/[escript]/trunk/escriptcore/py_src/flows.py
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revision 2881 by jfenwick, Thu Jan 28 02:03:15 2010 UTC revision 4154 by jfenwick, Tue Jan 22 09:30:23 2013 UTC
# Line 1  Line 1 
1  ########################################################  # -*- coding: utf-8 -*-
2    ##############################################################################
3  #  #
4  # Copyright (c) 2003-2010 by University of Queensland  # Copyright (c) 2003-2013 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) 2003-2010 by University of Queensland  __copyright__="""Copyright (c) 2003-2013 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 31  Some models for flow Line 33  Some models for flow
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 escriptcpp
37  import util  escore=escriptcpp
38  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions  #from . import escript
39  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES  from . import util
40    from .linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
41    from .pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
42    
43  class DarcyFlow(object):  class DarcyFlow(object):
44      """     """
45      solves the problem     solves the problem
46      
47      *u_i+k_{ij}*p_{,j} = g_i*     *u_i+k_{ij}*p_{,j} = g_i*
48      *u_{i,i} = f*     *u_{i,i} = f*
49      
50      where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,     where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
51      
52      :note: The problem is solved in a least squares formulation.     :cvar EVAL: direct pressure gradient evaluation for flux
53      """     :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*
54                   where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
55      def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):     :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
56          """     """
57          initializes the Darcy flux problem     EVAL="EVAL"
58          :param domain: domain of the problem     SIMPLE="EVAL"
59          :type domain: `Domain`     POST="POST"
60      :param useReduced: uses reduced oreder on flux and pressure     SMOOTH="SMOOTH"
61      :type useReduced: ``bool``     def __init__(self, domain, useReduced=False, solver="POST", verbose=False, w=1.):
62      :param adaptSubTolerance: switches on automatic subtolerance selection        """
63      :type adaptSubTolerance: ``bool``          initializes the Darcy flux problem.
64          """  
65          self.domain=domain        :param domain: domain of the problem
66          if weight == None:        :type domain: `Domain`
67             s=self.domain.getSize()        :param useReduced: uses reduced oreder on flux and pressure
68             self.__l=(3.*util.longestEdge(self.domain)*s/util.sup(s))**2        :type useReduced: ``bool``
69             # self.__l=(3.*util.longestEdge(self.domain))**2        :param solver: solver method
70             #self.__l=(0.1*util.longestEdge(self.domain)*s/util.sup(s))**2        :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST`, `DarcyFlow.SMOOTH` ]
71          else:        :param verbose: if ``True`` some information on the iteration progress are printed.
72             self.__l=weight        :type verbose: ``bool``
73          self.__pde_v=LinearPDESystem(domain)        :param w: weighting factor for `DarcyFlow.POST` solver
74          if useReduced: self.__pde_v.setReducedOrderOn()        :type w: ``float``
75          self.__pde_v.setSymmetryOn()        
76          self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))        """
77          self.__pde_p=LinearSinglePDE(domain)        if not solver in [DarcyFlow.EVAL, DarcyFlow.POST,  DarcyFlow.SMOOTH ] :
78          self.__pde_p.setSymmetryOn()            raise ValueError("unknown solver %d."%solver)
79          if useReduced: self.__pde_p.setReducedOrderOn()  
80          self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))        self.domain=domain
81          self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))        self.solver=solver
82          self.setTolerance()        self.useReduced=useReduced
83          self.setAbsoluteTolerance()        self.verbose=verbose
84      self.__adaptSubTolerance=adaptSubTolerance        self.l=None
85      self.verbose=False        self.w=None
86      def getSolverOptionsFlux(self):      
87      """        self.__pde_p=LinearSinglePDE(domain)
88      Returns the solver options used to solve the flux problems        self.__pde_p.setSymmetryOn()
89              if self.useReduced: self.__pde_p.setReducedOrderOn()
90      *(I+D^*D)u=F*  
91              if self.solver  == self.EVAL:
92      :return: `SolverOptions`           self.__pde_v=None
93      """           if self.verbose: print("DarcyFlow: simple solver is used.")
94      return self.__pde_v.getSolverOptions()  
95      def setSolverOptionsFlux(self, options=None):        elif self.solver  == self.POST:
96      """           if util.inf(w)<0.:
97      Sets the solver options used to solve the flux problems              raise ValueError("Weighting factor must be non-negative.")
98                 if self.verbose: print("DarcyFlow: global postprocessing of flux is used.")
99      *(I+D^*D)u=F*           self.__pde_v=LinearPDESystem(domain)
100             self.__pde_v.setSymmetryOn()
101             if self.useReduced: self.__pde_v.setReducedOrderOn()
102             self.w=w
103             x=self.domain.getX()
104             self.l=min( [util.sup(x[i])-util.inf(x[i]) for i in range(self.domain.getDim()) ] )
105             #self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
106    
107          elif self.solver  == self.SMOOTH:
108             self.__pde_v=LinearPDESystem(domain)
109             self.__pde_v.setSymmetryOn()
110             if self.useReduced: self.__pde_v.setReducedOrderOn()
111             if self.verbose: print("DarcyFlow: flux smoothing is used.")
112             self.w=0
113    
114          self.__f=escore.Data(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
115          self.__g=escore.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
116          self.__permeability_invXg=escore.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
117          self.__permeability_invXg_ref=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
118          self.ref_point_id=None
119          self.ref_point=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
120          self.location_of_fixed_pressure = escore.Data(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
121          self.location_of_fixed_flux = escore.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
122          self.perm_scale=1.
123        
124            
125       def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
126          """
127          assigns values to model parameters
128    
129          :param f: volumetic sources/sinks
130          :type f: scalar value on the domain (e.g. `escript.Data`)
131          :param g: flux sources/sinks
132          :type g: vector values on the domain (e.g. `escript.Data`)
133          :param location_of_fixed_pressure: mask for locations where pressure is fixed
134          :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
135          :param location_of_fixed_flux:  mask for locations where flux is fixed.
136          :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
137          :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
138          :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
139    
140          :note: the values of parameters which are not set by calling ``setValue`` are not altered.
141          :note: at any point on the boundary of the domain the pressure
142                 (``location_of_fixed_pressure`` >0) or the normal component of the
143                 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
144                 is along the *x_i* axis.
145    
146          """
147          if location_of_fixed_pressure!=None:
148               self.location_of_fixed_pressure=util.wherePositive(util.interpolate(location_of_fixed_pressure, self.__pde_p.getFunctionSpaceForCoefficient("q")))
149               self.ref_point_id=self.location_of_fixed_pressure.maxGlobalDataPoint()
150               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.")
151               self.ref_point=self.__pde_p.getFunctionSpaceForCoefficient("q").getX().getTupleForGlobalDataPoint(*self.ref_point_id)
152               if self.verbose: print(("DarcyFlow: reference point at %s."%(self.ref_point,)))
153               self.__pde_p.setValue(q=self.location_of_fixed_pressure)
154          if location_of_fixed_flux!=None:
155              self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
156              if not self.__pde_v == None:
157                  self.__pde_v.setValue(q=self.location_of_fixed_flux)
158                
159          if permeability!=None:
160            
161      If ``options`` is not present, the options are reset to default           perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
162      :param options: `SolverOptions`           self.perm_scale=util.Lsup(util.length(perm))
163      :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.           if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
164      """           perm=perm*(1./self.perm_scale)
165      return self.__pde_v.setSolverOptions(options)          
166      def getSolverOptionsPressure(self):           if perm.getRank()==0:
167      """  
168      Returns the solver options used to solve the pressure problems              perm_inv=(1./perm)
169                    perm_inv=perm_inv*util.kronecker(self.domain.getDim())
170      *(Q^*Q)p=Q^*G*              perm=perm*util.kronecker(self.domain.getDim())
171                
172      :return: `SolverOptions`          
173      """           elif perm.getRank()==2:
174      return self.__pde_p.getSolverOptions()              perm_inv=util.inverse(perm)
175      def setSolverOptionsPressure(self, options=None):           else:
176      """              raise ValueError("illegal rank of permeability.")
177      Sets the solver options used to solve the pressure problems          
178                 self.__permeability=perm
179      *(Q^*Q)p=Q^*G*           self.__permeability_inv=perm_inv
180            
181      If ``options`` is not present, the options are reset to default           #====================
182      :param options: `SolverOptions`           self.__pde_p.setValue(A=self.__permeability)
183      :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.           if self.solver  == self.EVAL:
184      """                pass # no extra work required
185      return self.__pde_p.setSolverOptions(options)           elif self.solver  == self.POST:
186                  k=util.kronecker(self.domain.getDim())
187      def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):                self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
188          """                #self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
189          assigns values to model parameters                self.__pde_v.setValue(D=self.__permeability_inv, A_reduced=self.omega*util.outer(k,k))
190             elif self.solver  == self.SMOOTH:
191          :param f: volumetic sources/sinks              self.__pde_v.setValue(D=self.__permeability_inv)
192          :type f: scalar value on the domain (e.g. `Data`)  
193          :param g: flux sources/sinks        if g != None:
194          :type g: vector values on the domain (e.g. `Data`)          g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
195          :param location_of_fixed_pressure: mask for locations where pressure is fixed          if g.isEmpty():
196          :type location_of_fixed_pressure: scalar value on the domain (e.g. `Data`)               g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
197          :param location_of_fixed_flux:  mask for locations where flux is fixed.          else:
198          :type location_of_fixed_flux: vector values on the domain (e.g. `Data`)               if not g.getShape()==(self.domain.getDim(),): raise ValueError("illegal shape of g")
199          :param permeability: permeability tensor. If scalar ``s`` is given the tensor with          self.__g=g
200                               ``s`` on the main diagonal is used. If vector ``v`` is given the tensor with          self.__permeability_invXg=util.tensor_mult(self.__permeability_inv,self.__g * (1./self.perm_scale ))
201                               ``v`` on the main diagonal is used.          self.__permeability_invXg_ref=util.integrate(self.__permeability_invXg)/util.vol(self.domain)
202          :type permeability: scalar, vector or tensor values on the domain (e.g. `Data`)        if f !=None:
203             f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
204          :note: the values of parameters which are not set by calling ``setValue`` are not altered.           if f.isEmpty():      
205          :note: at any point on the boundary of the domain the pressure (``location_of_fixed_pressure`` >0)               f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
206                 or the normal component of the flux (``location_of_fixed_flux[i]>0`` if direction of the normal           else:
207                 is along the *x_i* axis.               if f.getRank()>0: raise ValueError("illegal rank of f.")
208          """           self.__f=f
         if f !=None:  
            f=util.interpolate(f, self.__pde_v.getFunctionSpaceForCoefficient("X"))  
            if f.isEmpty():  
                f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))  
            else:  
                if f.getRank()>0: raise ValueError,"illegal rank of f."  
            self.__f=f  
         if g !=None:  
            g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))  
            if g.isEmpty():  
              g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))  
            else:  
              if not g.getShape()==(self.domain.getDim(),):  
                raise ValueError,"illegal shape of g"  
            self.__g=g  
   
         if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)  
         if location_of_fixed_flux!=None: self.__pde_v.setValue(q=location_of_fixed_flux)  
   
         if permeability!=None:  
            perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))  
            if perm.getRank()==0:  
                perm=perm*util.kronecker(self.domain.getDim())  
            elif perm.getRank()==1:  
                perm, perm2=Tensor(0.,self.__pde_p.getFunctionSpaceForCoefficient("A")), perm  
                for i in range(self.domain.getDim()): perm[i,i]=perm2[i]  
            elif perm.getRank()==2:  
               pass  
            else:  
               raise ValueError,"illegal rank of permeability."  
            self.__permeability=perm  
            self.__pde_p.setValue(A=util.transposed_tensor_mult(self.__permeability,self.__permeability))  
   
     def setTolerance(self,rtol=1e-4):  
         """  
         sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if  
   
         *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*  
   
         where ``atol`` is an absolut tolerance (see `setAbsoluteTolerance`), *|f|^2 = integrate(length(f)^2)* and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.  
   
         :param rtol: relative tolerance for the pressure  
         :type rtol: non-negative ``float``  
         """  
         if rtol<0:  
             raise ValueError,"Relative tolerance needs to be non-negative."  
         self.__rtol=rtol  
     def getTolerance(self):  
         """  
         returns the relative tolerance  
   
         :return: current relative tolerance  
         :rtype: ``float``  
         """  
         return self.__rtol  
   
     def setAbsoluteTolerance(self,atol=0.):  
         """  
         sets the absolute tolerance ``atol`` used to terminate the solution process. The iteration is terminated if  
   
         *|g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) )*  
   
         where ``rtol`` is an absolut tolerance (see `setTolerance`), *|f|^2 = integrate(length(f)^2)* and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.  
   
         :param atol: absolute tolerance for the pressure  
         :type atol: non-negative ``float``  
         """  
         if atol<0:  
             raise ValueError,"Absolute tolerance needs to be non-negative."  
         self.__atol=atol  
     def getAbsoluteTolerance(self):  
        """  
        returns the absolute tolerance  
         
        :return: current absolute tolerance  
        :rtype: ``float``  
        """  
        return self.__atol  
     def getSubProblemTolerance(self):  
     """  
     Returns a suitable subtolerance  
     @type: ``float``  
     """  
     return max(util.EPSILON**(0.75),self.getTolerance()**2)  
     def setSubProblemTolerance(self):  
          """  
          Sets the relative tolerance to solve the subproblem(s) if subtolerance adaption is selected.  
          """  
      if self.__adaptSubTolerance:  
          sub_tol=self.getSubProblemTolerance()  
              self.getSolverOptionsFlux().setTolerance(sub_tol)  
          self.getSolverOptionsFlux().setAbsoluteTolerance(0.)  
          self.getSolverOptionsPressure().setTolerance(sub_tol)  
          self.getSolverOptionsPressure().setAbsoluteTolerance(0.)  
          if self.verbose: print "DarcyFlux: relative subtolerance is set to %e."%sub_tol  
   
     def solve(self,u0,p0, max_iter=100, verbose=False, max_num_corrections=10):  
          """  
          solves the problem.  
   
          The iteration is terminated if the residual norm is less then self.getTolerance().  
   
          :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.  
          :type u0: vector value on the domain (e.g. `Data`).  
          :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.  
          :type p0: scalar value on the domain (e.g. `Data`).  
          :param verbose: if set some information on iteration progress are printed  
          :type verbose: ``bool``  
          :return: flux and pressure  
          :rtype: ``tuple`` of `Data`.  
   
          :note: The problem is solved as a least squares form  
   
          *(I+D^*D)u+Qp=D^*f+g*  
          *Q^*u+Q^*Qp=Q^*g*  
   
          where *D* is the *div* operator and *(Qp)_i=k_{ij}p_{,j}* for the permeability *k_{ij}*.  
          We eliminate the flux form the problem by setting  
   
          *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  
   
          *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 *Q^*Q*). In each iteration step  
          PDEs with operator *I+D^*D* and with *Q^*Q* needs to be solved using a sub iteration scheme.  
          """  
          self.verbose=verbose  
          rtol=self.getTolerance()  
          atol=self.getAbsoluteTolerance()  
      self.setSubProblemTolerance()  
          num_corrections=0  
          converged=False  
          p=p0  
          norm_r=None  
          while not converged:  
                v=self.getFlux(p, fixed_flux=u0)  
                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: L2 defect u = %e."%(util.integrate(util.length(self.__g-util.interpolate(v,Function(self.domain))-Qp)**2)**(0.5),)  
                     print "DarcyFlux: L2 defect div(v) = %e."%(util.integrate((self.__f-util.div(v))**2)**(0.5),)  
                     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=0.5*ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
                    num_corrections+=1  
                else:  
                    converged=True  
          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):  
           if self.getSolverOptionsFlux().isVerbose(): print "DarcyFlux: Applying operator"  
           Qdp=self.__Q(dp)  
           self.__pde_v.setValue(Y=-Qdp,X=Data(), r=Data())  
           du=self.__pde_v.getSolution()  
           # self.__pde_v.getOperator().saveMM("proj.mm")  
           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):  
       if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"  
           self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r), Y=Data(), r=Data())  
           # self.__pde_p.getOperator().saveMM("prec.mm")  
           return self.__pde_p.getSolution()  
209    
210      def getFlux(self,p=None, fixed_flux=Data()):     def getSolverOptionsFlux(self):
211          """
212          Returns the solver options used to solve the flux problems
213          :return: `SolverOptions`
214          """
215          if self.__pde_v == None:
216              return None
217          else:
218              return self.__pde_v.getSolverOptions()
219          
220       def setSolverOptionsFlux(self, options=None):
221          """
222          Sets the solver options used to solve the flux problems
223          If ``options`` is not present, the options are reset to default
224          :param options: `SolverOptions`
225          """
226          if not self.__pde_v == None:
227              self.__pde_v.setSolverOptions(options)
228        
229       def getSolverOptionsPressure(self):
230          """
231          Returns the solver options used to solve the pressure problems
232          :return: `SolverOptions`
233          """
234          return self.__pde_p.getSolverOptions()
235          
236       def setSolverOptionsPressure(self, options=None):
237          """
238          Sets the solver options used to solve the pressure problems
239          If ``options`` is not present, the options are reset to default
240          
241          :param options: `SolverOptions`
242          :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
243          """
244          return self.__pde_p.setSolverOptions(options)
245          
246       def solve(self, u0, p0):
247          """
248          solves the problem.
249          
250          :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.
251          :type u0: vector value on the domain (e.g. `escript.Data`).
252          :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.
253          :type p0: scalar value on the domain (e.g. `escript.Data`).
254          :return: flux and pressure
255          :rtype: ``tuple`` of `escript.Data`.
256    
257          """
258          p0=util.interpolate(p0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
259          if self.ref_point_id == None:
260              p_ref=0
261          else:
262              p_ref=p0.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
263          p0_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
264          g_2=self.__g - util.tensor_mult(self.__permeability, self.__permeability_invXg_ref * self.perm_scale)
265          self.__pde_p.setValue(X=g_2 * 1./self.perm_scale,
266                                Y=self.__f * 1./self.perm_scale,
267                                y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux * 1./self.perm_scale ),
268                                r=p0 - p0_hydrostatic)
269          pp=self.__pde_p.getSolution()
270          u = self._getFlux(pp, u0)
271          return u,pp + p0_hydrostatic
272          
273       def getFlux(self,p, u0=None):
274          """          """
275          returns the flux for a given pressure ``p`` where the flux is equal to ``fixed_flux``          returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
276          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
277          Note that ``g`` and ``f`` are used, see `setValue`.          Notice that ``g`` is used, see `setValue`.
278    
279          :param p: pressure.          :param p: pressure.
280          :type p: scalar value on the domain (e.g. `Data`).          :type p: scalar value on the domain (e.g. `escript.Data`).
281          :param fixed_flux: flux on the locations of the domain marked be ``location_of_fixed_flux``.          :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
282          :type fixed_flux: vector values on the domain (e.g. `Data`).          :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
283          :return: flux          :return: flux
284          :rtype: `Data`          :rtype: `escript.Data`
         :note: the method uses the least squares solution *u=(I+D^*D)^{-1}(D^*f-g-Qp)* where *D* is the *div* operator and *(Qp)_i=k_{ij}p_{,j}*  
                for the permeability *k_{ij}*  
285          """          """
286      self.setSubProblemTolerance()          p=util.interpolate(p, self.__pde_p.getFunctionSpaceForCoefficient("q"))
287          g=self.__g          if self.ref_point_id == None:
288          f=self.__f              p_ref=0
         self.__pde_v.setValue(X=self.__l*f*util.kronecker(self.domain), r=fixed_flux)  
         if p == None:  
            self.__pde_v.setValue(Y=g)  
289          else:          else:
290             self.__pde_v.setValue(Y=g-self.__Q(p))              p_ref=p.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
291          return self.__pde_v.getSolution()          p_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
292            return self._getFlux(p-p_hydrostatic, u0)
293    
294       def _getFlux(self, pp, u0=None):
295            """
296            returns the flux for a given pressure ``pp`` where the flux is equal to
297            ``u0`` on locations where ``location_of_fixed_flux`` is positive (see
298            `setValue`). Notice that ``g`` is used, see `setValue`.
299    
300            :param pp: pressure.
301            :type pp: scalar value on the domain (i.e. `escript.Data`).
302            :param u0: flux on the locations of the domain marked in ``location_of_fixed_flux``.
303            :type u0: vector values on the domain (i.e. `escript.Data`) or ``None``
304            :return: flux
305            :rtype: `escript.Data`
306            """
307            if self.solver  == self.EVAL:
308               u = self.__g - util.tensor_mult(self.__permeability, self.perm_scale * (util.grad(pp) + self.__permeability_invXg_ref))
309            elif self.solver  == self.POST or self.solver  == self.SMOOTH:
310                self.__pde_v.setValue(Y= self.__permeability_invXg - (util.grad(pp) + self.__permeability_invXg_ref))
311                print
312                if u0 == None:
313                   self.__pde_v.setValue(r=escore.Data())
314                else:
315                   if not isinstance(u0, escore.Data) : u0 = escore.Vector(u0, escore.Solution(self.domain))
316                   self.__pde_v.setValue(r=1./self.perm_scale * u0)
317                u= self.__pde_v.getSolution() * self.perm_scale
318            return u
319          
320  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  class StokesProblemCartesian(HomogeneousSaddlePointProblem):
321       """       """
322       solves       solves
# Line 376  class StokesProblemCartesian(Homogeneous Line 335  class StokesProblemCartesian(Homogeneous
335              sp.setTolerance()              sp.setTolerance()
336              sp.initialize(...)              sp.initialize(...)
337              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
338                sp.setStokesEquation(...) # new values for some parameters
339                v1,p1=sp.solve(v,p)
340       """       """
341       def __init__(self,domain,**kwargs):       def __init__(self,domain,**kwargs):
342           """           """
# Line 390  class StokesProblemCartesian(Homogeneous Line 351  class StokesProblemCartesian(Homogeneous
351           """           """
352           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
353           self.domain=domain           self.domain=domain
354           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
355           self.__pde_u.setSymmetryOn()           self.__pde_v.setSymmetryOn()
356            
357           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
358           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
# Line 399  class StokesProblemCartesian(Homogeneous Line 360  class StokesProblemCartesian(Homogeneous
360    
361           self.__pde_proj=LinearPDE(domain)           self.__pde_proj=LinearPDE(domain)
362           self.__pde_proj.setReducedOrderOn()           self.__pde_proj.setReducedOrderOn()
363       self.__pde_proj.setValue(D=1)           self.__pde_proj.setValue(D=1)
364           self.__pde_proj.setSymmetryOn()           self.__pde_proj.setSymmetryOn()
365    
366       def getSolverOptionsVelocity(self):       def getSolverOptionsVelocity(self):
# Line 408  class StokesProblemCartesian(Homogeneous Line 369  class StokesProblemCartesian(Homogeneous
369            
370       :rtype: `SolverOptions`       :rtype: `SolverOptions`
371       """       """
372       return self.__pde_u.getSolverOptions()           return self.__pde_v.getSolverOptions()
373       def setSolverOptionsVelocity(self, options=None):       def setSolverOptionsVelocity(self, options=None):
374           """           """
375       set the solver options for solving the equation for velocity.       set the solver options for solving the equation for velocity.
# Line 416  class StokesProblemCartesian(Homogeneous Line 377  class StokesProblemCartesian(Homogeneous
377       :param options: new solver  options       :param options: new solver  options
378       :type options: `SolverOptions`       :type options: `SolverOptions`
379       """       """
380           self.__pde_u.setSolverOptions(options)           self.__pde_v.setSolverOptions(options)
381       def getSolverOptionsPressure(self):       def getSolverOptionsPressure(self):
382           """           """
383       returns the solver options used  solve the equation for pressure.       returns the solver options used  solve the equation for pressure.
384       :rtype: `SolverOptions`       :rtype: `SolverOptions`
385       """       """
386       return self.__pde_prec.getSolverOptions()           return self.__pde_prec.getSolverOptions()
387       def setSolverOptionsPressure(self, options=None):       def setSolverOptionsPressure(self, options=None):
388           """           """
389       set the solver options for solving the equation for pressure.       set the solver options for solving the equation for pressure.
390       :param options: new solver  options       :param options: new solver  options
391       :type options: `SolverOptions`       :type options: `SolverOptions`
392       """       """
393       self.__pde_prec.setSolverOptions(options)           self.__pde_prec.setSolverOptions(options)
394    
395       def setSolverOptionsDiv(self, options=None):       def setSolverOptionsDiv(self, options=None):
396           """           """
# Line 439  class StokesProblemCartesian(Homogeneous Line 400  class StokesProblemCartesian(Homogeneous
400       :param options: new solver options       :param options: new solver options
401       :type options: `SolverOptions`       :type options: `SolverOptions`
402       """       """
403       self.__pde_proj.setSolverOptions(options)           self.__pde_proj.setSolverOptions(options)
404       def getSolverOptionsDiv(self):       def getSolverOptionsDiv(self):
405           """           """
406       returns the solver options for solving the equation to project the divergence of       returns the solver options for solving the equation to project the divergence of
# Line 447  class StokesProblemCartesian(Homogeneous Line 408  class StokesProblemCartesian(Homogeneous
408            
409       :rtype: `SolverOptions`       :rtype: `SolverOptions`
410       """       """
411       return self.__pde_proj.getSolverOptions()           return self.__pde_proj.getSolverOptions()
412    
413       def updateStokesEquation(self, v, p):       def updateStokesEquation(self, v, p):
414           """           """
415           updates the Stokes equation to consider dependencies from ``v`` and ``p``           updates the Stokes equation to consider dependencies from ``v`` and ``p``
416           :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values.           :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
417           """           """
418           pass           pass
419       def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):       def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
# Line 473  class StokesProblemCartesian(Homogeneous Line 434  class StokesProblemCartesian(Homogeneous
434          if eta !=None:          if eta !=None:
435              k=util.kronecker(self.domain.getDim())              k=util.kronecker(self.domain.getDim())
436              kk=util.outer(k,k)              kk=util.outer(k,k)
437              self.eta=util.interpolate(eta, Function(self.domain))              self.eta=util.interpolate(eta, escore.Function(self.domain))
438          self.__pde_prec.setValue(D=1/self.eta)              self.__pde_prec.setValue(D=1/self.eta)
439              self.__pde_u.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))              self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
440          if restoration_factor!=None:          if restoration_factor!=None:
441              n=self.domain.getNormal()              n=self.domain.getNormal()
442              self.__pde_u.setValue(d=restoration_factor*util.outer(n,n))              self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
443          if fixed_u_mask!=None:          if fixed_u_mask!=None:
444              self.__pde_u.setValue(q=fixed_u_mask)              self.__pde_v.setValue(q=fixed_u_mask)
445          if f!=None: self.__f=f          if f!=None: self.__f=f
446          if surface_stress!=None: self.__surface_stress=surface_stress          if surface_stress!=None: self.__surface_stress=surface_stress
447          if stress!=None: self.__stress=stress          if stress!=None: self.__stress=stress
448    
449       def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data(), restoration_factor=0):       def initialize(self,f=escore.Data(),fixed_u_mask=escore.Data(),eta=1,surface_stress=escore.Data(),stress=escore.Data(), restoration_factor=0):
450          """          """
451          assigns values to the model parameters          assigns values to the model parameters
452    
# Line 498  class StokesProblemCartesian(Homogeneous Line 459  class StokesProblemCartesian(Homogeneous
459          :param surface_stress: normal surface stress          :param surface_stress: normal surface stress
460          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
461          :param stress: initial stress          :param stress: initial stress
462      :type stress: `Tensor` object on `FunctionSpace` `Function` or similar          :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
463          """          """
464          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
465    
# Line 511  class StokesProblemCartesian(Homogeneous Line 472  class StokesProblemCartesian(Homogeneous
472           :rtype: ``float``           :rtype: ``float``
473           """           """
474           self.__pde_proj.setValue(Y=-util.div(v))           self.__pde_proj.setValue(Y=-util.div(v))
475       self.getSolverOptionsDiv().setTolerance(tol)           self.getSolverOptionsDiv().setTolerance(tol)
476       self.getSolverOptionsDiv().setAbsoluteTolerance(0.)           self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
477           out=self.__pde_proj.getSolution()           out=self.__pde_proj.getSolution()
478           return out           return out
479    
# Line 525  class StokesProblemCartesian(Homogeneous Line 486  class StokesProblemCartesian(Homogeneous
486           :return: inner product of element p and Bv=-div(v)           :return: inner product of element p and Bv=-div(v)
487           :rtype: ``float``           :rtype: ``float``
488           """           """
489           return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))           return util.integrate(util.interpolate(p,escore.Function(self.domain))*util.interpolate(Bv, escore.Function(self.domain)))
490    
491       def inner_p(self,p0,p1):       def inner_p(self,p0,p1):
492           """           """
# Line 536  class StokesProblemCartesian(Homogeneous Line 497  class StokesProblemCartesian(Homogeneous
497           :return: inner product of p0 and p1           :return: inner product of p0 and p1
498           :rtype: ``float``           :rtype: ``float``
499           """           """
500           s0=util.interpolate(p0,Function(self.domain))           s0=util.interpolate(p0, escore.Function(self.domain))
501           s1=util.interpolate(p1,Function(self.domain))           s1=util.interpolate(p1, escore.Function(self.domain))
502           return util.integrate(s0*s1)           return util.integrate(s0*s1)
503    
504       def norm_v(self,v):       def norm_v(self,v):
# Line 553  class StokesProblemCartesian(Homogeneous Line 514  class StokesProblemCartesian(Homogeneous
514    
515       def getDV(self, p, v, tol):       def getDV(self, p, v, tol):
516           """           """
517           return the value for v for a given p (overwrite)           return the value for v for a given p
518    
519           :param p: a pressure           :param p: a pressure
520           :param v: a initial guess for the value v to return.           :param v: a initial guess for the value v to return.
521           :return: dv given as *Adv=(f-Av-B^*p)*           :return: dv given as *Adv=(f-Av-B^*p)*
522           """           """
523           self.updateStokesEquation(v,p)           self.updateStokesEquation(v,p)
524           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
525       self.getSolverOptionsVelocity().setTolerance(tol)           self.getSolverOptionsVelocity().setTolerance(tol)
526       self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)           self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
527           if self.__stress.isEmpty():           if self.__stress.isEmpty():
528              self.__pde_u.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))              self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
529           else:           else:
530              self.__pde_u.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))              self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
531           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
532           return  out           return  out
533    
534       def norm_Bv(self,Bv):       def norm_Bv(self,Bv):
# Line 577  class StokesProblemCartesian(Homogeneous Line 538  class StokesProblemCartesian(Homogeneous
538          :rtype: equal to the type of p          :rtype: equal to the type of p
539          :note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
540          """          """
541          return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))          return util.sqrt(util.integrate(util.interpolate(Bv, escore.Function(self.domain))**2))
542    
543       def solve_AinvBt(self,p, tol):       def solve_AinvBt(self,p, tol):
544           """           """
# Line 587  class StokesProblemCartesian(Homogeneous Line 548  class StokesProblemCartesian(Homogeneous
548           :return: the solution of *Av=B^*p*           :return: the solution of *Av=B^*p*
549           :note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
550           """           """
551           self.__pde_u.setValue(Y=Data(), y=Data(), X=-p*util.kronecker(self.domain))           self.__pde_v.setValue(Y=escore.Data(), y=escore.Data(), X=-p*util.kronecker(self.domain))
552           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
553           return  out           return  out
554    
555       def solve_prec(self,Bv, tol):       def solve_prec(self,Bv, tol):
556           """           """
557           applies preconditioner for for *BA^{-1}B^** to *Bv*           applies preconditioner for for *BA^{-1}B^** to *Bv*
558           with accuracy `self.getSubProblemTolerance()`           with accuracy ``self.getSubProblemTolerance()``
559    
560           :param Bv: velocity increment           :param Bv: velocity increment
561           :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*           :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
562           :note: boundary conditions on p are zero.           :note: boundary conditions on p are zero.
563           """           """
564           self.__pde_prec.setValue(Y=Bv)           self.__pde_prec.setValue(Y=Bv)
565       self.getSolverOptionsPressure().setTolerance(tol)           self.getSolverOptionsPressure().setTolerance(tol)
566       self.getSolverOptionsPressure().setAbsoluteTolerance(0.)           self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
567           out=self.__pde_prec.getSolution()           out=self.__pde_prec.getSolution()
568           return out           return out

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