/[escript]/trunk/escriptcore/py_src/flows.py
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revision 2349 by gross, Mon Mar 30 08:14:23 2009 UTC revision 3990 by caltinay, Tue Sep 25 05:03:20 2012 UTC
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1  ########################################################  # -*- coding: utf-8 -*-
2    ##############################################################################
3  #  #
4  # Copyright (c) 2003-2008 by University of Queensland  # Copyright (c) 2003-2012 by University of Queensland
5  # Earth Systems Science Computational Center (ESSCC)  # http://www.uq.edu.au
 # http://www.uq.edu.au/esscc  
6  #  #
7  # Primary Business: Queensland, Australia  # Primary Business: Queensland, Australia
8  # Licensed under the Open Software License version 3.0  # Licensed under the Open Software License version 3.0
9  # http://www.opensource.org/licenses/osl-3.0.php  # http://www.opensource.org/licenses/osl-3.0.php
10  #  #
11  ########################################################  # Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12    # Development since 2012 by School of Earth Sciences
13    #
14    ##############################################################################
15    
16  __copyright__="""Copyright (c) 2003-2008 by University of Queensland  __copyright__="""Copyright (c) 2003-2012 by University of Queensland
17  Earth Systems Science Computational Center (ESSCC)  http://www.uq.edu.au
 http://www.uq.edu.au/esscc  
18  Primary Business: Queensland, Australia"""  Primary Business: Queensland, Australia"""
19  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
20  http://www.opensource.org/licenses/osl-3.0.php"""  http://www.opensource.org/licenses/osl-3.0.php"""
# Line 21  __url__="https://launchpad.net/escript-f Line 23  __url__="https://launchpad.net/escript-f
23  """  """
24  Some models for flow  Some models for flow
25    
26  @var __author__: name of author  :var __author__: name of author
27  @var __copyright__: copyrights  :var __copyright__: copyrights
28  @var __license__: licence agreement  :var __license__: licence agreement
29  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
30  @var __version__: version  :var __version__: version
31  @var __date__: date of the version  :var __date__: date of the version
32  """  """
33    
34  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
35    
36  from escript import *  from . import escript
37  import util  from . import util
38  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE  from .linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
39  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES  from .pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
40    
41  class DarcyFlow(object):  class DarcyFlow(object):
42      """     """
43      solves the problem     solves the problem
44      
45      M{u_i+k_{ij}*p_{,j} = g_i}     *u_i+k_{ij}*p_{,j} = g_i*
46      M{u_{i,i} = f}     *u_{i,i} = f*
47      
48      where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,     where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
49      
50      @note: The problem is solved in a least squares formulation.     :cvar EVAL: direct pressure gradient evaluation for flux
51      """     :cvar POST: global postprocessing of flux by solving the PDE *K_{ij} u_j + (w * K * l u_{k,k})_{,i}= - p_{,j} + K_{ij} g_j*
52                   where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
53      def __init__(self, domain,useReduced=False):     :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
54          """     """
55          initializes the Darcy flux problem     EVAL="EVAL"
56          @param domain: domain of the problem     SIMPLE="EVAL"
57          @type domain: L{Domain}     POST="POST"
58          """     SMOOTH="SMOOTH"
59          self.domain=domain     def __init__(self, domain, useReduced=False, solver="POST", verbose=False, w=1.):
60          self.__l=util.longestEdge(self.domain)**2        """
61          self.__pde_v=LinearPDESystem(domain)        initializes the Darcy flux problem.
62          if useReduced: self.__pde_v.setReducedOrderOn()  
63          self.__pde_v.setSymmetryOn()        :param domain: domain of the problem
64          self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))        :type domain: `Domain`
65          self.__pde_p=LinearSinglePDE(domain)        :param useReduced: uses reduced oreder on flux and pressure
66          self.__pde_p.setSymmetryOn()        :type useReduced: ``bool``
67          if useReduced: self.__pde_p.setReducedOrderOn()        :param solver: solver method
68          self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))        :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST`, `DarcyFlow.SMOOTH` ]
69          self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))        :param verbose: if ``True`` some information on the iteration progress are printed.
70          self.setTolerance()        :type verbose: ``bool``
71          self.setAbsoluteTolerance()        :param w: weighting factor for `DarcyFlow.POST` solver
72          self.setSubProblemTolerance()        :type w: ``float``
73          
74      def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):        """
75          """        if not solver in [DarcyFlow.EVAL, DarcyFlow.POST,  DarcyFlow.SMOOTH ] :
76          assigns values to model parameters            raise ValueError("unknown solver %d."%solver)
77    
78          @param f: volumetic sources/sinks        self.domain=domain
79          @type f: scalar value on the domain (e.g. L{Data})        self.solver=solver
80          @param g: flux sources/sinks        self.useReduced=useReduced
81          @type g: vector values on the domain (e.g. L{Data})        self.verbose=verbose
82          @param location_of_fixed_pressure: mask for locations where pressure is fixed        self.l=None
83          @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})        self.w=None
84          @param location_of_fixed_flux:  mask for locations where flux is fixed.      
85          @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})        self.__pde_p=LinearSinglePDE(domain)
86          @param permeability: permeability tensor. If scalar C{s} is given the tensor with        self.__pde_p.setSymmetryOn()
87                               C{s} on the main diagonal is used. If vector C{v} is given the tensor with        if self.useReduced: self.__pde_p.setReducedOrderOn()
88                               C{v} on the main diagonal is used.  
89          @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})        if self.solver  == self.EVAL:
90             self.__pde_v=None
91          @note: the values of parameters which are not set by calling C{setValue} are not altered.           if self.verbose: print("DarcyFlow: simple solver is used.")
92          @note: at any point on the boundary of the domain the pressure (C{location_of_fixed_pressure} >0)  
93                 or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal        elif self.solver  == self.POST:
94                 is along the M{x_i} axis.           if util.inf(w)<0.:
95          """              raise ValueError("Weighting factor must be non-negative.")
96          if f !=None:           if self.verbose: print("DarcyFlow: global postprocessing of flux is used.")
97             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))           self.__pde_v=LinearPDESystem(domain)
98             if f.isEmpty():           self.__pde_v.setSymmetryOn()
99                 f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))           if self.useReduced: self.__pde_v.setReducedOrderOn()
100             else:           self.w=w
101                 if f.getRank()>0: raise ValueError,"illegal rank of f."           x=self.domain.getX()
102             self.__f=f           self.l=min( [util.sup(x[i])-util.inf(x[i]) for i in xrange(self.domain.getDim()) ] )
103          if g !=None:           #self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
104             g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))  
105             if g.isEmpty():        elif self.solver  == self.SMOOTH:
106               g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))           self.__pde_v=LinearPDESystem(domain)
107             else:           self.__pde_v.setSymmetryOn()
108               if not g.getShape()==(self.domain.getDim(),):           if self.useReduced: self.__pde_v.setReducedOrderOn()
109                 raise ValueError,"illegal shape of g"           if self.verbose: print("DarcyFlow: flux smoothing is used.")
110             self.__g=g           self.w=0
111    
112          if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)        self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
113          if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)        self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
114          self.__permeability_invXg=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
115          if permeability!=None:        self.__permeability_invXg_ref=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
116             perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))        self.ref_point_id=None
117             if perm.getRank()==0:        self.ref_point=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
118                 perm=perm*util.kronecker(self.domain.getDim())        self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
119             elif perm.getRank()==1:        self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
120                 perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm        self.perm_scale=1.
121                 for i in range(self.domain.getDim()): perm[i,i]=perm2[i]      
122             elif perm.getRank()==2:          
123                pass     def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
124             else:        """
125                raise ValueError,"illegal rank of permeability."        assigns values to model parameters
126             self.__permeability=perm  
127             self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))        :param f: volumetic sources/sinks
128          :type f: scalar value on the domain (e.g. `escript.Data`)
129      def setTolerance(self,rtol=1e-4):        :param g: flux sources/sinks
130          """        :type g: vector values on the domain (e.g. `escript.Data`)
131          sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if        :param location_of_fixed_pressure: mask for locations where pressure is fixed
132          :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
133          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }        :param location_of_fixed_flux:  mask for locations where flux is fixed.
134          :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
135          where C{atol} is an absolut tolerance (see L{setAbsoluteTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.        :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
136          :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
137          @param rtol: relative tolerance for the pressure  
138          @type rtol: non-negative C{float}        :note: the values of parameters which are not set by calling ``setValue`` are not altered.
139          """        :note: at any point on the boundary of the domain the pressure
140          if rtol<0:               (``location_of_fixed_pressure`` >0) or the normal component of the
141              raise ValueError,"Relative tolerance needs to be non-negative."               flux (``location_of_fixed_flux[i]>0``) if direction of the normal
142          self.__rtol=rtol               is along the *x_i* axis.
143      def getTolerance(self):  
144          """        """
145          returns the relative tolerance        if location_of_fixed_pressure!=None:
146               self.location_of_fixed_pressure=util.wherePositive(util.interpolate(location_of_fixed_pressure, self.__pde_p.getFunctionSpaceForCoefficient("q")))
147          @return: current relative tolerance             self.ref_point_id=self.location_of_fixed_pressure.maxGlobalDataPoint()
148          @rtype: C{float}             if not self.location_of_fixed_pressure.getTupleForGlobalDataPoint(*self.ref_point_id)[0] > 0: raise ValueError("pressure needs to be fixed at least one point.")
149          """             self.ref_point=self.__pde_p.getFunctionSpaceForCoefficient("q").getX().getTupleForGlobalDataPoint(*self.ref_point_id)
150          return self.__rtol             if self.verbose: print(("DarcyFlow: reference point at %s."%(self.ref_point,)))
151               self.__pde_p.setValue(q=self.location_of_fixed_pressure)
152      def setAbsoluteTolerance(self,atol=0.):        if location_of_fixed_flux!=None:
153          """            self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
154          sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if            if not self.__pde_v == None:
155                  self.__pde_v.setValue(q=self.location_of_fixed_flux)
156          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }              
157          if permeability!=None:
158          where C{rtol} is an absolut tolerance (see L{setTolerance}), M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.      
159             perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
160          @param atol: absolute tolerance for the pressure           self.perm_scale=util.Lsup(util.length(perm))
161          @type atol: non-negative C{float}           if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
162          """           perm=perm*(1./self.perm_scale)
163          if atol<0:          
164              raise ValueError,"Absolute tolerance needs to be non-negative."           if perm.getRank()==0:
165          self.__atol=atol  
166      def getAbsoluteTolerance(self):              perm_inv=(1./perm)
167         """              perm_inv=perm_inv*util.kronecker(self.domain.getDim())
168         returns the absolute tolerance              perm=perm*util.kronecker(self.domain.getDim())
169                  
170         @return: current absolute tolerance          
171         @rtype: C{float}           elif perm.getRank()==2:
172         """              perm_inv=util.inverse(perm)
        return self.__atol  
   
     def setSubProblemTolerance(self,rtol=None):  
          """  
          Sets the relative tolerance to solve the subproblem(s). If C{rtol} is not present  
          C{self.getTolerance()**2} is used.  
   
          @param rtol: relative tolerence  
          @type rtol: positive C{float}  
          """  
          if rtol == None:  
               if self.getTolerance()<=0.:  
                   raise ValueError,"A positive relative tolerance must be set."  
               self.__sub_tol=max(util.EPSILON**(0.75),self.getTolerance()**2)  
173           else:           else:
174               if rtol<=0:              raise ValueError("illegal rank of permeability.")
175                   raise ValueError,"sub-problem tolerance must be positive."          
176               self.__sub_tol=max(util.EPSILON**(0.75),rtol)           self.__permeability=perm
177             self.__permeability_inv=perm_inv
178      def getSubProblemTolerance(self):      
179           """           #====================
180           Returns the subproblem reduction factor.           self.__pde_p.setValue(A=self.__permeability)
181             if self.solver  == self.EVAL:
182           @return: subproblem reduction factor                pass # no extra work required
183           @rtype: C{float}           elif self.solver  == self.POST:
184           """                k=util.kronecker(self.domain.getDim())
185           return self.__sub_tol                self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
186                  #self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
187      def solve(self,u0,p0, max_iter=100, verbose=False, show_details=False, max_num_corrections=10):                self.__pde_v.setValue(D=self.__permeability_inv, A_reduced=self.omega*util.outer(k,k))
188           """           elif self.solver  == self.SMOOTH:
189           solves the problem.              self.__pde_v.setValue(D=self.__permeability_inv)
190    
191           The iteration is terminated if the residual norm is less then self.getTolerance().        if g != None:
192            g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
193           @param u0: initial guess for the flux. At locations in the domain marked by C{location_of_fixed_flux} the value of C{u0} is kept unchanged.          if g.isEmpty():
194           @type u0: vector value on the domain (e.g. L{Data}).               g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
          @param p0: initial guess for the pressure. At locations in the domain marked by C{location_of_fixed_pressure} the value of C{p0} is kept unchanged.  
          @type p0: scalar value on the domain (e.g. L{Data}).  
          @param verbose: if set some information on iteration progress are printed  
          @type verbose: C{bool}  
          @param show_details:  if set information on the subiteration process are printed.  
          @type show_details: C{bool}  
          @return: flux and pressure  
          @rtype: C{tuple} of L{Data}.  
   
          @note: The problem is solved as a least squares form  
   
          M{(I+D^*D)u+Qp=D^*f+g}  
          M{Q^*u+Q^*Qp=Q^*g}  
   
          where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.  
          We eliminate the flux form the problem by setting  
   
          M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux  
   
          form the first equation. Inserted into the second equation we get  
   
          M{Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g))} with p=p0  on location_of_fixed_pressure  
   
          which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step  
          PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.  
          """  
          self.verbose=verbose or True  
          self.show_details= show_details and self.verbose  
          rtol=self.getTolerance()  
          atol=self.getAbsoluteTolerance()  
          if self.verbose: print "DarcyFlux: initial sub tolerance = %e"%self.getSubProblemTolerance()  
   
          num_corrections=0  
          converged=False  
          p=p0  
          norm_r=None  
          while not converged:  
                v=self.getFlux(p, fixed_flux=u0, show_details=self.show_details)  
                Qp=self.__Q(p)  
                norm_v=self.__L2(v)  
                norm_Qp=self.__L2(Qp)  
                if norm_v == 0.:  
                   if norm_Qp == 0.:  
                      return v,p  
                   else:  
                     fac=norm_Qp  
                else:  
                   if norm_Qp == 0.:  
                     fac=norm_v  
                   else:  
                     fac=2./(1./norm_v+1./norm_Qp)  
                ATOL=(atol+rtol*fac)  
                if self.verbose:  
                     print "DarcyFlux: L2 norm of v = %e."%norm_v  
                     print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp  
                     print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL  
                if norm_r == None or norm_r>ATOL:  
                    if num_corrections>max_num_corrections:  
                          raise ValueError,"maximum number of correction steps reached."  
                    p,r, norm_r=PCG(self.__g-util.interpolate(v,Function(self.domain))-Qp,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=0.1*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
                    num_corrections+=1  
                else:  
                    converged=True  
          return v,p  
 #  
 #                
 #               r_hat=g-util.interpolate(v,Function(self.domain))-Qp  
 #               #===========================================================================  
 #               norm_r_hat=self.__L2(r_hat)  
 #               norm_v=self.__L2(v)  
 #               norm_g=self.__L2(g)  
 #               norm_gv=self.__L2(g-v)  
 #               norm_Qp=self.__L2(Qp)  
 #               norm_gQp=self.__L2(g-Qp)  
 #               fac=min(max(norm_v,norm_gQp),max(norm_Qp,norm_gv))  
 #               fac=min(norm_v,norm_Qp,norm_gv)  
 #               norm_r_hat_PCG=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))  
 #               print "norm_r_hat = ",norm_r_hat,norm_r_hat_PCG, norm_r_hat_PCG/norm_r_hat  
 #               if r!=None:  
 #                   print "diff = ",self.__L2(r-r_hat)/norm_r_hat  
 #                   sub_tol=min(rtol/self.__L2(r-r_hat)*norm_r_hat,1.)*self.getSubProblemTolerance()  
 #                   self.setSubProblemTolerance(sub_tol)  
 #                   print "subtol_new=",self.getSubProblemTolerance()  
 #               print "norm_v = ",norm_v  
 #               print "norm_gv = ",norm_gv  
 #               print "norm_Qp = ",norm_Qp  
 #               print "norm_gQp = ",norm_gQp  
 #               print "norm_g = ",norm_g  
 #               print "max(norm_v,norm_gQp)=",max(norm_v,norm_gQp)  
 #               print "max(norm_Qp,norm_gv)=",max(norm_Qp,norm_gv)  
 #               if fac == 0:  
 #                   if self.verbose: print "DarcyFlux: trivial case!"  
 #                   return v,p  
 #               #===============================================================================  
 #               # norm_v=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(v),v))  
 #               # norm_Qp=self.__L2(Qp)  
 #               norm_r_hat=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))  
 #               # print "**** norm_v, norm_Qp :",norm_v,norm_Qp  
 #  
 #               ATOL=(atol+rtol*2./(1./norm_v+1./norm_Qp))  
 #               if self.verbose:  
 #                   print "DarcyFlux: residual = %e"%norm_r_hat  
 #                   print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL  
 #               if norm_r_hat <= ATOL:  
 #                   print "DarcyFlux: iteration finalized."  
 #                   converged=True  
 #               else:  
 #                   # p=GMRES(r_hat,self.__Aprod, p, self.__inner_GMRES, atol=ATOL, rtol=0., iter_max=max_iter, iter_restart=20, verbose=self.verbose,P_R=self.__Msolve_PCG)  
 #                   # p,r=PCG(r_hat,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=ATOL*min(0.1,norm_r_hat_PCG/norm_r_hat), rtol=0.,iter_max=max_iter, verbose=self.verbose)  
 #                   p,r, norm_r=PCG(r_hat,self.__Aprod,p,self.__Msolve_PCG,self.__inner_PCG,atol=0.1*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
 #               print "norm_r =",norm_r  
 #         return v,p  
     def __L2(self,v):  
          return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))  
   
     def __Q(self,p):  
           return util.tensor_mult(self.__permeability,util.grad(p))  
   
     def __Aprod(self,dp):  
           self.__pde_v.setTolerance(self.getSubProblemTolerance())  
           if self.show_details: print "DarcyFlux: Applying operator"  
           Qdp=self.__Q(dp)  
           self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())  
           du=self.__pde_v.getSolution(verbose=self.show_details, iter_max = 100000)  
           return Qdp+du  
     def __inner_GMRES(self,r,s):  
          return util.integrate(util.inner(r,s))  
   
     def __inner_PCG(self,p,r):  
          return util.integrate(util.inner(self.__Q(p), r))  
   
     def __Msolve_PCG(self,r):  
           self.__pde_p.setTolerance(self.getSubProblemTolerance())  
           if self.show_details: print "DarcyFlux: Applying preconditioner"  
           self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())  
           return self.__pde_p.getSolution(verbose=self.show_details, iter_max = 100000)  
   
     def getFlux(self,p=None, fixed_flux=Data(), show_details=False):  
         """  
         returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}  
         on locations where C{location_of_fixed_flux} is positive (see L{setValue}).  
         Note that C{g} and C{f} are used, see L{setValue}.  
   
         @param p: pressure.  
         @type p: scalar value on the domain (e.g. L{Data}).  
         @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.  
         @type fixed_flux: vector values on the domain (e.g. L{Data}).  
         @param tol: relative tolerance to be used.  
         @type tol: positive C{float}.  
         @return: flux  
         @rtype: L{Data}  
         @note: the method uses the least squares solution M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}}  
                for the permeability M{k_{ij}}  
         """  
         self.__pde_v.setTolerance(self.getSubProblemTolerance())  
         g=self.__g  
         f=self.__f  
         self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)  
         if p == None:  
            self.__pde_v.setValue(Y=g)  
195          else:          else:
196             self.__pde_v.setValue(Y=g-self.__Q(p))               if not g.getShape()==(self.domain.getDim(),): raise ValueError("illegal shape of g")
197          return self.__pde_v.getSolution(verbose=show_details, iter_max=100000)          self.__g=g
198            self.__permeability_invXg=util.tensor_mult(self.__permeability_inv,self.__g * (1./self.perm_scale ))
199            self.__permeability_invXg_ref=util.integrate(self.__permeability_invXg)/util.vol(self.domain)
200          if f !=None:
201             f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
202             if f.isEmpty():      
203                 f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
204             else:
205                 if f.getRank()>0: raise ValueError("illegal rank of f.")
206             self.__f=f
207    
208       def getSolverOptionsFlux(self):
209          """
210          Returns the solver options used to solve the flux problems
211          :return: `SolverOptions`
212          """
213          if self.__pde_v == None:
214              return None
215          else:
216              return self.__pde_v.getSolverOptions()
217          
218       def setSolverOptionsFlux(self, options=None):
219          """
220          Sets the solver options used to solve the flux problems
221          If ``options`` is not present, the options are reset to default
222          :param options: `SolverOptions`
223          """
224          if not self.__pde_v == None:
225              self.__pde_v.setSolverOptions(options)
226        
227       def getSolverOptionsPressure(self):
228          """
229          Returns the solver options used to solve the pressure problems
230          :return: `SolverOptions`
231          """
232          return self.__pde_p.getSolverOptions()
233          
234       def setSolverOptionsPressure(self, options=None):
235          """
236          Sets the solver options used to solve the pressure problems
237          If ``options`` is not present, the options are reset to default
238          
239          :param options: `SolverOptions`
240          :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
241          """
242          return self.__pde_p.setSolverOptions(options)
243          
244       def solve(self, u0, p0):
245          """
246          solves the problem.
247          
248          :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.
249          :type u0: vector value on the domain (e.g. `escript.Data`).
250          :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.
251          :type p0: scalar value on the domain (e.g. `escript.Data`).
252          :return: flux and pressure
253          :rtype: ``tuple`` of `escript.Data`.
254    
255          """
256          p0=util.interpolate(p0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
257          if self.ref_point_id == None:
258              p_ref=0
259          else:
260              p_ref=p0.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
261          p0_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
262          g_2=self.__g - util.tensor_mult(self.__permeability, self.__permeability_invXg_ref * self.perm_scale)
263          self.__pde_p.setValue(X=g_2 * 1./self.perm_scale,
264                                Y=self.__f * 1./self.perm_scale,
265                                y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux * 1./self.perm_scale ),
266                                r=p0 - p0_hydrostatic)
267          pp=self.__pde_p.getSolution()
268          u = self._getFlux(pp, u0)
269          return u,pp + p0_hydrostatic
270          
271       def getFlux(self,p, u0=None):
272            """
273            returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
274            on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
275            Notice that ``g`` is used, see `setValue`.
276    
277            :param p: pressure.
278            :type p: scalar value on the domain (e.g. `escript.Data`).
279            :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
280            :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
281            :return: flux
282            :rtype: `escript.Data`
283            """
284            p=util.interpolate(p, self.__pde_p.getFunctionSpaceForCoefficient("q"))
285            if self.ref_point_id == None:
286                p_ref=0
287            else:
288                p_ref=p.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
289            p_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
290            return self._getFlux(p-p_hydrostatic, u0)
291    
292       def _getFlux(self, pp, u0=None):
293            """
294            returns the flux for a given pressure ``pp`` where the flux is equal to
295            ``u0`` on locations where ``location_of_fixed_flux`` is positive (see
296            `setValue`). Notice that ``g`` is used, see `setValue`.
297    
298            :param pp: pressure.
299            :type pp: scalar value on the domain (i.e. `escript.Data`).
300            :param u0: flux on the locations of the domain marked in ``location_of_fixed_flux``.
301            :type u0: vector values on the domain (i.e. `escript.Data`) or ``None``
302            :return: flux
303            :rtype: `escript.Data`
304            """
305            if self.solver  == self.EVAL:
306               u = self.__g - util.tensor_mult(self.__permeability, self.perm_scale * (util.grad(pp) + self.__permeability_invXg_ref))
307            elif self.solver  == self.POST or self.solver  == self.SMOOTH:
308                self.__pde_v.setValue(Y= self.__permeability_invXg - (util.grad(pp) + self.__permeability_invXg_ref))
309                print
310                if u0 == None:
311                   self.__pde_v.setValue(r=escript.Data())
312                else:
313                   if not isinstance(u0, escript.Data) : u0 = escript.Vector(u0, escript.Solution(self.domain))
314                   self.__pde_v.setValue(r=1./self.perm_scale * u0)
315                u= self.__pde_v.getSolution() * self.perm_scale
316            return u
317          
318  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  class StokesProblemCartesian(HomogeneousSaddlePointProblem):
319       """       """
320       solves       solves
# Line 386  class StokesProblemCartesian(Homogeneous Line 333  class StokesProblemCartesian(Homogeneous
333              sp.setTolerance()              sp.setTolerance()
334              sp.initialize(...)              sp.initialize(...)
335              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
336                sp.setStokesEquation(...) # new values for some parameters
337                v1,p1=sp.solve(v,p)
338       """       """
339       def __init__(self,domain,**kwargs):       def __init__(self,domain,**kwargs):
340           """           """
341           initialize the Stokes Problem           initialize the Stokes Problem
342    
343           @param domain: domain of the problem. The approximation order needs to be two.           The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be
344           @type domain: L{Domain}           LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
345           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.           with macro elements for the pressure.
346    
347             :param domain: domain of the problem.
348             :type domain: `Domain`
349           """           """
350           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
351           self.domain=domain           self.domain=domain
352           self.vol=util.integrate(1.,Function(self.domain))           self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
353           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_v.setSymmetryOn()
354           self.__pde_u.setSymmetryOn()      
          # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)  
          # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.RILU)  
   
355           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
356           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
          # self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)  
357           self.__pde_prec.setSymmetryOn()           self.__pde_prec.setSymmetryOn()
358    
359       def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data()):           self.__pde_proj=LinearPDE(domain)
360             self.__pde_proj.setReducedOrderOn()
361             self.__pde_proj.setValue(D=1)
362             self.__pde_proj.setSymmetryOn()
363    
364         def getSolverOptionsVelocity(self):
365             """
366         returns the solver options used  solve the equation for velocity.
367        
368         :rtype: `SolverOptions`
369         """
370             return self.__pde_v.getSolverOptions()
371         def setSolverOptionsVelocity(self, options=None):
372             """
373         set the solver options for solving the equation for velocity.
374        
375         :param options: new solver  options
376         :type options: `SolverOptions`
377         """
378             self.__pde_v.setSolverOptions(options)
379         def getSolverOptionsPressure(self):
380             """
381         returns the solver options used  solve the equation for pressure.
382         :rtype: `SolverOptions`
383         """
384             return self.__pde_prec.getSolverOptions()
385         def setSolverOptionsPressure(self, options=None):
386             """
387         set the solver options for solving the equation for pressure.
388         :param options: new solver  options
389         :type options: `SolverOptions`
390         """
391             self.__pde_prec.setSolverOptions(options)
392    
393         def setSolverOptionsDiv(self, options=None):
394             """
395         set the solver options for solving the equation to project the divergence of
396         the velocity onto the function space of presure.
397        
398         :param options: new solver options
399         :type options: `SolverOptions`
400         """
401             self.__pde_proj.setSolverOptions(options)
402         def getSolverOptionsDiv(self):
403             """
404         returns the solver options for solving the equation to project the divergence of
405         the velocity onto the function space of presure.
406        
407         :rtype: `SolverOptions`
408         """
409             return self.__pde_proj.getSolverOptions()
410    
411         def updateStokesEquation(self, v, p):
412             """
413             updates the Stokes equation to consider dependencies from ``v`` and ``p``
414             :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
415             """
416             pass
417         def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
418            """
419            assigns new values to the model parameters.
420    
421            :param f: external force
422            :type f: `Vector` object in `FunctionSpace` `Function` or similar
423            :param fixed_u_mask: mask of locations with fixed velocity.
424            :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
425            :param eta: viscosity
426            :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
427            :param surface_stress: normal surface stress
428            :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
429            :param stress: initial stress
430        :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
431            """
432            if eta !=None:
433                k=util.kronecker(self.domain.getDim())
434                kk=util.outer(k,k)
435                self.eta=util.interpolate(eta, escript.Function(self.domain))
436                self.__pde_prec.setValue(D=1/self.eta)
437                self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
438            if restoration_factor!=None:
439                n=self.domain.getNormal()
440                self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
441            if fixed_u_mask!=None:
442                self.__pde_v.setValue(q=fixed_u_mask)
443            if f!=None: self.__f=f
444            if surface_stress!=None: self.__surface_stress=surface_stress
445            if stress!=None: self.__stress=stress
446    
447         def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
448          """          """
449          assigns values to the model parameters          assigns values to the model parameters
450    
451          @param f: external force          :param f: external force
452          @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar          :type f: `Vector` object in `FunctionSpace` `Function` or similar
453          @param fixed_u_mask: mask of locations with fixed velocity.          :param fixed_u_mask: mask of locations with fixed velocity.
454          @type fixed_u_mask: L{Vector} object on L{FunctionSpace} L{Solution} or similar          :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
455          @param eta: viscosity          :param eta: viscosity
456          @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar          :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
457          @param surface_stress: normal surface stress          :param surface_stress: normal surface stress
458          @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
459          @param stress: initial stress          :param stress: initial stress
460      @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar          :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
         @note: All values needs to be set.  
   
461          """          """
462          self.eta=eta          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
         A =self.__pde_u.createCoefficient("A")  
     self.__pde_u.setValue(A=Data())  
         for i in range(self.domain.getDim()):  
         for j in range(self.domain.getDim()):  
             A[i,j,j,i] += 1.  
             A[i,j,i,j] += 1.  
     self.__pde_prec.setValue(D=1/self.eta)  
         self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask)  
         self.__f=f  
         self.__surface_stress=surface_stress  
         self.__stress=stress  
463    
464       def inner_pBv(self,p,v):       def Bv(self,v,tol):
465           """           """
466           returns inner product of element p and div(v)           returns inner product of element p and div(v)
467    
468           @param p: a pressure increment           :param v: a residual
469           @param v: a residual           :return: inner product of element p and div(v)
470           @return: inner product of element p and div(v)           :rtype: ``float``
471           @rtype: C{float}           """
472             self.__pde_proj.setValue(Y=-util.div(v))
473             self.getSolverOptionsDiv().setTolerance(tol)
474             self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
475             out=self.__pde_proj.getSolution()
476             return out
477    
478         def inner_pBv(self,p,Bv):
479             """
480             returns inner product of element p and Bv=-div(v)
481    
482             :param p: a pressure increment
483             :param Bv: a residual
484             :return: inner product of element p and Bv=-div(v)
485             :rtype: ``float``
486           """           """
487           return util.integrate(-p*util.div(v))           return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
488    
489       def inner_p(self,p0,p1):       def inner_p(self,p0,p1):
490           """           """
491           Returns inner product of p0 and p1           Returns inner product of p0 and p1
492    
493           @param p0: a pressure           :param p0: a pressure
494           @param p1: a pressure           :param p1: a pressure
495           @return: inner product of p0 and p1           :return: inner product of p0 and p1
496           @rtype: C{float}           :rtype: ``float``
497           """           """
498           s0=util.interpolate(p0/self.eta,Function(self.domain))           s0=util.interpolate(p0, escript.Function(self.domain))
499           s1=util.interpolate(p1/self.eta,Function(self.domain))           s1=util.interpolate(p1, escript.Function(self.domain))
500           return util.integrate(s0*s1)           return util.integrate(s0*s1)
501    
502       def norm_v(self,v):       def norm_v(self,v):
503           """           """
504           returns the norm of v           returns the norm of v
505    
506           @param v: a velovity           :param v: a velovity
507           @return: norm of v           :return: norm of v
508           @rtype: non-negative C{float}           :rtype: non-negative ``float``
509           """           """
510           return util.sqrt(util.integrate(util.length(util.grad(v))))           return util.sqrt(util.integrate(util.length(util.grad(v))**2))
511    
512    
513       def getV(self, p, v0):       def getDV(self, p, v, tol):
514           """           """
515           return the value for v for a given p (overwrite)           return the value for v for a given p
516    
517           @param p: a pressure           :param p: a pressure
518           @param v0: a initial guess for the value v to return.           :param v: a initial guess for the value v to return.
519           @return: v given as M{v= A^{-1} (f-B^*p)}           :return: dv given as *Adv=(f-Av-B^*p)*
520           """           """
521           self.__pde_u.setTolerance(self.getSubProblemTolerance())           self.updateStokesEquation(v,p)
522           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
523             self.getSolverOptionsVelocity().setTolerance(tol)
524             self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
525           if self.__stress.isEmpty():           if self.__stress.isEmpty():
526              self.__pde_u.setValue(X=p*util.kronecker(self.domain))              self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
527           else:           else:
528              self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain))              self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
529           out=self.__pde_u.getSolution(verbose=self.show_details)           out=self.__pde_v.getSolution()
530           return  out           return  out
531    
532         def norm_Bv(self,Bv):
          raise NotImplementedError,"no v calculation implemented."  
   
   
      def norm_Bv(self,v):  
533          """          """
534          Returns Bv (overwrite).          Returns Bv (overwrite).
535    
536          @rtype: equal to the type of p          :rtype: equal to the type of p
537          @note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
538          """          """
539          return util.sqrt(util.integrate(util.div(v)**2))          return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
540    
541       def solve_AinvBt(self,p):       def solve_AinvBt(self,p, tol):
542           """           """
543           Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}           Solves *Av=B^*p* with accuracy `tol`
544    
545           @param p: a pressure increment           :param p: a pressure increment
546           @return: the solution of M{Av=B^*p}           :return: the solution of *Av=B^*p*
547           @note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
548           """           """
549           self.__pde_u.setTolerance(self.getSubProblemTolerance())           self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
550           self.__pde_u.setValue(Y=Data(), y=Data(), r=Data(),X=-p*util.kronecker(self.domain))           out=self.__pde_v.getSolution()
          out=self.__pde_u.getSolution(verbose=self.show_details)  
551           return  out           return  out
552    
553       def solve_precB(self,v):       def solve_prec(self,Bv, tol):
554           """           """
555           applies preconditioner for for M{BA^{-1}B^*} to M{Bv}           applies preconditioner for for *BA^{-1}B^** to *Bv*
556           with accuracy L{self.getSubProblemTolerance()} (overwrite).           with accuracy ``self.getSubProblemTolerance()``
557    
558           @param v: velocity increment           :param Bv: velocity increment
559           @return: M{p=P(Bv)} where M{P^{-1}} is an approximation of M{BA^{-1}B^*}           :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
560           @note: boundary conditions on p are zero.           :note: boundary conditions on p are zero.
561           """           """
562           self.__pde_prec.setValue(Y=-util.div(v))           self.__pde_prec.setValue(Y=Bv)
563           self.__pde_prec.setTolerance(self.getSubProblemTolerance())           self.getSolverOptionsPressure().setTolerance(tol)
564           return self.__pde_prec.getSolution(verbose=self.show_details)           self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
565             out=self.__pde_prec.getSolution()
566             return out

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