/[escript]/trunk/escriptcore/py_src/flows.py
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revision 2264 by gross, Wed Feb 11 06:48:28 2009 UTC revision 3515 by gross, Thu May 19 08:20:57 2011 UTC
# Line 1  Line 1 
1    # -*- coding: utf-8 -*-
2  ########################################################  ########################################################
3  #  #
4  # Copyright (c) 2003-2008 by University of Queensland  # Copyright (c) 2003-2010 by University of Queensland
5  # Earth Systems Science Computational Center (ESSCC)  # Earth Systems Science Computational Center (ESSCC)
6  # http://www.uq.edu.au/esscc  # http://www.uq.edu.au/esscc
7  #  #
# Line 10  Line 11 
11  #  #
12  ########################################################  ########################################################
13    
14  __copyright__="""Copyright (c) 2003-2008 by University of Queensland  __copyright__="""Copyright (c) 2003-2010 by University of Queensland
15  Earth Systems Science Computational Center (ESSCC)  Earth Systems Science Computational Center (ESSCC)
16  http://www.uq.edu.au/esscc  http://www.uq.edu.au/esscc
17  Primary Business: Queensland, Australia"""  Primary Business: Queensland, Australia"""
18  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
19  http://www.opensource.org/licenses/osl-3.0.php"""  http://www.opensource.org/licenses/osl-3.0.php"""
20  __url__="http://www.uq.edu.au/esscc/escript-finley"  __url__="https://launchpad.net/escript-finley"
21    
22  """  """
23  Some models for flow  Some models for flow
24    
25  @var __author__: name of author  :var __author__: name of author
26  @var __copyright__: copyrights  :var __copyright__: copyrights
27  @var __license__: licence agreement  :var __license__: licence agreement
28  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
29  @var __version__: version  :var __version__: version
30  @var __date__: date of the version  :var __date__: date of the version
31  """  """
32    
33  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
34    
35  from escript import *  import escript
36  import util  import util
37  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
38  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
39    
40  class DarcyFlow(object):  class DarcyFlow(object):
41      """     """
42      solves the problem     solves the problem
43      
44      M{u_i+k_{ij}*p_{,j} = g_i}     *u_i+k_{ij}*p_{,j} = g_i*
45      M{u_{i,i} = f}     *u_{i,i} = f*
46      
47      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,
48      
49      @note: The problem is solved in a least squares formulation.     :cvar SIMPLE: simple solver
50      """     :cvar POST: solver using global postprocessing of flux
51       :cvar STAB: solver uses (non-symmetric) stabilization
52      def __init__(self, domain,useReduced=False):     :cvar SYMSTAB: solver uses symmetric stabilization
53          """     """
54          initializes the Darcy flux problem     SIMPLE="SIMPLE"
55          @param domain: domain of the problem     POST="POST"
56          @type domain: L{Domain}     STAB="STAB"
57          """     SYMSTAB="SYMSTAB"
58          self.domain=domain     def __init__(self, domain, useReduced=False, solver="SYMSTAB", verbose=False, w=1.):
59          self.__pde_v=LinearPDESystem(domain)        """
60          if useReduced: self.__pde_v.setReducedOrderOn()        initializes the Darcy flux problem
61          self.__pde_v.setSymmetryOn()        :param domain: domain of the problem
62          self.__pde_v.setValue(D=util.kronecker(domain), A=util.outer(util.kronecker(domain),util.kronecker(domain)))        :type domain: `Domain`
63          self.__pde_p=LinearSinglePDE(domain)        :param useReduced: uses reduced oreder on flux and pressure
64          self.__pde_p.setSymmetryOn()        :type useReduced: ``bool``
65          if useReduced: self.__pde_p.setReducedOrderOn()        :param solver: solver method
66          self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))        :type solver: in [`DarcyFlow.SIMPLE`, `DarcyFlow.POST', `DarcyFlow.STAB`, `DarcyFlow.SYMSTAB` ]
67          self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))        :param verbose: if ``True`` some information on the iteration progress are printed.
68          self.setTolerance()        :type verbose: ``bool``
69          self.setAbsoluteTolerance()        :param w: weighting factor for `DarcyFlow.POST` solver
70          self.setSubProblemTolerance()        :type w: ``float``
71          
72      def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):        """
73          """        self.domain=domain
74          assigns values to model parameters        self.solver=solver
75          self.useReduced=useReduced
76          @param f: volumetic sources/sinks        self.verbose=verbose
77          @type f: scalar value on the domain (e.g. L{Data})        self.scale=1.
78          @param g: flux sources/sinks        
79          @type g: vector values on the domain (e.g. L{Data})        
80          @param location_of_fixed_pressure: mask for locations where pressure is fixed        self.__pde_v=LinearPDESystem(domain)
81          @type location_of_fixed_pressure: scalar value on the domain (e.g. L{Data})        self.__pde_v.setSymmetryOn()
82          @param location_of_fixed_flux:  mask for locations where flux is fixed.        if self.useReduced: self.__pde_v.setReducedOrderOn()
83          @type location_of_fixed_flux: vector values on the domain (e.g. L{Data})        self.__pde_p=LinearSinglePDE(domain)
84          @param permeability: permeability tensor. If scalar C{s} is given the tensor with        self.__pde_p.setSymmetryOn()
85                               C{s} on the main diagonal is used. If vector C{v} is given the tensor with        if self.useReduced: self.__pde_p.setReducedOrderOn()
86                               C{v} on the main diagonal is used.        
87          @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})        if self.solver  == self.SIMPLE:
88         if self.verbose: print "DarcyFlow: simple solver is used."
89          @note: the values of parameters which are not set by calling C{setValue} are not altered.           self.__pde_v.setValue(D=util.kronecker(self.domain.getDim()))
90          @note: at any point on the boundary of the domain the pressure (C{location_of_fixed_pressure} >0)        elif self.solver  == self.POST:
91                 or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal       self.w=w
92                 is along the M{x_i} axis.       if util.inf(w)<0.:
93          """          raise ValueError,"Weighting factor must be non-negative."
94          if f !=None:       if self.verbose: print "DarcyFlow: global postprocessing of flux is used."
95             f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))        elif self.solver  == self.STAB:
96             if f.isEmpty():        if self.verbose: print "DarcyFlow: (non-symmetric) stabilization is used."
97                 f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))        elif  self.solver  == self.SYMSTAB:
98             else:        if self.verbose: print "DarcyFlow: symmetric stabilization is used."
99                 if f.getRank()>0: raise ValueError,"illegal rank of f."        else:
100             self.f=f      raise ValueError,"unknown solver %s"%self.solver
101          if g !=None:        self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
102             g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))        self.__g=escript.Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
103             if g.isEmpty():        self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
104               g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))        self.location_of_fixed_flux = escript.Vector(0, self.__pde_v.getFunctionSpaceForCoefficient("q"))
105             else:        self.setTolerance()
106               if not g.getShape()==(self.domain.getDim(),):      
107                 raise ValueError,"illegal shape of g"          
108             self.__g=g     def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
109          """
110          if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)        assigns values to model parameters
111          if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)  
112          :param f: volumetic sources/sinks
113          if permeability!=None:        :type f: scalar value on the domain (e.g. `escript.Data`)
114             perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))        :param g: flux sources/sinks
115             if perm.getRank()==0:        :type g: vector values on the domain (e.g. `escript.Data`)
116                 perm=perm*util.kronecker(self.domain.getDim())        :param location_of_fixed_pressure: mask for locations where pressure is fixed
117             elif perm.getRank()==1:        :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
118                 perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm        :param location_of_fixed_flux:  mask for locations where flux is fixed.
119                 for i in range(self.domain.getDim()): perm[i,i]=perm2[i]        :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
120             elif perm.getRank()==2:        :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
121                pass        :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
122             else:  
123                raise ValueError,"illegal rank of permeability."        :note: the values of parameters which are not set by calling ``setValue`` are not altered.
124             self.__permeability=perm        :note: at any point on the boundary of the domain the pressure
125             self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))               (``location_of_fixed_pressure`` >0) or the normal component of the
126                 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
127      def setTolerance(self,rtol=1e-4):               is along the *x_i* axis.
128          """  
129          sets the relative tolerance C{rtol} used to terminate the solution process. The iteration is terminated if        """
130          if location_of_fixed_pressure!=None:
131          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }             self.location_of_fixed_pressure=util.wherePositive(location_of_fixed_pressure)
132               self.__pde_p.setValue(q=self.location_of_fixed_pressure)
133          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}}.        if location_of_fixed_flux!=None:
134              self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
135          @param rtol: relative tolerance for the pressure            self.__pde_v.setValue(q=self.location_of_fixed_flux)
136          @type rtol: non-negative C{float}        
137          """              
138          if rtol<0:        # pressure  is rescaled by the factor 1/self.scale
139              raise ValueError,"Relative tolerance needs to be non-negative."        if permeability!=None:
140          self.__rtol=rtol      
141      def getTolerance(self):       perm=util.interpolate(permeability,self.__pde_v.getFunctionSpaceForCoefficient("A"))
142          """           V=util.vol(self.domain)
143          returns the relative tolerance           l=V**(1./self.domain.getDim())
144            
145          @return: current relative tolerance       if perm.getRank()==0:
146          @rtype: C{float}          perm_inv=(1./perm)
147          """              self.scale=util.integrate(perm_inv)/V*l
148          return self.__rtol          perm_inv=perm_inv*((1./self.scale)*util.kronecker(self.domain.getDim()))
149            perm=perm*(self.scale*util.kronecker(self.domain.getDim()))
150      def setAbsoluteTolerance(self,atol=0.):          
151          """          
152          sets the absolute tolerance C{atol} used to terminate the solution process. The iteration is terminated if       elif perm.getRank()==2:
153            perm_inv=util.inverse(perm)
154          M{|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) }              self.scale=util.sqrt(util.integrate(util.length(perm_inv)**2)/V)*l
155            perm_inv*=(1./self.scale)
156          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}}.          perm=perm*self.scale
157         else:
158          @param atol: absolute tolerance for the pressure          raise ValueError,"illegal rank of permeability."
159          @type atol: non-negative C{float}          
160          """       self.__permeability=perm
161          if atol<0:       self.__permeability_inv=perm_inv
162              raise ValueError,"Absolute tolerance needs to be non-negative."       if self.verbose: print "DarcyFlow: scaling factor for pressure is %e."%self.scale
163          self.__atol=atol      
164      def getAbsoluteTolerance(self):       if self.solver  == self.SIMPLE:
165         """          self.__pde_p.setValue(A=self.__permeability)
166         returns the absolute tolerance       elif self.solver  == self.POST:
167                  self.__pde_p.setValue(A=self.__permeability)
168         @return: current absolute tolerance          k=util.kronecker(self.domain.getDim())
169         @rtype: C{float}          self.lamb = self.w*util.length(perm_inv)*l
170         """          self.__pde_v.setValue(D=self.__permeability_inv, A=self.lamb*self.domain.getSize()*util.outer(k,k))
171         return self.__atol       elif self.solver  == self.STAB:
172            self.__pde_p.setValue(A=0.5*self.__permeability)
173      def setSubProblemTolerance(self,rtol=None):          self.__pde_v.setValue(D=0.5*self.__permeability_inv)
174           """       elif  self.solver  == self.SYMSTAB:
175           Sets the relative tolerance to solve the subproblem(s). If C{rtol} is not present          self.__pde_p.setValue(A=0.5*self.__permeability)
176           C{self.getTolerance()**2} is used.          self.__pde_v.setValue(D=0.5*self.__permeability_inv)
177    
178           @param rtol: relative tolerence        if g != None:
179           @type rtol: positive C{float}      g=util.interpolate(g, self.__pde_v.getFunctionSpaceForCoefficient("Y"))
180           """      if g.isEmpty():
181           if rtol == None:            g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
182                if self.getTolerance()<=0.:      else:
183                    raise ValueError,"A positive relative tolerance must be set."          if not g.getShape()==(self.domain.getDim(),): raise ValueError,"illegal shape of g"
184                self.__sub_tol=max(util.EPSILON**(0.75),self.getTolerance()**2)      self.__g=g
185           else:        if f !=None:
186               if rtol<=0:       f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
187                   raise ValueError,"sub-problem tolerance must be positive."       if f.isEmpty():      
188               self.__sub_tol=max(util.EPSILON**(0.75),rtol)            f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
189         else:
190      def getSubProblemTolerance(self):           if f.getRank()>0: raise ValueError,"illegal rank of f."
191           """       self.__f=f
192           Returns the subproblem reduction factor.     def getSolverOptionsFlux(self):
193          """
194           @return: subproblem reduction factor        Returns the solver options used to solve the flux problems
195           @rtype: C{float}        :return: `SolverOptions`
196           """        """
197           return self.__sub_tol        return self.__pde_v.getSolverOptions()
198          
199      def solve(self,u0,p0, max_iter=100, verbose=False, show_details=False, max_num_corrections=10):     def setSolverOptionsFlux(self, options=None):
200           """        """
201           solves the problem.        Sets the solver options used to solve the flux problems
202          If ``options`` is not present, the options are reset to default
203           The iteration is terminated if the residual norm is less then self.getTolerance().        :param options: `SolverOptions`
204          """
205           @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.        return self.__pde_v.setSolverOptions(options)
206           @type u0: vector value on the domain (e.g. L{Data}).      
207           @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.     def getSolverOptionsPressure(self):
208           @type p0: scalar value on the domain (e.g. L{Data}).        """
209           @param verbose: if set some information on iteration progress are printed        Returns the solver options used to solve the pressure problems
210           @type verbose: C{bool}        :return: `SolverOptions`
211           @param show_details:  if set information on the subiteration process are printed.        """
212           @type show_details: C{bool}        return self.__pde_p.getSolverOptions()
213           @return: flux and pressure        
214           @rtype: C{tuple} of L{Data}.     def setSolverOptionsPressure(self, options=None):
215          """
216           @note: The problem is solved as a least squares form        Sets the solver options used to solve the pressure problems
217          If ``options`` is not present, the options are reset to default
218           M{(I+D^*D)u+Qp=D^*f+g}        
219           M{Q^*u+Q^*Qp=Q^*g}        :param options: `SolverOptions`
220          :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
221           where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.        """
222           We eliminate the flux form the problem by setting        return self.__pde_p.setSolverOptions(options)
223          
224           M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux     def setTolerance(self,rtol=1e-4):
225          """
226           form the first equation. Inserted into the second equation we get        sets the relative tolerance ``rtol`` for the pressure for the stabelized solvers.
227          
228           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        :param rtol: relative tolerance for the pressure
229          :type rtol: non-negative ``float``
230           which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step        """
231           PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.        if rtol<0:
232           """       raise ValueError,"Relative tolerance needs to be non-negative."
233           self.verbose=verbose        self.__rtol=rtol
234           self.show_details= show_details and self.verbose        
235           rtol=self.getTolerance()     def getTolerance(self):
236           atol=self.getAbsoluteTolerance()        """
237           if self.verbose: print "DarcyFlux: initial sub tolerance = %e"%self.getSubProblemTolerance()        returns the relative tolerance
238          :return: current relative tolerance
239           num_corrections=0        :rtype: ``float``
240           converged=False        """
241           p=p0        return self.__rtol
242           norm_r=None        
243           while not converged:     def solve(self,u0,p0, max_iter=100, iter_restart=20):
244                 v=self.getFlux(p, fixed_flux=u0, show_details=self.show_details)        """
245                 Qp=self.__Q(p)        solves the problem.
246                 norm_v=self.__L2(v)        
247                 norm_Qp=self.__L2(Qp)        The iteration is terminated if the residual norm is less then self.getTolerance().
248                 if norm_v == 0.:  
249                    if norm_Qp == 0.:        :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.
250                       return v,p        :type u0: vector value on the domain (e.g. `escript.Data`).
251                    else:        :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.
252                      fac=norm_Qp        :type p0: scalar value on the domain (e.g. `escript.Data`).
253                 else:        :param max_iter: maximum number of (outer) iteration steps for the stabilization solvers,
254                    if norm_Qp == 0.:        :type max_iter: ``int``
255                      fac=norm_v        :param iter_restart: number of steps after which the iteration is restarted. The larger ``iter_restart`` the larger the required memory.
256                    else:                             A small value for ``iter_restart`` may require a large number of iteration steps or may even lead to a failure
257                      fac=2./(1./norm_v+1./norm_Qp)                             of the iteration. ``iter_restart`` is relevant for the stabilization solvers only.
258                 ATOL=(atol+rtol*fac)        :type iter_restart: ``int``
259                 if self.verbose:        :return: flux and pressure
260                      print "DarcyFlux: L2 norm of v = %e."%norm_v        :rtype: ``tuple`` of `escript.Data`.
261                      print "DarcyFlux: L2 norm of k.grad(p) = %e."%norm_Qp  
262                      print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL        """
263                 if norm_r == None or norm_r>ATOL:        # rescale initial guess:
264                     if num_corrections>max_num_corrections:        p0=p0/self.scale
265                           raise ValueError,"maximum number of correction steps reached."        if self.solver  == self.SIMPLE or self.solver  == self.POST :
266                     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)          self.__pde_p.setValue(X=self.__g ,
267                     num_corrections+=1                                Y=self.__f,
268                 else:                                y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux),
269                     converged=True                                r=p0)
270           return v,p          p=self.__pde_p.getSolution()
271  #          u = self.getFlux(p, u0)
272  #                      elif  self.solver  == self.STAB:
273  #               r_hat=g-util.interpolate(v,Function(self.domain))-Qp      u,p = self.__solve_STAB(u0,p0, max_iter, iter_restart)
274  #               #===========================================================================        elif  self.solver  == self.SYMSTAB:
275  #               norm_r_hat=self.__L2(r_hat)      u,p = self.__solve_SYMSTAB(u0,p0, max_iter, iter_restart)
276  #               norm_v=self.__L2(v)      
277  #               norm_g=self.__L2(g)        if self.verbose:
278  #               norm_gv=self.__L2(g-v)          KGp=util.tensor_mult(self.__permeability,util.grad(p))
279  #               norm_Qp=self.__L2(Qp)          def_p=self.__g-(u+KGp)
280  #               norm_gQp=self.__L2(g-Qp)          def_v=self.__f-util.div(u, self.__pde_v.getFunctionSpaceForCoefficient("X"))
281  #               fac=min(max(norm_v,norm_gQp),max(norm_Qp,norm_gv))          print "DarcyFlux: |g-u-K*grad(p)|_2 = %e (|u|_2 = %e)."%(self.__L2(def_p),self.__L2(u))
282  #               fac=min(norm_v,norm_Qp,norm_gv)          print "DarcyFlux: |f-div(u)|_2 = %e (|grad(u)|_2 = %e)."%(self.__L2(def_v),self.__L2(util.grad(u)))
283  #               norm_r_hat_PCG=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))        #rescale result
284  #               print "norm_r_hat = ",norm_r_hat,norm_r_hat_PCG, norm_r_hat_PCG/norm_r_hat        p=p*self.scale
285  #               if r!=None:        return u,p
286  #                   print "diff = ",self.__L2(r-r_hat)/norm_r_hat        
287  #                   sub_tol=min(rtol/self.__L2(r-r_hat)*norm_r_hat,1.)*self.getSubProblemTolerance()     def getFlux(self,p, u0=None):
288  #                   self.setSubProblemTolerance(sub_tol)          """
289  #                   print "subtol_new=",self.getSubProblemTolerance()          returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
290  #               print "norm_v = ",norm_v          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
291  #               print "norm_gv = ",norm_gv          Notice that ``g`` and ``f`` are used, see `setValue`.
292  #               print "norm_Qp = ",norm_Qp  
293  #               print "norm_gQp = ",norm_gQp          :param p: pressure.
294  #               print "norm_g = ",norm_g          :type p: scalar value on the domain (e.g. `escript.Data`).
295  #               print "max(norm_v,norm_gQp)=",max(norm_v,norm_gQp)          :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
296  #               print "max(norm_Qp,norm_gv)=",max(norm_Qp,norm_gv)          :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
297  #               if fac == 0:          :return: flux
298  #                   if self.verbose: print "DarcyFlux: trivial case!"          :rtype: `escript.Data`
299  #                   return v,p          """
300  #               #===============================================================================          if self.solver  == self.SIMPLE or self.solver  == self.POST  :
301  #               # norm_v=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(v),v))              KGp=util.tensor_mult(self.__permeability,util.grad(p))
302  #               # norm_Qp=self.__L2(Qp)              self.__pde_v.setValue(Y=self.__g-KGp, X=escript.Data())
303  #               norm_r_hat=util.sqrt(self.__inner_PCG(self.__Msolve_PCG(r_hat),r_hat))              if u0 == None:
304  #               # print "**** norm_v, norm_Qp :",norm_v,norm_Qp             self.__pde_v.setValue(r=escript.Data())
305  #          else:
306  #               ATOL=(atol+rtol*2./(1./norm_v+1./norm_Qp))             self.__pde_v.setValue(r=u0)
307  #               if self.verbose:              u= self.__pde_v.getSolution()
308  #                   print "DarcyFlux: residual = %e"%norm_r_hat      elif self.solver  == self.POST:
309  #                   print "DarcyFlux: absolute tolerance ATOL = %e."%ATOL              self.__pde_v.setValue(Y=util.tensor_mult(self.__permeability_inv,self.__g)-util.grad(p),
310  #               if norm_r_hat <= ATOL:                                    X=self.lamb * self.__f * util.kronecker(self.domain.getDim()))
311  #                   print "DarcyFlux: iteration finalized."              if u0 == None:
312  #                   converged=True             self.__pde_v.setValue(r=escript.Data())
313  #               else:          else:
314  #                   # 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)             self.__pde_v.setValue(r=u0)
315  #                   # 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)              u= self.__pde_v.getSolution()
316  #                   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)      elif self.solver  == self.STAB:
317  #               print "norm_r =",norm_r           gp=util.grad(p)
318  #         return v,p           self.__pde_v.setValue(Y=0.5*(util.tensor_mult(self.__permeability_inv,self.__g)+gp),
319      def __L2(self,v):                                 X= p * util.kronecker(self.domain.getDim()),
320           return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))                                 y= - p * self.domain.getNormal())                          
321             if u0 == None:
322      def __Q(self,p):             self.__pde_v.setValue(r=escript.Data())
323            return util.tensor_mult(self.__permeability,util.grad(p))           else:
324               self.__pde_v.setValue(r=u0)
325      def __Aprod(self,dp):           u= self.__pde_v.getSolution()
326            self.__pde_v.setTolerance(self.getSubProblemTolerance())      elif  self.solver  == self.SYMSTAB:
327            if self.show_details: print "DarcyFlux: Applying operator"           gp=util.grad(p)
328            Qdp=self.__Q(dp)           self.__pde_v.setValue(Y=0.5*(util.tensor_mult(self.__permeability_inv,self.__g)-gp),
329            self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())                                 X= escript.Data() ,
330            du=self.__pde_v.getSolution(verbose=self.show_details)                                 y= escript.Data() )                          
331            return Qdp+du           if u0 == None:
332      def __inner_GMRES(self,r,s):             self.__pde_v.setValue(r=escript.Data())
333           return util.integrate(util.inner(r,s))           else:
334               self.__pde_v.setValue(r=u0)
335      def __inner_PCG(self,p,r):           u= self.__pde_v.getSolution()
336           return util.integrate(util.inner(self.__Q(p), r))      return u
337          
338      def __Msolve_PCG(self,r):      
339            self.__pde_p.setTolerance(self.getSubProblemTolerance())     def __solve_STAB(self, u0, p0, max_iter, iter_restart):
340            if self.show_details: print "DarcyFlux: Applying preconditioner"            # p0 is used as an initial guess
341            self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())        u=self.getFlux(p0, u0)  
342            return self.__pde_p.getSolution(verbose=self.show_details)            self.__pde_p.setValue( Y=self.__f-util.div(u),
343                                     X=0.5*(self.__g - u - util.tensor_mult(self.__permeability,util.grad(p0)) ),
344                                     y= escript.Data(),
345      def getFlux(self,p=None, fixed_flux=Data(), show_details=False):                                   r=escript.Data())
346          """  
347          returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}        dp=self.__pde_p.getSolution()
348          on locations where C{location_of_fixed_flux} is positive (see L{setValue}).        p=GMRES(dp,
349          Note that C{g} and C{f} are used, see L{setValue}.                self.__STAB_Aprod,
350              p0,
351          @param p: pressure.            self.__inner,
352          @type p: scalar value on the domain (e.g. L{Data}).            atol=self.__norm(p0+dp)*self.getTolerance() ,
353          @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.            rtol=0.,
354          @type fixed_flux: vector values on the domain (e.g. L{Data}).            iter_max=max_iter,
355          @param tol: relative tolerance to be used.            iter_restart=iter_restart,
356          @type tol: positive C{float}.            verbose=self.verbose,P_R=None)
357          @return: flux              
358          @rtype: L{Data}            u=self.getFlux(p, u0)
359          @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}}            return u,p
360                 for the permeability M{k_{ij}}  
361          """     def __solve_SYMSTAB(self, u0, p0, max_iter, iter_restart):
362          self.__pde_v.setTolerance(self.getSubProblemTolerance())            # p0 is used as an initial guess
363          g=self.__g        u=self.getFlux(p0, u0)  
364          f=self.__f            self.__pde_p.setValue( Y= self.__f,
365          self.__pde_v.setValue(X=f*util.kronecker(self.domain), r=fixed_flux)                                   X=  0.5*(self.__g + u - util.tensor_mult(self.__permeability,util.grad(p0)) ),
366          if p == None:                                   y=  -  util.inner(self.domain.getNormal(), u),
367             self.__pde_v.setValue(Y=g)                                   r=escript.Data())
368          else:        dp=self.__pde_p.getSolution()
369             self.__pde_v.setValue(Y=g-self.__Q(p))        
370          return self.__pde_v.getSolution(verbose=show_details)        p=GMRES(dp,
371                  self.__SYMSTAB_Aprod,
372              p0,
373              self.__inner,
374              atol=self.__norm(p0+dp)*self.getTolerance() ,
375              rtol=0.,
376              iter_max=max_iter,
377              iter_restart=iter_restart,
378              verbose=self.verbose,P_R=None)
379                
380              u=self.getFlux(p, u0)
381              return u,p
382    
383       def __L2(self,v):
384             return util.sqrt(util.integrate(util.length(util.interpolate(v,escript.Function(self.domain)))**2))      
385      
386       def __norm(self,r):
387             return util.sqrt(self.__inner(r,r))
388            
389       def __inner(self,r,s):
390             return util.integrate(util.inner(r,s), escript.Function(self.domain))
391            
392       def __STAB_Aprod(self,p):
393          gp=util.grad(p)
394          self.__pde_v.setValue(Y=-0.5*gp,
395                                X=-p*util.kronecker(self.__pde_v.getDomain()),
396                                y= p * self.domain.getNormal(),  
397                                r=escript.Data())
398          u = -self.__pde_v.getSolution()
399          self.__pde_p.setValue(Y=util.div(u),
400                                X=0.5*(u+util.tensor_mult(self.__permeability,gp)),
401                                y=escript.Data(),
402                                r=escript.Data())
403        
404          return  self.__pde_p.getSolution()
405      
406       def __SYMSTAB_Aprod(self,p):
407          gp=util.grad(p)
408          self.__pde_v.setValue(Y=0.5*gp ,
409                                X=escript.Data(),
410                                y=escript.Data(),  
411                                r=escript.Data())
412          u = -self.__pde_v.getSolution()
413          self.__pde_p.setValue(Y=escript.Data(),
414                                X=0.5*(-u+util.tensor_mult(self.__permeability,gp)),
415                                y=escript.Data(),
416                                r=escript.Data())
417        
418          return  self.__pde_p.getSolution()
419          
420    
421  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  class StokesProblemCartesian(HomogeneousSaddlePointProblem):
422       """       """
# Line 391  class StokesProblemCartesian(Homogeneous Line 441  class StokesProblemCartesian(Homogeneous
441           """           """
442           initialize the Stokes Problem           initialize the Stokes Problem
443    
444           @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
445           @type domain: L{Domain}           LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
446           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.           with macro elements for the pressure.
447    
448             :param domain: domain of the problem.
449             :type domain: `Domain`
450           """           """
451           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
452           self.domain=domain           self.domain=domain
453           self.vol=util.integrate(1.,Function(self.domain))           self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
454           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_v.setSymmetryOn()
455           self.__pde_u.setSymmetryOn()      
          # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)  
          # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.RILU)  
   
456           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
457           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
          # self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)  
458           self.__pde_prec.setSymmetryOn()           self.__pde_prec.setSymmetryOn()
459    
460       def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data()):           self.__pde_proj=LinearPDE(domain)
461             self.__pde_proj.setReducedOrderOn()
462         self.__pde_proj.setValue(D=1)
463             self.__pde_proj.setSymmetryOn()
464    
465         def getSolverOptionsVelocity(self):
466             """
467         returns the solver options used  solve the equation for velocity.
468        
469         :rtype: `SolverOptions`
470         """
471         return self.__pde_v.getSolverOptions()
472         def setSolverOptionsVelocity(self, options=None):
473             """
474         set the solver options for solving the equation for velocity.
475        
476         :param options: new solver  options
477         :type options: `SolverOptions`
478         """
479             self.__pde_v.setSolverOptions(options)
480         def getSolverOptionsPressure(self):
481             """
482         returns the solver options used  solve the equation for pressure.
483         :rtype: `SolverOptions`
484         """
485         return self.__pde_prec.getSolverOptions()
486         def setSolverOptionsPressure(self, options=None):
487             """
488         set the solver options for solving the equation for pressure.
489         :param options: new solver  options
490         :type options: `SolverOptions`
491         """
492         self.__pde_prec.setSolverOptions(options)
493    
494         def setSolverOptionsDiv(self, options=None):
495             """
496         set the solver options for solving the equation to project the divergence of
497         the velocity onto the function space of presure.
498        
499         :param options: new solver options
500         :type options: `SolverOptions`
501         """
502         self.__pde_proj.setSolverOptions(options)
503         def getSolverOptionsDiv(self):
504             """
505         returns the solver options for solving the equation to project the divergence of
506         the velocity onto the function space of presure.
507        
508         :rtype: `SolverOptions`
509         """
510         return self.__pde_proj.getSolverOptions()
511    
512         def updateStokesEquation(self, v, p):
513             """
514             updates the Stokes equation to consider dependencies from ``v`` and ``p``
515             :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values.
516             """
517             pass
518         def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
519            """
520            assigns new values to the model parameters.
521    
522            :param f: external force
523            :type f: `Vector` object in `FunctionSpace` `Function` or similar
524            :param fixed_u_mask: mask of locations with fixed velocity.
525            :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
526            :param eta: viscosity
527            :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
528            :param surface_stress: normal surface stress
529            :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
530            :param stress: initial stress
531        :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
532            """
533            if eta !=None:
534                k=util.kronecker(self.domain.getDim())
535                kk=util.outer(k,k)
536                self.eta=util.interpolate(eta, escript.Function(self.domain))
537            self.__pde_prec.setValue(D=1/self.eta)
538                self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
539            if restoration_factor!=None:
540                n=self.domain.getNormal()
541                self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
542            if fixed_u_mask!=None:
543                self.__pde_v.setValue(q=fixed_u_mask)
544            if f!=None: self.__f=f
545            if surface_stress!=None: self.__surface_stress=surface_stress
546            if stress!=None: self.__stress=stress
547    
548         def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
549          """          """
550          assigns values to the model parameters          assigns values to the model parameters
551    
552          @param f: external force          :param f: external force
553          @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar          :type f: `Vector` object in `FunctionSpace` `Function` or similar
554          @param fixed_u_mask: mask of locations with fixed velocity.          :param fixed_u_mask: mask of locations with fixed velocity.
555          @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
556          @param eta: viscosity          :param eta: viscosity
557          @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar          :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
558          @param surface_stress: normal surface stress          :param surface_stress: normal surface stress
559          @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
560          @param stress: initial stress          :param stress: initial stress
561      @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.  
   
562          """          """
563          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  
564    
565       def inner_pBv(self,p,v):       def Bv(self,v,tol):
566           """           """
567           returns inner product of element p and div(v)           returns inner product of element p and div(v)
568    
569           @param p: a pressure increment           :param v: a residual
570           @param v: a residual           :return: inner product of element p and div(v)
571           @return: inner product of element p and div(v)           :rtype: ``float``
572           @rtype: C{float}           """
573             self.__pde_proj.setValue(Y=-util.div(v))
574         self.getSolverOptionsDiv().setTolerance(tol)
575         self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
576             out=self.__pde_proj.getSolution()
577             return out
578    
579         def inner_pBv(self,p,Bv):
580             """
581             returns inner product of element p and Bv=-div(v)
582    
583             :param p: a pressure increment
584             :param Bv: a residual
585             :return: inner product of element p and Bv=-div(v)
586             :rtype: ``float``
587           """           """
588           return util.integrate(-p*util.div(v))           return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
589    
590       def inner_p(self,p0,p1):       def inner_p(self,p0,p1):
591           """           """
592           Returns inner product of p0 and p1           Returns inner product of p0 and p1
593    
594           @param p0: a pressure           :param p0: a pressure
595           @param p1: a pressure           :param p1: a pressure
596           @return: inner product of p0 and p1           :return: inner product of p0 and p1
597           @rtype: C{float}           :rtype: ``float``
598           """           """
599           s0=util.interpolate(p0/self.eta,Function(self.domain))           s0=util.interpolate(p0, escript.Function(self.domain))
600           s1=util.interpolate(p1/self.eta,Function(self.domain))           s1=util.interpolate(p1, escript.Function(self.domain))
601           return util.integrate(s0*s1)           return util.integrate(s0*s1)
602    
603       def norm_v(self,v):       def norm_v(self,v):
604           """           """
605           returns the norm of v           returns the norm of v
606    
607           @param v: a velovity           :param v: a velovity
608           @return: norm of v           :return: norm of v
609           @rtype: non-negative C{float}           :rtype: non-negative ``float``
610           """           """
611           return util.sqrt(util.integrate(util.length(util.grad(v))))           return util.sqrt(util.integrate(util.length(util.grad(v))**2))
612    
613       def getV(self, p, v0):  
614         def getDV(self, p, v, tol):
615           """           """
616           return the value for v for a given p (overwrite)           return the value for v for a given p (overwrite)
617    
618           @param p: a pressure           :param p: a pressure
619           @param v0: a initial guess for the value v to return.           :param v: a initial guess for the value v to return.
620           @return: v given as M{v= A^{-1} (f-B^*p)}           :return: dv given as *Adv=(f-Av-B^*p)*
621           """           """
622           self.__pde_u.setTolerance(self.getSubProblemTolerance())           self.updateStokesEquation(v,p)
623           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress, r=v0)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
624         self.getSolverOptionsVelocity().setTolerance(tol)
625         self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
626           if self.__stress.isEmpty():           if self.__stress.isEmpty():
627              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)))
628           else:           else:
629              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)))
630           out=self.__pde_u.getSolution(verbose=self.show_details)           out=self.__pde_v.getSolution()
631           return  out           return  out
632    
633         def norm_Bv(self,Bv):
          raise NotImplementedError,"no v calculation implemented."  
   
   
      def norm_Bv(self,v):  
634          """          """
635          Returns Bv (overwrite).          Returns Bv (overwrite).
636    
637          @rtype: equal to the type of p          :rtype: equal to the type of p
638          @note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
639          """          """
640          return util.sqrt(util.integrate(util.div(v)**2))          return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
641    
642       def solve_AinvBt(self,p):       def solve_AinvBt(self,p, tol):
643           """           """
644           Solves M{Av=B^*p} with accuracy L{self.getSubProblemTolerance()}           Solves *Av=B^*p* with accuracy `tol`
645    
646           @param p: a pressure increment           :param p: a pressure increment
647           @return: the solution of M{Av=B^*p}           :return: the solution of *Av=B^*p*
648           @note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
649           """           """
650           self.__pde_u.setTolerance(self.getSubProblemTolerance())           self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
651           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)  
652           return  out           return  out
653    
654       def solve_precB(self,v):       def solve_prec(self,Bv, tol):
655           """           """
656           applies preconditioner for for M{BA^{-1}B^*} to M{Bv}           applies preconditioner for for *BA^{-1}B^** to *Bv*
657           with accuracy L{self.getSubProblemTolerance()} (overwrite).           with accuracy `self.getSubProblemTolerance()`
658    
659           @param v: velocity increment           :param Bv: velocity increment
660           @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^ * )*
661           @note: boundary conditions on p are zero.           :note: boundary conditions on p are zero.
662           """           """
663           self.__pde_prec.setValue(Y=-util.div(v))           self.__pde_prec.setValue(Y=Bv)
664           self.__pde_prec.setTolerance(self.getSubProblemTolerance())       self.getSolverOptionsPressure().setTolerance(tol)
665           return self.__pde_prec.getSolution(verbose=self.show_details)       self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
666             out=self.__pde_prec.getSolution()
667             return out

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