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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 531 by gross, Wed Feb 15 08:11:10 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():
1536                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1537                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1538                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1539                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1540                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1541                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1542                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1543                   if self.debug() : print "PDE Debug: New lumped operator is built."                   D=self.getCoefficientOfGeneralPDE("D")
1544                   mat=self.__getNewOperator()                   if not D.isEmpty():
1545                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                       if self.getNumSolutions()>1:
1546                             self.getCoefficientOfPDE("A"), \                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1547                             self.getCoefficientOfPDE("B"), \                       else:
1548                             self.getCoefficientOfPDE("C"), \                          D_times_e=D
1549                             self.getCoefficientOfPDE("D"), \                   else:
1550                             escript.Data(), \                      D_times_e=escript.Data()
1551                             escript.Data(), \                   d=self.getCoefficientOfGeneralPDE("d")
1552                             self.getCoefficientOfPDE("d"), \                   if not d.isEmpty():
1553                             escript.Data(),\                       if self.getNumSolutions()>1:
1554                             self.getCoefficientOfPDE("d_contact"), \                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1555                             escript.Data())                       else:
1556                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                          d_times_e=d
1557                   self.__applyConstraint()                   else:
1558                   self.__operator_isValid=True                      d_times_e=escript.Data()
1559                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1560                     if not d_contact.isEmpty():
1561                         if self.getNumSolutions()>1:
1562                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1563                         else:
1564                            d_contact_times_e=d_contact
1565                     else:
1566                        d_contact_times_e=escript.Data()
1567        
1568                     self.__operator=self.__getNewRightHandSide()
1569                     self.getDomain().addPDEToRHS(self.__operator, \
1570                                                  escript.Data(), \
1571                                                  D_times_e, \
1572                                                  d_times_e,\
1573                                                  d_contact_times_e)
1574                     self.__operator=1./self.__operator
1575                     self.trace("New lumped operator has been built.")
1576                     self.__operator_is_Valid=True
1577                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1578                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1579                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1580                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1581                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1582                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1583                   self.__copyConstraint()                   self.trace("New right hand side as been built.")
1584                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1585            else:            else:
1586               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."  
1587                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1588                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1589                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1590                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1591                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1592                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1593                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1594                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1595                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1596                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1597                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1598                   self.__applyConstraint()                   self.__applyConstraint()
1599                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1600                   self.__operator_isValid=True                   self.trace("New system has been built.")
1601                     self.__operator_is_Valid=True
1602                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1603               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1604                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1605                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1606                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1607                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1608                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1609                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1610                     self.trace("New right hand side has been built.")
1611                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1612               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1613                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1614                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1615                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1616                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1617                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1618                              escript.Data(), \                              escript.Data(), \
1619                              escript.Data(), \                              escript.Data(), \
1620                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d"), \
1621                              escript.Data(),\                              escript.Data(),\
1622                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1623                              escript.Data())                              escript.Data())
1624                   self.__applyConstraint()                   self.__applyConstraint()
1625                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1626                     self.__operator_is_Valid=True
1627         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1628    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
1629    
1630     def solve(self,**options):  class Poisson(LinearPDE):
1631        """     """
1632        solve the PDE     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
1633    
1634        @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  
1635    
1636     def getSolution(self,**options):     with natural boundary conditons
        """  
        returns the solution of the PDE  
1637    
1638         @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  
1639    
1640       and constraints:
1641    
1642       M{u=0} where M{q>0}
1643    
1644  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)  
1645    
1646  def HALF(P):     def __init__(self,domain,debug=False):
1647      """ """       """
1648      return escript.Scalar(0.5,P.getFunctionSpace())       initializes a new Poisson equation
1649    
1650         @param domain: domain of the PDE
1651         @type domain: L{Domain<escript.Domain>}
1652         @param debug: if True debug informations are printed.
1653    
1654         """
1655         super(Poisson, self).__init__(domain,1,1,debug)
1656         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1657                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1658         self.setSymmetryOn()
1659    
1660       def setValue(self,**coefficients):
1661         """
1662         sets new values to coefficients
1663    
1664         @param coefficients: new values assigned to coefficients
1665         @keyword f: value for right hand side M{f}
1666         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1667         @keyword q: mask for location of constraints
1668         @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>}
1669                   depending of reduced order is used for the representation of the equation.
1670         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1671         """
1672         super(Poisson, self).setValue(**coefficients)
1673    
1674       def getCoefficientOfGeneralPDE(self,name):
1675         """
1676         return the value of the coefficient name of the general PDE
1677         @param name: name of the coefficient requested.
1678         @type name: C{string}
1679         @return: the value of the coefficient  name
1680         @rtype: L{Data<escript.Data>}
1681         @raise IllegalCoefficient: if name is not one of coefficients
1682                      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}.
1683         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1684         """
1685         if name == "A" :
1686             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1687         elif name == "B" :
1688             return escript.Data()
1689         elif name == "C" :
1690             return escript.Data()
1691         elif name == "D" :
1692             return escript.Data()
1693         elif name == "X" :
1694             return escript.Data()
1695         elif name == "Y" :
1696             return self.getCoefficient("f")
1697         elif name == "d" :
1698             return escript.Data()
1699         elif name == "y" :
1700             return escript.Data()
1701         elif name == "d_contact" :
1702             return escript.Data()
1703         elif name == "y_contact" :
1704             return escript.Data()
1705         elif name == "r" :
1706             return escript.Data()
1707         elif name == "q" :
1708             return self.getCoefficient("q")
1709         else:
1710            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1711    
1712    class Helmholtz(LinearPDE):
1713       """
1714       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1715    
1716       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1717    
1718       with natural boundary conditons
1719    
1720       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1721    
1722       and constraints:
1723    
1724       M{u=r} where M{q>0}
1725    
 class AdvectivePDE(LinearPDE):  
1726     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1727    
1728     \f[     def __init__(self,domain,debug=False):
1729     -(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       """
1730     \f]       initializes a new Poisson equation
1731    
1732     with boundary conditons:       @param domain: domain of the PDE
1733         @type domain: L{Domain<escript.Domain>}
1734         @param debug: if True debug informations are printed.
1735    
1736         """
1737         super(Helmholtz, self).__init__(domain,1,1,debug)
1738         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1739                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1740                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1741                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1742                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1743                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1744                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1745         self.setSymmetryOn()
1746    
1747     \f[     def setValue(self,**coefficients):
1748     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i       """
1749     \f]       sets new values to coefficients
1750    
1751     and contact conditions       @param coefficients: new values assigned to coefficients
1752         @keyword omega: value for coefficient M{S{omega}}
1753         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1754         @keyword k: value for coefficeint M{k}
1755         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1756         @keyword f: value for right hand side M{f}
1757         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1758         @keyword alpha: value for right hand side M{S{alpha}}
1759         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1760         @keyword g: value for right hand side M{g}
1761         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1762         @keyword r: prescribed values M{r} for the solution in constraints.
1763         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1764                   depending of reduced order is used for the representation of the equation.
1765         @keyword q: mask for location of constraints
1766         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1767                   depending of reduced order is used for the representation of the equation.
1768         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1769         """
1770         super(Helmholtz, self).setValue(**coefficients)
1771    
1772     \f[     def getCoefficientOfGeneralPDE(self,name):
1773     n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}       """
1774     \f]       return the value of the coefficient name of the general PDE
1775    
1776         @param name: name of the coefficient requested.
1777         @type name: C{string}
1778         @return: the value of the coefficient  name
1779         @rtype: L{Data<escript.Data>}
1780         @raise IllegalCoefficient: if name is not one of coefficients
1781                      "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}.
1782         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1783         """
1784         if name == "A" :
1785             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1786         elif name == "B" :
1787             return escript.Data()
1788         elif name == "C" :
1789             return escript.Data()
1790         elif name == "D" :
1791             return self.getCoefficient("omega")
1792         elif name == "X" :
1793             return escript.Data()
1794         elif name == "Y" :
1795             return self.getCoefficient("f")
1796         elif name == "d" :
1797             return self.getCoefficient("alpha")
1798         elif name == "y" :
1799             return self.getCoefficient("g")
1800         elif name == "d_contact" :
1801             return escript.Data()
1802         elif name == "y_contact" :
1803             return escript.Data()
1804         elif name == "r" :
1805             return self.getCoefficient("r")
1806         elif name == "q" :
1807             return self.getCoefficient("q")
1808         else:
1809            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1810    
1811    class LameEquation(LinearPDE):
1812       """
1813       Class to define a Lame equation problem:
1814    
1815       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] }
1816    
1817       with natural boundary conditons:
1818    
1819       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] }
1820    
1821     and constraints:     and constraints:
1822    
1823     \f[     M{u[i]=r[i]} where M{q[i]>0}
1824     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1825     """     """
1826     def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
1827        LinearPDE.__init__(self,domain,numEquations,numSolutions)     def __init__(self,domain,debug=False):
1828        self.__xi=xi        super(LameEquation, self).__init__(domain,\
1829                                             domain.getDim(),domain.getDim(),debug)
1830          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1831                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1832                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1833                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1834                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1835                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1836                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1837          self.setSymmetryOn()
1838    
1839       def setValue(self,**coefficients):
1840         """
1841         sets new values to coefficients
1842    
1843         @param coefficients: new values assigned to coefficients
1844         @keyword lame_mu: value for coefficient M{S{mu}}
1845         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1846         @keyword lame_lambda: value for coefficient M{S{lambda}}
1847         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1848         @keyword F: value for internal force M{F}
1849         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1850         @keyword sigma: value for initial stress M{S{sigma}}
1851         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1852         @keyword f: value for extrenal force M{f}
1853         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1854         @keyword r: prescribed values M{r} for the solution in constraints.
1855         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1856                   depending of reduced order is used for the representation of the equation.
1857         @keyword q: mask for location of constraints
1858         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1859                   depending of reduced order is used for the representation of the equation.
1860         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1861         """
1862         super(LameEquation, self).setValue(**coefficients)
1863    
1864       def getCoefficientOfGeneralPDE(self,name):
1865         """
1866         return the value of the coefficient name of the general PDE
1867    
1868         @param name: name of the coefficient requested.
1869         @type name: C{string}
1870         @return: the value of the coefficient  name
1871         @rtype: L{Data<escript.Data>}
1872         @raise IllegalCoefficient: if name is not one of coefficients
1873                      "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}.
1874         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1875         """
1876         if name == "A" :
1877             out =self.createCoefficientOfGeneralPDE("A")
1878             for i in range(self.getDim()):
1879               for j in range(self.getDim()):
1880                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1881                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1882                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1883             return out
1884         elif name == "B" :
1885             return escript.Data()
1886         elif name == "C" :
1887             return escript.Data()
1888         elif name == "D" :
1889             return escript.Data()
1890         elif name == "X" :
1891             return self.getCoefficient("sigma")
1892         elif name == "Y" :
1893             return self.getCoefficient("F")
1894         elif name == "d" :
1895             return escript.Data()
1896         elif name == "y" :
1897             return self.getCoefficient("f")
1898         elif name == "d_contact" :
1899             return escript.Data()
1900         elif name == "y_contact" :
1901             return escript.Data()
1902         elif name == "r" :
1903             return self.getCoefficient("r")
1904         elif name == "q" :
1905             return self.getCoefficient("q")
1906         else:
1907            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1908    
1909    class AdvectivePDE(LinearPDE):
1910       """
1911       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1912       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1913    
1914       In the following we set
1915    
1916       M{Z[j]=C[j]-B[j]}
1917    
1918       or
1919    
1920       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1921    
1922       To measure the dominance of the advective terms over the diffusive term M{A} the
1923       X{Pelclet number} M{P} is used. It is defined as
1924    
1925       M{P=h|Z|/(2|A|)}
1926    
1927       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1928       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1929    
1930       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1931    
1932       M{S{Xi}=S{xi}(P) h/|Z|}
1933    
1934       where M{S{xi}} is a suitable function of the Peclet number.
1935    
1936       In the case of a single PDE the coefficient are up-dated in the following way:
1937             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1938             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1939             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1940             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1941    
1942       Similar for the case of a systems of PDEs:
1943             - 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]}
1944             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1945             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1946             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1947    
1948       where M{S{delta}} is L{kronecker}.
1949       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1950       but with the intension to stabilize the solution.
1951    
1952       """
1953       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1954          """
1955          creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1956    
1957          @param domain: domain of the PDE
1958          @type domain: L{Domain<escript.Domain>}
1959          @param numEquations: number of equations. If numEquations==None the number of equations
1960                               is exracted from the PDE coefficients.
1961          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1962                               is exracted from the PDE coefficients.
1963          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1964                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1965          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1966          @param debug: if True debug informations are printed.
1967          """
1968          super(AdvectivePDE, self).__init__(domain,\
1969                                             numEquations,numSolutions,debug)
1970          if xi==None:
1971             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1972          else:
1973             self.__xi=xi
1974        self.__Xi=escript.Data()        self.__Xi=escript.Data()
1975    
1976     def __calculateXi(self,peclet_factor,Z,h):     def setValue(**coefficients):
1977         Z_max=util.Lsup(Z)        """
1978         if Z_max>0.:        sets new values to coefficients
1979            return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
1980          @param coefficients: new values assigned to coefficients
1981          @keyword A: value for coefficient A.
1982          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1983          @keyword B: value for coefficient B
1984          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1985          @keyword C: value for coefficient C
1986          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1987          @keyword D: value for coefficient D
1988          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1989          @keyword X: value for coefficient X
1990          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1991          @keyword Y: value for coefficient Y
1992          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1993          @keyword d: value for coefficient d
1994          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1995          @keyword y: value for coefficient y
1996          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1997          @keyword d_contact: value for coefficient d_contact
1998          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1999                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2000          @keyword y_contact: value for coefficient y_contact
2001          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
2002                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2003          @keyword r: values prescribed to the solution at the locations of constraints
2004          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2005                   depending of reduced order is used for the solution.
2006          @keyword q: mask for location of constraints
2007          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2008                   depending of reduced order is used for the representation of the equation.
2009          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2010    
2011          """
2012          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2013          super(AdvectivePDE, self).setValue(**coefficients)
2014    
2015       def ELMAN_RAMAGE(self,P):
2016         """
2017         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2018         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2019              - M{S{xi}(P)=0} for M{P<1}
2020              - M{S{xi}(P)=(1-1/P)/2} otherwise
2021    
2022         @param P: Preclet number
2023         @type P: L{Scalar<escript.Scalar>}
2024         @return: up-wind weightimg factor
2025         @rtype: L{Scalar<escript.Scalar>}
2026         """
2027         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2028    
2029       def SIMPLIFIED_BROOK_HUGHES(self,P):
2030         """
2031         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2032         The original methods is
2033    
2034         M{S{xi}(P)=coth(P)-1/P}
2035    
2036         As the evaluation of M{coth} is expensive we are using the approximation:
2037    
2038             - M{S{xi}(P)=P/3} where M{P<3}
2039             - M{S{xi}(P)=1/2} otherwise
2040    
2041         @param P: Preclet number
2042         @type P: L{Scalar<escript.Scalar>}
2043         @return: up-wind weightimg factor
2044         @rtype: L{Scalar<escript.Scalar>}
2045         """
2046         c=util.whereNegative(P-3.)
2047         return P/6.*c+1./2.*(1.-c)
2048    
2049       def HALF(self,P):
2050         """
2051         Predefined function to set value M{1/2} for M{S{xi}}
2052    
2053         @param P: Preclet number
2054         @type P: L{Scalar<escript.Scalar>}
2055         @return: up-wind weightimg factor
2056         @rtype: L{Scalar<escript.Scalar>}
2057         """
2058         return escript.Scalar(0.5,P.getFunctionSpace())
2059    
2060       def __calculateXi(self,peclet_factor,flux,h):
2061           flux=util.Lsup(flux)
2062           if flux_max>0.:
2063              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2064         else:         else:
2065            return 0.            return 0.
2066    
2067     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):  
2068        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2069           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2070           C=self.getCoefficient("C")           C=self.getCoefficient("C")
# Line 1060  class AdvectivePDE(LinearPDE): Line 2073  class AdvectivePDE(LinearPDE):
2073           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2074           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2075              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
2076                  Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))                  flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2077                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2078                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2079                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2080                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2081                              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
2082                          # flux=C-util.reorderComponents(B,[0,2,1])
2083                     else:                     else:
2084                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2085                           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
2086                          # flux=C-B
2087                  else:                  else:
2088                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2089                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2090                           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
2091                          # flux=C-util.reorderComponents(B,[1,0])
2092                     else:                     else:
2093                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2094                  length_of_Z=util.sqrt(Z2)                        #flux=C-B
2095                    length_of_flux=util.sqrt(flux2)
2096              elif C.isEmpty():              elif C.isEmpty():
2097                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2098                  #flux=B
2099              else:              else:
2100                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2101                  #flux=C
2102    
2103              Z_max=util.Lsup(length_of_Z)              #length_of_flux=util.length(flux)
2104              if Z_max>0.:              flux_max=util.Lsup(length_of_flux)
2105                if flux_max>0.:
2106                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2107                 length_of_A=util.length(A)                 length_of_A=util.length(A)
2108                 A_max=util.Lsup(length_of_A)                 A_max=util.Lsup(length_of_A)
2109                 if A_max>0:                 if A_max>0:
2110                      inv_A=1./(length_of_A+A_max*self.TOL)                      inv_A=1./(length_of_A+A_max*self.__TOL)
2111                 else:                 else:
2112                      inv_A=1./self.TOL                      inv_A=1./self.__TOL
2113                 peclet_number=length_of_Z*h/2*inv_A                 peclet_number=length_of_flux*h/2*inv_A
2114                 xi=self.__xi(peclet_number)                 xi=self.__xi(peclet_number)
2115                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                 self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2116                 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))
2117        return self.__Xi        return self.__Xi
         
2118    
2119     def getCoefficientOfPDE(self,name):  
2120       def getCoefficientOfGeneralPDE(self,name):
2121       """       """
2122       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2123    
2124       @param name:       @param name: name of the coefficient requested.
2125         @type name: C{string}
2126         @return: the value of the coefficient name
2127         @rtype: L{Data<escript.Data>}
2128         @raise IllegalCoefficient: if name is not one of coefficients
2129                      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}.
2130         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2131       """       """
2132       if not self.getNumEquations() == self.getNumSolutions():       if not self.getNumEquations() == self.getNumSolutions():
2133            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."
2134    
2135       if name == "A" :       if name == "A" :
2136           A=self.getCoefficient("A")           A=self.getCoefficient("A")
2137           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2138           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2139           if B.isEmpty() and C.isEmpty():           if B.isEmpty() and C.isEmpty():
2140              Aout=A              Aout=A
2141           else:           else:
2142              if A.isEmpty():              if A.isEmpty():
2143                 Aout=self.createNewCoefficient("A")                 Aout=self.createNewCoefficient("A")
2144              else:              else:
2145                 Aout=A[:]                 Aout=A[:]
2146              Xi=self.getXi()              Xi=self.__getXi()
2147              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2148                  for i in range(self.getNumEquations()):                  for i in range(self.getNumEquations()):
2149                     for j in range(self.getDim()):                     for j in range(self.getDim()):
2150                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2151                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2152                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2153                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2154                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2155                                 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])
2156                              elif C.isEmpty():                              elif C.isEmpty():
2157                                 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]
2158                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2159                              else:                              else:
2160                                 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]
2161                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2162              else:              else:
2163                  for j in range(self.getDim()):                  for j in range(self.getDim()):
2164                     for l in range(self.getDim()):                     for l in range(self.getDim()):
# Line 1137  class AdvectivePDE(LinearPDE): Line 2168  class AdvectivePDE(LinearPDE):
2168                            Aout[j,l]+=Xi*B[j]*B[l]                            Aout[j,l]+=Xi*B[j]*B[l]
2169                        else:                        else:
2170                            Aout[j,l]+=Xi*C[j]*C[l]                            Aout[j,l]+=Xi*C[j]*C[l]
2171                     # if not C.isEmpty() and not B.isEmpty():
2172                     #    tmp=C-B
2173                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2174                     # elif C.isEmpty():
2175                     #    Aout=Aout+Xi*util.outer(B,B)
2176                     # else:
2177                     # Aout=Aout+Xi*util.outer(C,C)
2178           return Aout           return Aout
2179       elif name == "B" :       elif name == "B" :
2180           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2181           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2182           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2183           if C.isEmpty() or D.isEmpty():           if C.isEmpty() or D.isEmpty():
2184              Bout=B              Bout=B
2185           else:           else:
2186              Xi=self.getXi()              Xi=self.__getXi()
2187              if B.isEmpty():              if B.isEmpty():
2188                  Bout=self.createNewCoefficient("B")                  Bout=self.createNewCoefficient("B")
2189              else:              else:
2190                  Bout=B[:]                  Bout=B[:]
2191              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2192                 for k in range(self.getNumSolutions()):                 for k in range(self.getNumSolutions()):
2193                    for p in range(self.getNumEquations()):                    for p in range(self.getNumEquations()):
2194                       tmp=Xi*D[p,k]                       tmp=Xi*D[p,k]
2195                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2196                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2197                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2198                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2199              else:              else:
2200                 tmp=Xi*D                 tmp=Xi*D
2201                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]                 for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2202                   # Bout=Bout+Xi*D*C
2203           return Bout           return Bout
2204       elif name == "C" :       elif name == "C" :
2205           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2206           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2207           D=self.getCoefficient("D")           D=self.getCoefficient("D")
2208           if B.isEmpty() or D.isEmpty():           if B.isEmpty() or D.isEmpty():
2209              Cout=C              Cout=C
2210           else:           else:
2211              Xi=self.getXi()              Xi=self.__getXi()
2212              if C.isEmpty():              if C.isEmpty():
2213                  Cout=self.createNewCoefficient("C")                  Cout=self.createNewCoefficient("C")
2214              else:              else:
2215                  Cout=C[:]                  Cout=C[:]
# Line 1180  class AdvectivePDE(LinearPDE): Line 2220  class AdvectivePDE(LinearPDE):
2220                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2221                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2222                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2223                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2224              else:              else:
2225                 tmp=Xi*D                 tmp=Xi*D
2226                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]                 for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2227                   # Cout=Cout+tmp*D*B
2228           return Cout           return Cout
2229       elif name == "D" :       elif name == "D" :
2230           return self.getCoefficient("D")           return self.getCoefficient("D")
2231       elif name == "X" :       elif name == "X" :
2232           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2233           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2234           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 1198  class AdvectivePDE(LinearPDE): Line 2240  class AdvectivePDE(LinearPDE):
2240                  Xout=self.createNewCoefficient("X")                  Xout=self.createNewCoefficient("X")
2241              else:              else:
2242                  Xout=X[:]                  Xout=X[:]
2243              Xi=self.getXi()              Xi=self.__getXi()
2244              if self.getNumEquations()>1:              if self.getNumEquations()>1:
2245                   for p in range(self.getNumEquations()):                   for p in range(self.getNumEquations()):
2246                      tmp=Xi*Y[p]                      tmp=Xi*Y[p]
2247                      for i in range(self.getNumEquations()):                      for i in range(self.getNumEquations()):
2248                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2249                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2250                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2251                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2252                            elif C.isEmpty():                            elif C.isEmpty():
2253                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2254                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2255                            else:                            else:
2256                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2257                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2258              else:              else:
2259                   tmp=Xi*Y                   tmp=Xi*Y
2260                   for j in range(self.getDim()):                   for j in range(self.getDim()):
2261                      if not C.isEmpty() and not B.isEmpty():                      if not C.isEmpty() and not B.isEmpty():
2262                         Xout[j]+=tmp*(C[j]-B[j])                         Xout[j]+=tmp*(C[j]-B[j])
2263                           # Xout=Xout+Xi*Y*(C-B)
2264                      elif C.isEmpty():                      elif C.isEmpty():
2265                         Xout[j]-=tmp*B[j]                         Xout[j]-=tmp*B[j]
2266                           # Xout=Xout-Xi*Y*B
2267                      else:                      else:
2268                         Xout[j]+=tmp*C[j]                         Xout[j]+=tmp*C[j]
2269                           # Xout=Xout+Xi*Y*C
2270           return Xout           return Xout
2271       elif name == "Y" :       elif name == "Y" :
2272           return self.getCoefficient("Y")           return self.getCoefficient("Y")
2273       elif name == "d" :       elif name == "d" :
2274           return self.getCoefficient("d")           return self.getCoefficient("d")
2275       elif name == "y" :       elif name == "y" :
2276           return self.getCoefficient("y")           return self.getCoefficient("y")
2277       elif name == "d_contact" :       elif name == "d_contact" :
2278           return self.getCoefficient("d_contact")           return self.getCoefficient("d_contact")
2279       elif name == "y_contact" :       elif name == "y_contact" :
2280           return self.getCoefficient("y_contact")           return self.getCoefficient("y_contact")
2281       elif name == "r" :       elif name == "r" :
2282           return self.getCoefficient("r")           return self.getCoefficient("r")
2283       elif name == "q" :       elif name == "q" :
2284           return self.getCoefficient("q")           return self.getCoefficient("q")
2285       else:       else:
2286           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
   
2287    
2288  class Poisson(LinearPDE):  class AdvectionDiffusion(LinearPDE):
2289     """     """
2290     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
2291    
2292       M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
2293    
2294       with natural boundary conditons
2295    
2296     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]  
2297    
2298     and constraints:     and constraints:
2299    
2300     \f[     M{u=r} where M{q>0}
2301     u=0 \quad \mathrm{where} \quad q>0  
2302     \f]     and
2303    
2304       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2305    
2306     """     """
2307    
2308     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2309         LinearPDE.__init__(self,domain,1,1)       """
2310         self.COEFFICIENTS={       initializes a new Poisson equation
2311         "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
2312         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}       @param domain: domain of the PDE
2313         self.setSymmetryOn()       @type domain: L{Domain<escript.Domain>}
2314         self.setValue(f,q)       @param debug: if True debug informations are printed.
2315    
2316         """
2317         super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2318         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2319                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2320                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2321                            "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2322                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2323                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2324                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2325                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2326                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2327    
2328     def setValue(self,f=escript.Data(),q=escript.Data()):     def setValue(self,**coefficients):
2329         self._LinearPDE__setValue(f=f,q=q)       """
2330         sets new values to coefficients
2331    
2332     def getCoefficientOfPDE(self,name):       @param coefficients: new values assigned to coefficients
2333         @keyword omega: value for coefficient M{S{omega}}
2334         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2335         @keyword k: value for coefficient M{k}
2336         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2337         @keyword v: value for coefficient M{v}
2338         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2339         @keyword upwind: value for upwind term M{upwind}
2340         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2341         @keyword f: value for right hand side M{f}
2342         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2343         @keyword alpha: value for right hand side M{S{alpha}}
2344         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2345         @keyword g: value for right hand side M{g}
2346         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2347         @keyword r: prescribed values M{r} for the solution in constraints.
2348         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2349                   depending of reduced order is used for the representation of the equation.
2350         @keyword q: mask for location of constraints
2351         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2352                   depending of reduced order is used for the representation of the equation.
2353         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2354       """       """
2355       return the value of the coefficient name of the general PDE       super(AdvectionDiffusion, self).setValue(**coefficients)
2356    
2357       @param name:     def getCoefficientOfGeneralPDE(self,name):
2358       """       """
2359       if name == "A" :       return the value of the coefficient name of the general PDE
2360           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
2361       elif name == "B" :       @param name: name of the coefficient requested.
2362           return escript.Data()       @type name: C{string}
2363       elif name == "C" :       @return: the value of the coefficient  name
2364           return escript.Data()       @rtype: L{Data<escript.Data>}
2365       elif name == "D" :       @raise IllegalCoefficient: if name is not one of coefficients
2366                      "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}.
2367         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2368         """
2369         if name == "A" :
2370             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2371         elif name == "B" :
2372           return escript.Data()           return escript.Data()
2373       elif name == "X" :       elif name == "C" :
2374             return self.getCoefficient("v")
2375         elif name == "D" :
2376             return self.getCoefficient("omega")
2377         elif name == "X" :
2378           return escript.Data()           return escript.Data()
2379       elif name == "Y" :       elif name == "Y" :
2380           return self.getCoefficient("f")           return self.getCoefficient("f")
2381       elif name == "d" :       elif name == "d" :
2382           return escript.Data()           return self.getCoefficient("alpha")
2383       elif name == "y" :       elif name == "y" :
2384           return escript.Data()           return self.getCoefficient("g")
2385       elif name == "d_contact" :       elif name == "d_contact" :
2386           return escript.Data()           return escript.Data()
2387       elif name == "y_contact" :       elif name == "y_contact" :
2388           return escript.Data()           return escript.Data()
2389       elif name == "r" :       elif name == "r" :
2390           return escript.Data()           return self.getCoefficient("r")
2391       elif name == "q" :       elif name == "q" :
2392           return self.getCoefficient("q")           return self.getCoefficient("q")
2393       else:       else:
2394           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2395    
2396    
2397  # $Log$  # $Log$
2398  # Revision 1.8  2005/06/09 05:37:59  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2399  # 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
2400    #
2401    # Revision 1.13  2005/09/15 03:44:19  jgs
2402    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2403    #
2404    # Revision 1.12  2005/09/01 03:31:28  jgs
2405    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2406    #
2407    # Revision 1.11  2005/08/23 01:24:28  jgs
2408    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2409  #  #
2410  # Revision 1.7  2005/05/06 04:26:10  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2411  # 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
2412    #
2413    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2414    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2415    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2416    # modified to instead use portable/cooperative "super" calls to extend base
2417    # class methods.
2418    #
2419    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2420    # Removed redundant if-loop.
2421    #
2422    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2423    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2424    #
2425    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2426    # the solver from finley are put into the standalone package paso now
2427    #
2428    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2429    # in the case of lumping no new system is allocated if the constraint is changed.
2430    #
2431    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2432    # test for Lumping added
2433    #
2434    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2435    # bug in format fixed.
2436    #
2437    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2438    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2439    #
2440    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2441    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2442    #
2443    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2444    # gneric unit testing for linearPDE
2445    #
2446    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2447    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2448    #
2449    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2450    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2451    #
2452    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2453    # epydoc mark up partially fixed
2454    #
2455    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2456    # some problems with LinearPDEs fixed.
2457    #
2458    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2459    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2460    #
2461    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2462    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2463    #
2464    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2465    # new functions in util and a new pde type in linearPDEs
2466    #
2467    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2468    # Lame equation: (linear elastic, isotropic) added
2469    #
2470    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2471    # some extensions to modellib and linearPDEs
2472  #  #
2473  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2474  # 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 2579  class Poisson(LinearPDE):
2579  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2580  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2581  #  #
 #  

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