()
793                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
794                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
795                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
796                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
797                 self.trace("PDE is resolved.")
798                 self.trace("solver options: %s"%str(options))
799                 self.__solution=mat.solve(f,options)
800              self.__solution_isValid=True
801           return self.__solution
802    
803       def getFlux(self,u=None):
804         """
805         returns the flux M{J} for a given M{u}
806    
807         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
808    
809         or
810    
811         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
812    
813         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
814         @type u: L{Data<escript.Data>} or None
815         @return: flux
816         @rtype: L{Data<escript.Data>}
817         """
818         if u==None: u=self.getSolution()
819         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
820       # =============================================================================
821       #   solver settings:
822       # =============================================================================
823       def setSolverMethod(self,solver=None,preconditioner=None):
824         """         """
825         self.__debug=None         sets a new solver
826    
827           @param solver: sets a new solver method.
828           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
829           @param preconditioner: sets a new solver method.
830           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
831           """
832           if solver==None: solve=self.DEFAULT
833           if preconditioner==None: preconditioner=self.DEFAULT
834           if not (solver,preconditioner)==self.getSolverMethod():
835               self.__solver_method=solver
836               self.__preconditioner=preconditioner
837               self.__checkMatrixType()
838               self.trace("New solver is %s"%self.getSolverMethodName())
839    
840     def debug(self):     def getSolverMethodName(self):
841         """         """
842         returns true if the PDE is in the debug mode         returns the name of the solver currently used
843    
844           @return: the name of the solver currently used.
845           @rtype: C{string}
846         """         """
        return self.__debug  
847    
848     #===== Lumping ===========================         m=self.getSolverMethod()
849     def setLumpingOn(self):         p=self.getSolverPackage()
850        """         method=""
851        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
852        """         elif m[0]==self.DIRECT: method= "DIRECT"
853        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
854           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
855           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
856           self.__lumping=True         elif m[0]==self.CR: method= "CR"
857           elif m[0]==self.CGS: method= "CGS"
858           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
859           elif m[0]==self.SSOR: method= "SSOR"
860           elif m[0]==self.GMRES: method= "GMRES"
861           elif m[0]==self.PRES20: method= "PRES20"
862           elif m[0]==self.LUMPING: method= "LUMPING"
863           elif m[0]==self.AMG: method= "AMG"
864           if m[1]==self.DEFAULT: method+="+DEFAULT"
865           elif m[1]==self.JACOBI: method+= "+JACOBI"
866           elif m[1]==self.ILU0: method+= "+ILU0"
867           elif m[1]==self.ILUT: method+= "+ILUT"
868           elif m[1]==self.SSOR: method+= "+SSOR"
869           elif m[1]==self.AMG: method+= "+AMG"
870           elif m[1]==self.RILU: method+= "+RILU"
871           if p==self.DEFAULT: package="DEFAULT"
872           elif p==self.PASO: package= "PASO"
873           elif p==self.MKL: package= "MKL"
874           elif p==self.SCSL: package= "SCSL"
875           elif p==self.UMFPACK: package= "UMFPACK"
876           else : method="unknown"
877           return "%s solver of %s package"%(method,package)
878    
    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  
879    
880     def setLumping(self,flag=False):     def getSolverMethod(self):
881        """         """
882        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
883    
884     def isUsingLumping(self):         @return: the solver method currently be used.
885        """         @rtype: C{int}
886                 """
887        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
888    
889     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
890         """         """
891         sets a new solver         sets a new solver package
892    
893           @param solver: sets a new solver method.
894           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
895         """         """
896         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
897           if not package==self.getSolverPackage():
898             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
899             self.__checkMatrixType()             self.__checkMatrixType()
900               self.trace("New solver is %s"%self.getSolverMethodName())
901    
902     def getSolverMethod(self):     def getSolverPackage(self):
903         """         """
904         returns the solver method         returns the package of the solver
905    
906           @return: the solver package currently being used.
907           @rtype: C{int}
908         """         """
909         return self.__solver_method         return self.__solver_package
910    
911       def isUsingLumping(self):
912          """
913          checks if matrix lumping is used a solver method
914    
915          @return: True is lumping is currently used a solver method.
916          @rtype: C{bool}
917          """
918          return self.getSolverMethod()[0]==self.LUMPING
919    
    #============ tolerance business =========================================================  
920     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
921         """         """
922         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
923    
924           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
925    
926           defines the stopping criterion.
927    
928           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
929                       the system will be resolved.
930           @type tol: positive C{float}
931           @raise ValueException: if tolerance is not positive.
932         """         """
933         if not tol>0:         if not tol>0:
934             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
935         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
936         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
937         self.__tolerance=tol         self.__tolerance=tol
938         return         return
939    
940     def getTolerance(self):     def getTolerance(self):
941         """         """
942         returns the tolerance set for the solution         returns the tolerance set for the solution
943    
944           @return: tolerance currently used.
945           @rtype: C{float}
946         """         """
947         return self.__tolerance         return self.__tolerance
948    
949     #===== symmetry  flag ==========================     # =============================================================================
950       #    symmetry  flag:
951       # =============================================================================
952     def isSymmetric(self):     def isSymmetric(self):
953        """        """
954        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
955    
956          @return: True is a symmetric PDE is indicated, otherwise False is returned
957          @rtype: C{bool}
958        """        """
959        return self.__sym        return self.__sym
960    
961     def setSymmetryOn(self):     def setSymmetryOn(self):
962        """        """
963        sets the symmetry flag to true        sets the symmetry flag.
964        """        """
965        if not self.isSymmetric():        if not self.isSymmetric():
966           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
967           self.__sym=True           self.__sym=True
968           self.__checkMatrixType()           self.__checkMatrixType()
969    
970     def setSymmetryOff(self):     def setSymmetryOff(self):
971        """        """
972        sets the symmetry flag to false        removes the symmetry flag.
973        """        """
974        if self.isSymmetric():        if self.isSymmetric():
975           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
976           self.__sym=False           self.__sym=False
977           self.__checkMatrixType()           self.__checkMatrixType()
978    
979     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
980       """        """
981       sets the symmetry flag to flag        sets the symmetry flag to flag
982    
983       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
984       """        @type flag: C{bool}
985       if flag:        """
986          self.setSymmetryOn()        if flag:
987       else:           self.setSymmetryOn()
988          self.setSymmetryOff()        else:
989             self.setSymmetryOff()
990    
991     #===== order reduction ==========================     # =============================================================================
992       # function space handling for the equation as well as the solution
993       # =============================================================================
994     def setReducedOrderOn(self):     def setReducedOrderOn(self):
995       """       """
996       switches to on reduced order       switches on reduced order for solution and equation representation
997    
998         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
999       """       """
1000       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1001       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1002    
1003     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1004       """       """
1005       switches to full order       switches off reduced order for solution and equation representation
1006    
1007         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1008       """       """
1009       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1010       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1011    
1012     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1013       """       """
1014       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1015         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1016       @param flag:                    if flag is not present order reduction is switched off
1017         @type flag: C{bool}
1018         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1019       """       """
1020       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1021       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1022    
1023     #===== order reduction solution ==========================  
1024     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1025       """       """
1026       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1027    
1028         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1029       """       """
1030       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1031       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1032           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1033           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1034           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1035             self.__resetSystem()
1036    
1037     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1038       """       """
1039       switches to full order to interpolate solution       switches off reduced order for solution representation
1040    
1041         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1042       """       """
1043       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1044       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1045           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1046           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1047           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1048             self.__resetSystem()
1049    
1050     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1051       """       """
1052       sets order for test functions according to flag       sets order for test functions according to flag
1053    
1054       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1055                      if flag is not present order reduction is switched off
1056         @type flag: C{bool}
1057         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1058       """       """
1059       if flag:       if flag:
1060          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1061       else:       else:
1062          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1063                                                                                                                                                              
    #===== order reduction equation ==========================  
1064     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1065       """       """
1066       switches to reduced order for test functions       switches on reduced order for equation representation
1067    
1068         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1069       """       """
1070       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1071       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1072           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1073           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1074           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1075             self.__resetSystem()
1076    
1077     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1078       """       """
1079       switches to full order for test functions       switches off reduced order for equation representation
1080    
1081         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1082       """       """
1083       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1084       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1085           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1086           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1087           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1088             self.__resetSystem()
1089    
1090     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1091       """       """
1092       sets order for test functions according to flag       sets order for test functions according to flag
1093    
1094       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1095                      if flag is not present order reduction is switched off
1096         @type flag: C{bool}
1097         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1098       """       """
1099       if flag:       if flag:
1100          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1101       else:       else:
1102          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1103                                                                                                                                                              
1104     # ==== initialization =====================================================================     # =============================================================================
1105       # private method:
1106       # =============================================================================
1107       def __checkMatrixType(self):
1108         """
1109         reassess the matrix type and, if a new matrix is needed, resets the system.
1110         """
1111         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1112         if not new_matrix_type==self.__matrix_type:
1113             self.trace("Matrix type is now %d."%new_matrix_type)
1114             self.__matrix_type=new_matrix_type
1115             self.__resetSystem()
1116       #
1117       #   rebuild switches :
1118       #
1119       def __invalidateSolution(self):
1120           """
1121           indicates the PDE has to be resolved if the solution is requested
1122           """
1123           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1124           self.__solution_isValid=False
1125    
1126       def __invalidateOperator(self):
1127           """
1128           indicates the operator has to be rebuilt next time it is used
1129           """
1130           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1131           self.__invalidateSolution()
1132           self.__operator_is_Valid=False
1133    
1134       def __invalidateRightHandSide(self):
1135           """
1136           indicates the right hand side has to be rebuild next time it is used
1137           """
1138           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1139           self.__invalidateSolution()
1140           self.__righthandside_isValid=False
1141    
1142       def __invalidateSystem(self):
1143           """
1144           annonced that everthing has to be rebuild:
1145           """
1146           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1147           self.__invalidateSolution()
1148           self.__invalidateOperator()
1149           self.__invalidateRightHandSide()
1150    
1151       def __resetSystem(self):
1152           """
1153           annonced that everthing has to be rebuild:
1154           """
1155           self.trace("New System is built from scratch.")
1156           self.__operator=escript.Operator()
1157           self.__operator_is_Valid=False
1158           self.__righthandside=escript.Data()
1159           self.__righthandside_isValid=False
1160           self.__solution=escript.Data()
1161           self.__solution_isValid=False
1162       #
1163       #    system initialization:
1164       #
1165     def __getNewOperator(self):     def __getNewOperator(self):
1166         """         """
1167           returns an instance of a new operator
1168         """         """
1169           self.trace("New operator is allocated.")
1170         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1171                             self.getNumEquations(), \                             self.getNumEquations(), \
1172                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1174  class LinearPDE:
1174                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1175                             self.__matrix_type)                             self.__matrix_type)
1176    
1177     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1178         """         """
1179           returns an instance of a new right hand side
1180         """         """
1181         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1182         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1183             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1184         else:         else:
1185             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1186    
1187     def __getNewSolution(self):     def __getNewSolution(self):
1188         """         """
1189           returns an instance of a new solution
1190         """         """
1191         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1192         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1193             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1194         else:         else:
1195             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1196    
1197       def __makeFreshSolution(self):
1198           """
1199           makes sure that the solution is instantiated and returns it initialized by zeros
1200           """
1201           if self.__solution.isEmpty():
1202               self.__solution=self.__getNewSolution()
1203           else:
1204               self.__solution*=0
1205               self.trace("Solution is reset to zero.")
1206           return self.__solution
1207    
1208       def __makeFreshRightHandSide(self):
1209           """
1210           makes sure that the right hand side is instantiated and returns it initialized by zeros
1211           """
1212           if self.__righthandside.isEmpty():
1213               self.__righthandside=self.__getNewRightHandSide()
1214           else:
1215               self.__righthandside*=0
1216               self.trace("Right hand side is reset to zero.")
1217           return self.__righthandside
1218    
1219     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1220         """         """
1221           makes sure that the operator is instantiated and returns it initialized by zeros
1222         """         """
1223         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1224             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1225         else:         else:
1226             self.__operator.setValue(0.)             self.__operator.resetValues()
1227             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1228         return self.__operator         return self.__operator
1229    
1230     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1231     def getDomain(self):         """
1232           applies the constraints defined by q and r to the system
1233           """
1234           if not self.isUsingLumping():
1235              q=self.getCoefficientOfGeneralPDE("q")
1236              r=self.getCoefficientOfGeneralPDE("r")
1237              if not q.isEmpty() and not self.__operator.isEmpty():
1238                 # q is the row and column mask to indicate where constraints are set:
1239                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1240                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1241                 u=self.__getNewSolution()
1242                 if r.isEmpty():
1243                    r_s=self.__getNewSolution()
1244                 else:
1245                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1246                 u.copyWithMask(r_s,col_q)
1247                 if not self.__righthandside.isEmpty():
1248                    self.__righthandside-=self.__operator*u
1249                    self.__righthandside=self.copyConstraint(self.__righthandside)
1250                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1251       # =============================================================================
1252       # function giving access to coefficients of the general PDE:
1253       # =============================================================================
1254       def getCoefficientOfGeneralPDE(self,name):
1255         """
1256         return the value of the coefficient name of the general PDE.
1257    
1258         @note: This method is called by the assembling routine it can be overwritten
1259               to map coefficients of a particular PDE to the general PDE.
1260         @param name: name of the coefficient requested.
1261         @type name: C{string}
1262         @return: the value of the coefficient  name
1263         @rtype: L{Data<escript.Data>}
1264         @raise IllegalCoefficient: if name is not one of coefficients
1265                      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}.
1266       """       """
1267       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1268            return self.getCoefficient(name)
1269         else:
1270            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1271    
1272       def hasCoefficientOfGeneralPDE(self,name):
1273       """       """
1274       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1275    
1276         @param name: name of the coefficient enquired.
1277         @type name: C{string}
1278         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1279         @rtype: C{bool}
1280    
    def getDim(self):  
1281       """       """
1282       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1283    
1284       def createCoefficientOfGeneralPDE(self,name):
1285       """       """
1286       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1287    
1288     def getNumEquations(self):       @param name: name of the coefficient requested.
1289         @type name: C{string}
1290         @return: a coefficient name initialized to 0.
1291         @rtype: L{Data<escript.Data>}
1292         @raise IllegalCoefficient: if name is not one of coefficients
1293                      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}.
1294       """       """
1295       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1296            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1297         else:
1298            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1299    
1300       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1301       """       """
1302       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1303           return self.__numEquations  
1304         @param name: name of the coefficient enquired.
1305         @type name: C{string}
1306         @return: the function space to be used for coefficient name
1307         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1308         @raise IllegalCoefficient: if name is not one of coefficients
1309                      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}.
1310         """
1311         if self.hasCoefficientOfGeneralPDE(name):
1312            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1313       else:       else:
1314           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1315    
1316     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1317       """       """
1318       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1319    
1320         @param name: name of the coefficient enquired.
1321         @type name: C{string}
1322         @return: the shape of the coefficient name
1323         @rtype: C{tuple} of C{int}
1324         @raise IllegalCoefficient: if name is not one of coefficients
1325                      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}.
1326       """       """
1327       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1328          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1329       else:       else:
1330          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1331    
1332       # =============================================================================
1333       # functions giving access to coefficients of a particular PDE implementation:
1334       # =============================================================================
1335       def getCoefficient(self,name):
1336         """
1337         returns the value of the coefficient name
1338    
1339     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1340        """       @type name: C{string}
1341        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
1342        """       @rtype: L{Data<escript.Data>}
1343        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1344        out=True       """
1345        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1346           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1347           out=False       else:
1348        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  
1349    
1350     def getFlux(self,u):     def hasCoefficient(self,name):
1351         """       """
1352         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1353    
1354         \f[       @param name: name of the coefficient enquired.
1355         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1356         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1357         @rtype: C{bool}
1358         """
1359         return self.COEFFICIENTS.has_key(name)
1360    
1361         @param u: argument of the operator     def createCoefficient(self, name):
1362         """       """
1363         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1364    
1365     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1366         """       @rtype: L{Data<escript.Data>}
1367         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.
1368         """
1369         if self.hasCoefficient(name):
1370            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1371         else:
1372            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1373    
1374         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1375         """       """
1376         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  
1377    
1378         @param u:       @param name: name of the coefficient enquired.
1379         """       @type name: C{string}
1380         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1381         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1382         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1383         """
1384         if self.hasCoefficient(name):
1385            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1386         else:
1387            raise ValueError,"unknown coefficient %s requested"%name
1388       def getShapeOfCoefficient(self,name):
1389         """
1390         return the shape of the coefficient name
1391    
1392         @param name: name of the coefficient enquired.
1393         @type name: C{string}
1394         @return: the shape of the coefficient name
1395         @rtype: C{tuple} of C{int}
1396         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1397         """
1398         if self.hasCoefficient(name):
1399            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1400         else:
1401            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1402    
1403       def resetCoefficients(self):
1404         """
1405         resets all coefficients to there default values.
1406         """
1407         for i in self.COEFFICIENTS.iterkeys():
1408             self.COEFFICIENTS[i].resetValue()
1409    
1410       def alteredCoefficient(self,name):
1411         """
1412         announce that coefficient name has been changed
1413    
1414     def __setValue(self,**coefficients):       @param name: name of the coefficient enquired.
1415         @type name: C{string}
1416         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1417         @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.
1418         """
1419         if self.hasCoefficient(name):
1420            self.trace("Coefficient %s has been altered."%name)
1421            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1422               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1423               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1424         else:
1425            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1426    
1427       def copyConstraint(self,u):
1428          """
1429          copies the constraint into u and returns u.
1430    
1431          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1432          @type u: L{Data<escript.Data>}
1433          @return: the input u modified by the constraints.
1434          @rtype: L{Data<escript.Data>}
1435          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1436          """
1437          q=self.getCoefficientOfGeneralPDE("q")
1438          r=self.getCoefficientOfGeneralPDE("r")
1439          if not q.isEmpty():
1440             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1441             if r.isEmpty():
1442                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1443             else:
1444                 r=escript.Data(r,u.getFunctionSpace())
1445             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1446          return u
1447    
1448       def setValue(self,**coefficients):
1449        """        """
1450        sets new values to coefficient        sets new values to coefficients
1451    
1452        @param coefficients:        @param coefficients: new values assigned to coefficients
1453          @keyword A: value for coefficient A.
1454          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1455          @keyword B: value for coefficient B
1456          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1457          @keyword C: value for coefficient C
1458          @type C: 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{Function<escript.Function>}.
1461          @keyword X: value for coefficient X
1462          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1463          @keyword Y: value for coefficient Y
1464          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1465          @keyword d: value for coefficient d
1466          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1467          @keyword y: value for coefficient y
1468          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1469          @keyword d_contact: value for coefficient d_contact
1470          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1471                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1472          @keyword y_contact: value for coefficient y_contact
1473          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1474                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1475          @keyword r: values prescribed to the solution at the locations of constraints
1476          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1477                   depending of reduced order is used for the solution.
1478          @keyword q: mask for location of constraints
1479          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1480                   depending of reduced order is used for the representation of the equation.
1481          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1482        """        """
1483        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1484        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1485           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1486              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1487        # 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:
1488        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1489           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1490              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1491                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1495  class LinearPDE:
1495                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1496              if s!=None:              if s!=None:
1497                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1498                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1499                  if res==None:                  if res==None:
1500                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1501                  else:                  else:
1502                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1503                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1504        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1505        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1506        # 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:
1507        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1508          if d==None:          try:
1509               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1510          elif isinstance(d,escript.Data):          except IllegalCoefficientValue,m:
1511               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)  
1512          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()  
   
1513    
1514     def __rebuildOperator(self,deep=False):        self.__altered_coefficients=True
1515         """        # check if the systrem is inhomogeneous:
1516         indicates the operator has to be rebuilt next time it is used        if len(coefficients)>0 and not self.isUsingLumping():
1517         """           q=self.getCoefficientOfGeneralPDE("q")
1518         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."           r=self.getCoefficientOfGeneralPDE("r")
1519         self.__rebuildSolution(deep)           homogeneous_constraint=True
1520         self.__operator_isValid=False           if not q.isEmpty() and not r.isEmpty():
1521         if deep: self.__operator=escript.Operator()               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1522                   self.trace("Inhomogeneous constraint detected.")
1523     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.)  
1524    
1525     def getSystem(self):     def getSystem(self):
1526         """         """
1527         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1528    
1529           @return: the discrete version of the PDE
1530           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1531         """         """
1532         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1533            if self.isUsingLumping():            if self.isUsingLumping():
1534                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1535                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1536                         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"
1537                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1538                            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."  
1539                   mat=self.__getNewOperator()                   mat=self.__getNewOperator()
1540                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   self.getDomain().addPDEToSystem(mat,escript.Data(), \
1541                             self.getCoefficientOfPDE("A"), \                             self.getCoefficientOfGeneralPDE("A"), \
1542                             self.getCoefficientOfPDE("B"), \                             self.getCoefficientOfGeneralPDE("B"), \
1543                             self.getCoefficientOfPDE("C"), \                             self.getCoefficientOfGeneralPDE("C"), \
1544                             self.getCoefficientOfPDE("D"), \                             self.getCoefficientOfGeneralPDE("D"), \
1545                             escript.Data(), \                             escript.Data(), \
1546                             escript.Data(), \                             escript.Data(), \
1547                             self.getCoefficientOfPDE("d"), \                             self.getCoefficientOfGeneralPDE("d"), \
1548                             escript.Data(),\                             escript.Data(),\
1549                             self.getCoefficientOfPDE("d_contact"), \                             self.getCoefficientOfGeneralPDE("d_contact"), \
1550                             escript.Data())                             escript.Data())
1551                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1552                   self.__applyConstraint()                   del mat
1553                   self.__operator_isValid=True                   self.trace("New lumped operator has been built.")
1554                     self.__operator_is_Valid=True
1555                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1556                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1557                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1558                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1559                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1560                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1561                   self.__copyConstraint()                   self.trace("New right hand side as been built.")
1562                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1563            else:            else:
1564               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."  
1565                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1566                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1567                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1568                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1569                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1570                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1571                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1572                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1573                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1574                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1575                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1576                   self.__applyConstraint()                   self.__applyConstraint()
1577                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1578                   self.__operator_isValid=True                   self.trace("New system has been built.")
1579                     self.__operator_is_Valid=True
1580                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1581               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1582                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1583                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1584                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1585                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1586                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1587                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1588                     self.trace("New right hand side has been built.")
1589                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1590               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1591                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1592                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1593                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1594                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1595                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1596                              escript.Data(), \                              escript.Data(), \
1597                              escript.Data(), \                              escript.Data(), \
1598                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1599                              escript.Data(),\                              escript.Data(),\
1600                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1601                              escript.Data())                              escript.Data())
1602                   self.__applyConstraint()                   self.__applyConstraint()
1603                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1604                     self.__operator_is_Valid=True
1605         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1606    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1607    
1608     def solve(self,**options):  class Poisson(LinearPDE):
1609        """     """
1610        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1611    
1612        @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  
1613    
1614     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
1615    
1616         @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  
1617    
1618       and constraints:
1619    
1620       M{u=0} where M{q>0}
1621    
1622  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)  
1623    
1624  def HALF(P):     def __init__(self,domain,debug=False):
1625      """ """       """
1626      return escript.Scalar(0.5,P.getFunctionSpace())       initializes a new Poisson equation
1627    
1628         @param domain: domain of the PDE
1629         @type domain: L{Domain<escript.Domain>}
1630         @param debug: if True debug informations are printed.
1631    
1632         """
1633         super(Poisson, self).__init__(domain,1,1,debug)
1634         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1635                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1636         self.setSymmetryOn()
1637    
1638       def setValue(self,**coefficients):
1639         """
1640         sets new values to coefficients
1641    
1642         @param coefficients: new values assigned to coefficients
1643         @keyword f: value for right hand side M{f}
1644         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1645         @keyword q: mask for location of constraints
1646         @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>}
1647                   depending of reduced order is used for the representation of the equation.
1648         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1649         """
1650         super(Poisson, self).setValue(**coefficients)
1651    
1652       def getCoefficientOfGeneralPDE(self,name):
1653         """
1654         return the value of the coefficient name of the general PDE
1655         @param name: name of the coefficient requested.
1656         @type name: C{string}
1657         @return: the value of the coefficient  name
1658         @rtype: L{Data<escript.Data>}
1659         @raise IllegalCoefficient: if name is not one of coefficients
1660                      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}.
1661         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1662         """
1663         if name == "A" :
1664             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1665         elif name == "B" :
1666             return escript.Data()
1667         elif name == "C" :
1668             return escript.Data()
1669         elif name == "D" :
1670             return escript.Data()
1671         elif name == "X" :
1672             return escript.Data()
1673         elif name == "Y" :
1674             return self.getCoefficient("f")
1675         elif name == "d" :
1676             return escript.Data()
1677         elif name == "y" :
1678             return escript.Data()
1679         elif name == "d_contact" :
1680             return escript.Data()
1681         elif name == "y_contact" :
1682             return escript.Data()
1683         elif name == "r" :
1684             return escript.Data()
1685         elif name == "q" :
1686             return self.getCoefficient("q")
1687         else:
1688            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1689    
1690    class Helmholtz(LinearPDE):
1691       """
1692       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1693    
1694       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1695    
1696       with natural boundary conditons
1697    
1698       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1699    
1700       and constraints:
1701    
1702       M{u=r} where M{q>0}
1703    
 class AdvectivePDE(LinearPDE):  
1704     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1705    
1706     \f[     def __init__(self,domain,debug=False):
1707     -(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       """
1708     \f]       initializes a new Poisson equation
1709    
1710     with boundary conditons:       @param domain: domain of the PDE
1711         @type domain: L{Domain<escript.Domain>}
1712         @param debug: if True debug informations are printed.
1713    
1714         """
1715         super(Helmholtz, self).__init__(domain,1,1,debug)
1716         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1717                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1718                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1719                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1720                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1721                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1722                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1723         self.setSymmetryOn()
1724    
1725     \f[     def setValue(self,**coefficients):
1726     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       """
1727     \f]       sets new values to coefficients
1728    
1729     and contact conditions       @param coefficients: new values assigned to coefficients
1730         @keyword omega: value for coefficient M{S{omega}}
1731         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1732         @keyword k: value for coefficeint M{k}
1733         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1734         @keyword f: value for right hand side M{f}
1735         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1736         @keyword alpha: value for right hand side M{S{alpha}}
1737         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1738         @keyword g: value for right hand side M{g}
1739         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1740         @keyword r: prescribed values M{r} for the solution in constraints.
1741         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1742                   depending of reduced order is used for the representation of the equation.
1743         @keyword q: mask for location of constraints
1744         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1745                   depending of reduced order is used for the representation of the equation.
1746         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1747         """
1748         super(Helmholtz, self).setValue(**coefficients)
1749    
1750     \f[     def getCoefficientOfGeneralPDE(self,name):
1751     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}       """
1752     \f]       return the value of the coefficient name of the general PDE
1753    
1754         @param name: name of the coefficient requested.
1755         @type name: C{string}
1756         @return: the value of the coefficient  name
1757         @rtype: L{Data<escript.Data>}
1758         @raise IllegalCoefficient: if name is not one of coefficients
1759                      "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}.
1760         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1761         """
1762         if name == "A" :
1763             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1764         elif name == "B" :
1765             return escript.Data()
1766         elif name == "C" :
1767             return escript.Data()
1768         elif name == "D" :
1769             return self.getCoefficient("omega")
1770         elif name == "X" :
1771             return escript.Data()
1772         elif name == "Y" :
1773             return self.getCoefficient("f")
1774         elif name == "d" :
1775             return self.getCoefficient("alpha")
1776         elif name == "y" :
1777             return self.getCoefficient("g")
1778         elif name == "d_contact" :
1779             return escript.Data()
1780         elif name == "y_contact" :
1781             return escript.Data()
1782         elif name == "r" :
1783             return self.getCoefficient("r")
1784         elif name == "q" :
1785             return self.getCoefficient("q")
1786         else:
1787            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1788    
1789    class LameEquation(LinearPDE):
1790       """
1791       Class to define a Lame equation problem:
1792    
1793       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] }
1794    
1795       with natural boundary conditons:
1796    
1797       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] }
1798    
1799     and constraints:     and constraints:
1800    
1801     \f[     M{u[i]=r[i]} where M{q[i]>0}
1802     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1803     """     """
1804     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
1805        LinearPDE.__init__(self,domain,numEquations,numSolutions)     def __init__(self,domain,debug=False):
1806        self.__xi=xi        super(LameEquation, self).__init__(domain,\
1807                                             domain.getDim(),domain.getDim(),debug)
1808          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1809                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1810                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1811                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1812                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1813                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1814                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1815          self.setSymmetryOn()
1816    
1817       def setValue(self,**coefficients):
1818         """
1819         sets new values to coefficients
1820    
1821         @param coefficients: new values assigned to coefficients
1822         @keyword lame_mu: value for coefficient M{S{mu}}
1823         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1824         @keyword lame_lambda: value for coefficient M{S{lambda}}
1825         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1826         @keyword F: value for internal force M{F}
1827         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1828         @keyword sigma: value for initial stress M{S{sigma}}
1829         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1830         @keyword f: value for extrenal force M{f}
1831         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1832         @keyword r: prescribed values M{r} for the solution in constraints.
1833         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1834                   depending of reduced order is used for the representation of the equation.
1835         @keyword q: mask for location of constraints
1836         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1837                   depending of reduced order is used for the representation of the equation.
1838         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1839         """
1840         super(LameEquation, self).setValue(**coefficients)
1841    
1842       def getCoefficientOfGeneralPDE(self,name):
1843         """
1844         return the value of the coefficient name of the general PDE
1845    
1846         @param name: name of the coefficient requested.
1847         @type name: C{string}
1848         @return: the value of the coefficient  name
1849         @rtype: L{Data<escript.Data>}
1850         @raise IllegalCoefficient: if name is not one of coefficients
1851                      "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}.
1852         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1853         """
1854         if name == "A" :
1855             out =self.createCoefficientOfGeneralPDE("A")
1856             for i in range(self.getDim()):
1857               for j in range(self.getDim()):
1858                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1859                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1860                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1861             return out
1862         elif name == "B" :
1863             return escript.Data()
1864         elif name == "C" :
1865             return escript.Data()
1866         elif name == "D" :
1867             return escript.Data()
1868         elif name == "X" :
1869             return self.getCoefficient("sigma")
1870         elif name == "Y" :
1871             return self.getCoefficient("F")
1872         elif name == "d" :
1873             return escript.Data()
1874         elif name == "y" :
1875             return self.getCoefficient("f")
1876         elif name == "d_contact" :
1877             return escript.Data()
1878         elif name == "y_contact" :
1879             return escript.Data()
1880         elif name == "r" :
1881             return self.getCoefficient("r")
1882         elif name == "q" :
1883             return self.getCoefficient("q")
1884         else:
1885            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1886    
1887    class AdvectivePDE(LinearPDE):
1888       """
1889       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1890       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1891    
1892       In the following we set
1893    
1894       M{Z[j]=C[j]-B[j]}
1895    
1896       or
1897    
1898       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1899    
1900       To measure the dominance of the advective terms over the diffusive term M{A} the
1901       X{Pelclet number} M{P} is used. It is defined as
1902    
1903       M{P=h|Z|/(2|A|)}
1904    
1905       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1906       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1907    
1908       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1909    
1910       M{S{Xi}=S{xi}(P) h/|Z|}
1911    
1912       where M{S{xi}} is a suitable function of the Peclet number.
1913    
1914       In the case of a single PDE the coefficient are up-dated in the following way:
1915             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1916             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1917             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1918             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1919    
1920       Similar for the case of a systems of PDEs:
1921             - 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]}
1922             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1923             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1924             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1925    
1926       where M{S{delta}} is L{kronecker}.
1927       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1928       but with the intension to stabilize the solution.
1929    
1930       """
1931       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1932          """
1933          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1934    
1935          @param domain: domain of the PDE
1936          @type domain: L{Domain<escript.Domain>}
1937          @param numEquations: number of equations. If numEquations==None the number of equations
1938                               is exracted from the PDE coefficients.
1939          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1940                               is exracted from the PDE coefficients.
1941          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1942                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1943          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1944          @param debug: if True debug informations are printed.
1945          """
1946          super(AdvectivePDE, self).__init__(domain,\
1947                                             numEquations,numSolutions,debug)
1948          if xi==None:
1949             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1950          else:
1951             self.__xi=xi
1952        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1953    
1954     def __calculateXi(self,peclet_factor,Z,h):     def setValue(**coefficients):
1955         Z_max=util.Lsup(Z)        """
1956         if Z_max>0.:        sets new values to coefficients
1957            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1958          @param coefficients: new values assigned to coefficients
1959          @keyword A: value for coefficient A.
1960          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1961          @keyword B: value for coefficient B
1962          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1963          @keyword C: value for coefficient C
1964          @type C: 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{Function<escript.Function>}.
1967          @keyword X: value for coefficient X
1968          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1969          @keyword Y: value for coefficient Y
1970          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1971          @keyword d: value for coefficient d
1972          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1973          @keyword y: value for coefficient y
1974          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1975          @keyword d_contact: value for coefficient d_contact
1976          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1977                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1978          @keyword y_contact: value for coefficient y_contact
1979          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1980                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1981          @keyword r: values prescribed to the solution at the locations of constraints
1982          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1983                   depending of reduced order is used for the solution.
1984          @keyword q: mask for location of constraints
1985          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1986                   depending of reduced order is used for the representation of the equation.
1987          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1988    
1989          """
1990          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1991          super(AdvectivePDE, self).setValue(**coefficients)
1992    
1993       def ELMAN_RAMAGE(self,P):
1994         """
1995         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1996         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1997              - M{S{xi}(P)=0} for M{P<1}
1998              - M{S{xi}(P)=(1-1/P)/2} otherwise
1999    
2000         @param P: Preclet number
2001         @type P: L{Scalar<escript.Scalar>}
2002         @return: up-wind weightimg factor
2003         @rtype: L{Scalar<escript.Scalar>}
2004         """
2005         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2006    
2007       def SIMPLIFIED_BROOK_HUGHES(self,P):
2008         """
2009         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2010         The original methods is
2011    
2012         M{S{xi}(P)=coth(P)-1/P}
2013    
2014         As the evaluation of M{coth} is expensive we are using the approximation:
2015    
2016             - M{S{xi}(P)=P/3} where M{P<3}
2017             - M{S{xi}(P)=1/2} otherwise
2018    
2019         @param P: Preclet number
2020         @type P: L{Scalar<escript.Scalar>}
2021         @return: up-wind weightimg factor
2022         @rtype: L{Scalar<escript.Scalar>}
2023         """
2024         c=util.whereNegative(P-3.)
2025         return P/6.*c+1./2.*(1.-c)
2026    
2027       def HALF(self,P):
2028         """
2029         Predefined function to set value M{1/2} for M{S{xi}}
2030    
2031         @param P: Preclet number
2032         @type P: L{Scalar<escript.Scalar>}
2033         @return: up-wind weightimg factor
2034         @rtype: L{Scalar<escript.Scalar>}
2035         """
2036         return escript.Scalar(0.5,P.getFunctionSpace())
2037    
2038       def __calculateXi(self,peclet_factor,flux,h):
2039           flux=util.Lsup(flux)
2040           if flux_max>0.:
2041              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2042         else:         else:
2043            return 0.            return 0.
2044    
2045     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):  
2046        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2047           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2048           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1060  class AdvectivePDE(LinearPDE): Line 2051  class AdvectivePDE(LinearPDE):
2051           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2052           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2053              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
2054                  Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))                  flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2055                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2056                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2057                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2058                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2059                              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
2060                          # flux=C-util.reorderComponents(B,[0,2,1])
2061                     else:                     else:
2062                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2063                           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
2064                          # flux=C-B
2065                  else:                  else:
2066                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2067                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2068                           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
2069                          # flux=C-util.reorderComponents(B,[1,0])
2070                     else:                     else:
2071                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2072                  length_of_Z=util.sqrt(Z2)                        #flux=C-B
2073                    length_of_flux=util.sqrt(flux2)
2074              elif C.isEmpty():              elif C.isEmpty():
2075                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2076                  #flux=B
2077              else:              else:
2078                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2079                  #flux=C
2080    
2081              Z_max=util.Lsup(length_of_Z)              #length_of_flux=util.length(flux)
2082              if Z_max>0.:              flux_max=util.Lsup(length_of_flux)
2083                if flux_max>0.:
2084                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2085                 length_of_A=util.length(A)                 length_of_A=util.length(A)
2086                 A_max=util.Lsup(length_of_A)                 A_max=util.Lsup(length_of_A)
2087                 if A_max>0:                 if A_max>0:
2088                      inv_A=1./(length_of_A+A_max*self.TOL)                      inv_A=1./(length_of_A+A_max*self.__TOL)
2089                 else:                 else:
2090                      inv_A=1./self.TOL                      inv_A=1./self.__TOL
2091                 peclet_number=length_of_Z*h/2*inv_A                 peclet_number=length_of_flux*h/2*inv_A
2092                 xi=self.__xi(peclet_number)                 xi=self.__xi(peclet_number)
2093                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2094                 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))
2095        return self.__Xi        return self.__Xi
         
2096    
2097     def getCoefficientOfPDE(self,name):  
2098       def getCoefficientOfGeneralPDE(self,name):
2099       """       """
2100       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2101    
2102       @param name:       @param name: name of the coefficient requested.
2103         @type name: C{string}
2104         @return: the value of the coefficient name
2105         @rtype: L{Data<escript.Data>}
2106         @raise IllegalCoefficient: if name is not one of coefficients
2107                      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}.
2108         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2109       """       """
2110       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2111            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."
2112    
2113       if name == "A" :       if name == "A" :
2114           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2115           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2116           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2117           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2118              Aout=A              Aout=A
2119           else:           else:
2120              if A.isEmpty():              if A.isEmpty():
2121                 Aout=self.createNewCoefficient("A")                 Aout=self.createNewCoefficient("A")
2122              else:              else:
2123                 Aout=A[:]                 Aout=A[:]
2124              Xi=self.getXi()              Xi=self.__getXi()
2125              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2126                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2127                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2128                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2129                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2130                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2131                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2132                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2133                                 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])
2134                              elif C.isEmpty():                              elif C.isEmpty():
2135                                 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]
2136                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2137                              else:                              else:
2138                                 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]
2139                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2140              else:              else:
2141                  for j in range(self.getDim()):                  for j in range(self.getDim()):
2142                     for l in range(self.getDim()):                     for l in range(self.getDim()):
# Line 1137  class AdvectivePDE(LinearPDE): Line 2146  class AdvectivePDE(LinearPDE):
2146                            Aout[j,l]+=Xi*B[j]*B[l]                            Aout[j,l]+=Xi*B[j]*B[l]
2147                        else:                        else:
2148                            Aout[j,l]+=Xi*C[j]*C[l]                            Aout[j,l]+=Xi*C[j]*C[l]
2149                     # if not C.isEmpty() and not B.isEmpty():
2150                     #    tmp=C-B
2151                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2152                     # elif C.isEmpty():
2153                     #    Aout=Aout+Xi*util.outer(B,B)
2154                     # else:
2155                     # Aout=Aout+Xi*util.outer(C,C)
2156           return Aout           return Aout
2157       elif name == "B" :       elif name == "B" :
2158           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2159           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2160           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2161           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2162              Bout=B              Bout=B
2163           else:           else:
2164              Xi=self.getXi()              Xi=self.__getXi()
2165              if B.isEmpty():              if B.isEmpty():
2166                  Bout=self.createNewCoefficient("B")                  Bout=self.createNewCoefficient("B")
2167              else:              else:
2168                  Bout=B[:]                  Bout=B[:]
2169              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2170                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2171                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2172                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2173                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2174                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2175                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2176                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2177              else:              else:
2178                 tmp=Xi*D                 tmp=Xi*D
2179                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2180                   # Bout=Bout+Xi*D*C
2181           return Bout           return Bout
2182       elif name == "C" :       elif name == "C" :
2183           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2184           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2185           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2186           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2187              Cout=C              Cout=C
2188           else:           else:
2189              Xi=self.getXi()              Xi=self.__getXi()
2190              if C.isEmpty():              if C.isEmpty():
2191                  Cout=self.createNewCoefficient("C")                  Cout=self.createNewCoefficient("C")
2192              else:              else:
2193                  Cout=C[:]                  Cout=C[:]
# Line 1180  class AdvectivePDE(LinearPDE): Line 2198  class AdvectivePDE(LinearPDE):
2198                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2199                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2200                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2201                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2202              else:              else:
2203                 tmp=Xi*D                 tmp=Xi*D
2204                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2205                   # Cout=Cout+tmp*D*B
2206           return Cout           return Cout
2207       elif name == "D" :       elif name == "D" :
2208           return self.getCoefficient("D")           return self.getCoefficient("D")
2209       elif name == "X" :       elif name == "X" :
2210           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2211           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2212           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1198  class AdvectivePDE(LinearPDE): Line 2218  class AdvectivePDE(LinearPDE):
2218                  Xout=self.createNewCoefficient("X")                  Xout=self.createNewCoefficient("X")
2219              else:              else:
2220                  Xout=X[:]                  Xout=X[:]
2221              Xi=self.getXi()              Xi=self.__getXi()
2222              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2223                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2224                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2225                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2226                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2227                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2228                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2229                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2230                            elif C.isEmpty():                            elif C.isEmpty():
2231                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2232                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2233                            else:                            else:
2234                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2235                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2236              else:              else:
2237                   tmp=Xi*Y                   tmp=Xi*Y
2238                   for j in range(self.getDim()):                   for j in range(self.getDim()):
2239                      if not C.isEmpty() and not B.isEmpty():                      if not C.isEmpty() and not B.isEmpty():
2240                         Xout[j]+=tmp*(C[j]-B[j])                         Xout[j]+=tmp*(C[j]-B[j])
2241                           # Xout=Xout+Xi*Y*(C-B)
2242                      elif C.isEmpty():                      elif C.isEmpty():
2243                         Xout[j]-=tmp*B[j]                         Xout[j]-=tmp*B[j]
2244                           # Xout=Xout-Xi*Y*B
2245                      else:                      else:
2246                         Xout[j]+=tmp*C[j]                         Xout[j]+=tmp*C[j]
2247                           # Xout=Xout+Xi*Y*C
2248           return Xout           return Xout
2249       elif name == "Y" :       elif name == "Y" :
2250           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2251       elif name == "d" :       elif name == "d" :
2252           return self.getCoefficient("d")           return self.getCoefficient("d")
2253       elif name == "y" :       elif name == "y" :
2254           return self.getCoefficient("y")           return self.getCoefficient("y")
2255       elif name == "d_contact" :       elif name == "d_contact" :
2256           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2257       elif name == "y_contact" :       elif name == "y_contact" :
2258           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2259       elif name == "r" :       elif name == "r" :
2260           return self.getCoefficient("r")           return self.getCoefficient("r")
2261       elif name == "q" :       elif name == "q" :
2262           return self.getCoefficient("q")           return self.getCoefficient("q")
2263       else:       else:
2264           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2265    
2266  class Poisson(LinearPDE):  class AdvectionDiffusion(LinearPDE):
2267     """     """
2268     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
2269    
2270       M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
2271    
2272       with natural boundary conditons
2273    
2274     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]  
2275    
2276     and constraints:     and constraints:
2277    
2278     \f[     M{u=r} where M{q>0}
2279     u=0 \quad \mathrm{where} \quad q>0  
2280     \f]     and
2281    
2282       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2283    
2284     """     """
2285    
2286     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2287         LinearPDE.__init__(self,domain,1,1)       """
2288         self.COEFFICIENTS={       initializes a new Poisson equation
2289         "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
2290         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}       @param domain: domain of the PDE
2291         self.setSymmetryOn()       @type domain: L{Domain<escript.Domain>}
2292         self.setValue(f,q)       @param debug: if True debug informations are printed.
2293    
2294         """
2295         super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2296         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2297                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2298                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2299                            "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2300                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2301                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2302                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2303                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2304                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2305    
2306     def setValue(self,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
2307         self._LinearPDE__setValue(f=f,q=q)       """
2308         sets new values to coefficients
2309    
2310     def getCoefficientOfPDE(self,name):       @param coefficients: new values assigned to coefficients
2311         @keyword omega: value for coefficient M{S{omega}}
2312         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2313         @keyword k: value for coefficient M{k}
2314         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2315         @keyword v: value for coefficient M{v}
2316         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2317         @keyword upwind: value for upwind term M{upwind}
2318         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2319         @keyword f: value for right hand side M{f}
2320         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2321         @keyword alpha: value for right hand side M{S{alpha}}
2322         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2323         @keyword g: value for right hand side M{g}
2324         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2325         @keyword r: prescribed values M{r} for the solution in constraints.
2326         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2327                   depending of reduced order is used for the representation of the equation.
2328         @keyword q: mask for location of constraints
2329         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2330                   depending of reduced order is used for the representation of the equation.
2331         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2332       """       """
2333       return the value of the coefficient name of the general PDE       super(AdvectionDiffusion, self).setValue(**coefficients)
2334    
2335       @param name:     def getCoefficientOfGeneralPDE(self,name):
2336       """       """
2337       if name == "A" :       return the value of the coefficient name of the general PDE
2338           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
2339       elif name == "B" :       @param name: name of the coefficient requested.
2340           return escript.Data()       @type name: C{string}
2341       elif name == "C" :       @return: the value of the coefficient  name
2342           return escript.Data()       @rtype: L{Data<escript.Data>}
2343       elif name == "D" :       @raise IllegalCoefficient: if name is not one of coefficients
2344                      "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}.
2345         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2346         """
2347         if name == "A" :
2348             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2349         elif name == "B" :
2350           return escript.Data()           return escript.Data()
2351       elif name == "X" :       elif name == "C" :
2352             return self.getCoefficient("v")
2353         elif name == "D" :
2354             return self.getCoefficient("omega")
2355         elif name == "X" :
2356           return escript.Data()           return escript.Data()
2357       elif name == "Y" :       elif name == "Y" :
2358           return self.getCoefficient("f")           return self.getCoefficient("f")
2359       elif name == "d" :       elif name == "d" :
2360           return escript.Data()           return self.getCoefficient("alpha")
2361       elif name == "y" :       elif name == "y" :
2362           return escript.Data()           return self.getCoefficient("g")
2363       elif name == "d_contact" :       elif name == "d_contact" :
2364           return escript.Data()           return escript.Data()
2365       elif name == "y_contact" :       elif name == "y_contact" :
2366           return escript.Data()           return escript.Data()
2367       elif name == "r" :       elif name == "r" :
2368           return escript.Data()           return self.getCoefficient("r")
2369       elif name == "q" :       elif name == "q" :
2370           return self.getCoefficient("q")           return self.getCoefficient("q")
2371       else:       else:
2372           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2373    
2374    
2375  # $Log$  # $Log$
2376  # Revision 1.8  2005/06/09 05:37:59  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2377  # 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
2378    #
2379    # Revision 1.13  2005/09/15 03:44:19  jgs
2380    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2381    #
2382    # Revision 1.12  2005/09/01 03:31:28  jgs
2383    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2384    #
2385    # Revision 1.11  2005/08/23 01:24:28  jgs
2386    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2387  #  #
2388  # Revision 1.7  2005/05/06 04:26:10  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2389  # 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
2390    #
2391    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2392    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2393    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2394    # modified to instead use portable/cooperative "super" calls to extend base
2395    # class methods.
2396    #
2397    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2398    # Removed redundant if-loop.
2399    #
2400    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2401    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2402    #
2403    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2404    # the solver from finley are put into the standalone package paso now
2405    #
2406    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2407    # in the case of lumping no new system is allocated if the constraint is changed.
2408    #
2409    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2410    # test for Lumping added
2411    #
2412    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2413    # bug in format fixed.
2414    #
2415    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2416    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2417    #
2418    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2419    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2420    #
2421    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2422    # gneric unit testing for linearPDE
2423    #
2424    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2425    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2426    #
2427    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2428    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2429    #
2430    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2431    # epydoc mark up partially fixed
2432    #
2433    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2434    # some problems with LinearPDEs fixed.
2435    #
2436    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2437    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2438    #
2439    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2440    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2441    #
2442    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2443    # new functions in util and a new pde type in linearPDEs
2444    #
2445    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2446    # Lame equation: (linear elastic, isotropic) added
2447    #
2448    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2449    # some extensions to modellib and linearPDEs
2450  #  #
2451  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2452  # 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 2557  class Poisson(LinearPDE):
2557  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2558  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2559  #  #
 #  

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