/[escript]/trunk/escriptcore/py_src/flows.py
ViewVC logotype

Diff of /trunk/escriptcore/py_src/flows.py

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

revision 3360 by jfenwick, Thu Nov 18 00:20:21 2010 UTC revision 3990 by caltinay, Tue Sep 25 05:03:20 2012 UTC
# Line 1  Line 1 
1  # -*- coding: utf-8 -*-  # -*- coding: utf-8 -*-
2  ########################################################  ##############################################################################
3  #  #
4  # Copyright (c) 2003-2010 by University of Queensland  # Copyright (c) 2003-2012 by University of Queensland
5  # Earth Systems Science Computational Center (ESSCC)  # http://www.uq.edu.au
 # http://www.uq.edu.au/esscc  
6  #  #
7  # Primary Business: Queensland, Australia  # Primary Business: Queensland, Australia
8  # Licensed under the Open Software License version 3.0  # Licensed under the Open Software License version 3.0
9  # http://www.opensource.org/licenses/osl-3.0.php  # http://www.opensource.org/licenses/osl-3.0.php
10  #  #
11  ########################################################  # Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12    # Development since 2012 by School of Earth Sciences
13    #
14    ##############################################################################
15    
16  __copyright__="""Copyright (c) 2003-2010 by University of Queensland  __copyright__="""Copyright (c) 2003-2012 by University of Queensland
17  Earth Systems Science Computational Center (ESSCC)  http://www.uq.edu.au
 http://www.uq.edu.au/esscc  
18  Primary Business: Queensland, Australia"""  Primary Business: Queensland, Australia"""
19  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
20  http://www.opensource.org/licenses/osl-3.0.php"""  http://www.opensource.org/licenses/osl-3.0.php"""
# Line 32  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 escript
37  import util  from . import util
38  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions  from .linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
39  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES  from .pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
40    
41  class DarcyFlow(object):  class DarcyFlow(object):
42     """     """
# Line 46  class DarcyFlow(object): Line 47  class DarcyFlow(object):
47        
48     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,
49        
50     :note: The problem is solved in a least squares formulation.     :cvar EVAL: direct pressure gradient evaluation for flux
51       :cvar POST: global postprocessing of flux by solving the PDE *K_{ij} u_j + (w * K * l u_{k,k})_{,i}= - p_{,j} + K_{ij} g_j*
52                   where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
53       :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
54     """     """
55         EVAL="EVAL"
56     def __init__(self, domain, useReduced=False, adaptSubTolerance=True, solveForFlux=False):     SIMPLE="EVAL"
57       POST="POST"
58       SMOOTH="SMOOTH"
59       def __init__(self, domain, useReduced=False, solver="POST", verbose=False, w=1.):
60        """        """
61        initializes the Darcy flux problem        initializes the Darcy flux problem.
62    
63        :param domain: domain of the problem        :param domain: domain of the problem
64        :type domain: `Domain`        :type domain: `Domain`
65        :param useReduced: uses reduced oreder on flux and pressure        :param useReduced: uses reduced oreder on flux and pressure
66        :type useReduced: ``bool``        :type useReduced: ``bool``
67        :param adaptSubTolerance: switches on automatic subtolerance selection        :param solver: solver method
68        :type adaptSubTolerance: ``bool``        :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST`, `DarcyFlow.SMOOTH` ]
69        :param solveForFlux: if True the solver solves for the flux (do not use!)        :param verbose: if ``True`` some information on the iteration progress are printed.
70        :type solveForFlux: ``bool``          :type verbose: ``bool``
71          :param w: weighting factor for `DarcyFlow.POST` solver
72          :type w: ``float``
73          
74        """        """
75          if not solver in [DarcyFlow.EVAL, DarcyFlow.POST,  DarcyFlow.SMOOTH ] :
76              raise ValueError("unknown solver %d."%solver)
77    
78        self.domain=domain        self.domain=domain
79        self.solveForFlux=solveForFlux        self.solver=solver
80        self.useReduced=useReduced        self.useReduced=useReduced
81        self.__adaptSubTolerance=adaptSubTolerance        self.verbose=verbose
82        self.verbose=False        self.l=None
83                self.w=None
84        self.__pde_k=LinearPDESystem(domain)      
       self.__pde_k.setSymmetryOn()  
       if self.useReduced: self.__pde_k.setReducedOrderOn()  
   
85        self.__pde_p=LinearSinglePDE(domain)        self.__pde_p=LinearSinglePDE(domain)
86        self.__pde_p.setSymmetryOn()        self.__pde_p.setSymmetryOn()
87        if self.useReduced: self.__pde_p.setReducedOrderOn()        if self.useReduced: self.__pde_p.setReducedOrderOn()
88    
89        self.__pde_l=LinearSinglePDE(domain)   # this is here for getSolverOptionsWeighting        if self.solver  == self.EVAL:
90        # self.__pde_l.setSymmetryOn()           self.__pde_v=None
91        # if self.useReduced: self.__pde_l.setReducedOrderOn()           if self.verbose: print("DarcyFlow: simple solver is used.")
92        self.setTolerance()  
93        self.setAbsoluteTolerance()        elif self.solver  == self.POST:
94        self.__f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))           if util.inf(w)<0.:
95        self.__g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))              raise ValueError("Weighting factor must be non-negative.")
96                   if self.verbose: print("DarcyFlow: global postprocessing of flux is used.")
97             self.__pde_v=LinearPDESystem(domain)
98             self.__pde_v.setSymmetryOn()
99             if self.useReduced: self.__pde_v.setReducedOrderOn()
100             self.w=w
101             x=self.domain.getX()
102             self.l=min( [util.sup(x[i])-util.inf(x[i]) for i in xrange(self.domain.getDim()) ] )
103             #self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
104    
105          elif self.solver  == self.SMOOTH:
106             self.__pde_v=LinearPDESystem(domain)
107             self.__pde_v.setSymmetryOn()
108             if self.useReduced: self.__pde_v.setReducedOrderOn()
109             if self.verbose: print("DarcyFlow: flux smoothing is used.")
110             self.w=0
111    
112          self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
113          self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
114          self.__permeability_invXg=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
115          self.__permeability_invXg_ref=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
116          self.ref_point_id=None
117          self.ref_point=util.numpy.zeros((self.domain.getDim()),util.numpy.float64)
118          self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
119          self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
120          self.perm_scale=1.
121        
122            
123       def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
124          """
125          assigns values to model parameters
126    
127          :param f: volumetic sources/sinks
128          :type f: scalar value on the domain (e.g. `escript.Data`)
129          :param g: flux sources/sinks
130          :type g: vector values on the domain (e.g. `escript.Data`)
131          :param location_of_fixed_pressure: mask for locations where pressure is fixed
132          :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
133          :param location_of_fixed_flux:  mask for locations where flux is fixed.
134          :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
135          :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
136          :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
137    
138          :note: the values of parameters which are not set by calling ``setValue`` are not altered.
139          :note: at any point on the boundary of the domain the pressure
140                 (``location_of_fixed_pressure`` >0) or the normal component of the
141                 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
142                 is along the *x_i* axis.
143    
144          """
145          if location_of_fixed_pressure!=None:
146               self.location_of_fixed_pressure=util.wherePositive(util.interpolate(location_of_fixed_pressure, self.__pde_p.getFunctionSpaceForCoefficient("q")))
147               self.ref_point_id=self.location_of_fixed_pressure.maxGlobalDataPoint()
148               if not self.location_of_fixed_pressure.getTupleForGlobalDataPoint(*self.ref_point_id)[0] > 0: raise ValueError("pressure needs to be fixed at least one point.")
149               self.ref_point=self.__pde_p.getFunctionSpaceForCoefficient("q").getX().getTupleForGlobalDataPoint(*self.ref_point_id)
150               if self.verbose: print(("DarcyFlow: reference point at %s."%(self.ref_point,)))
151               self.__pde_p.setValue(q=self.location_of_fixed_pressure)
152          if location_of_fixed_flux!=None:
153              self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
154              if not self.__pde_v == None:
155                  self.__pde_v.setValue(q=self.location_of_fixed_flux)
156                
157          if permeability!=None:
158        
159             perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
160             self.perm_scale=util.Lsup(util.length(perm))
161             if self.verbose: print(("DarcyFlow: permeability scaling factor = %e."%self.perm_scale))
162             perm=perm*(1./self.perm_scale)
163            
164             if perm.getRank()==0:
165    
166                perm_inv=(1./perm)
167                perm_inv=perm_inv*util.kronecker(self.domain.getDim())
168                perm=perm*util.kronecker(self.domain.getDim())
169            
170            
171             elif perm.getRank()==2:
172                perm_inv=util.inverse(perm)
173             else:
174                raise ValueError("illegal rank of permeability.")
175            
176             self.__permeability=perm
177             self.__permeability_inv=perm_inv
178        
179             #====================
180             self.__pde_p.setValue(A=self.__permeability)
181             if self.solver  == self.EVAL:
182                  pass # no extra work required
183             elif self.solver  == self.POST:
184                  k=util.kronecker(self.domain.getDim())
185                  self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
186                  #self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
187                  self.__pde_v.setValue(D=self.__permeability_inv, A_reduced=self.omega*util.outer(k,k))
188             elif self.solver  == self.SMOOTH:
189                self.__pde_v.setValue(D=self.__permeability_inv)
190    
191          if g != None:
192            g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
193            if g.isEmpty():
194                 g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
195            else:
196                 if not g.getShape()==(self.domain.getDim(),): raise ValueError("illegal shape of g")
197            self.__g=g
198            self.__permeability_invXg=util.tensor_mult(self.__permeability_inv,self.__g * (1./self.perm_scale ))
199            self.__permeability_invXg_ref=util.integrate(self.__permeability_invXg)/util.vol(self.domain)
200          if f !=None:
201             f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
202             if f.isEmpty():      
203                 f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
204             else:
205                 if f.getRank()>0: raise ValueError("illegal rank of f.")
206             self.__f=f
207    
208     def getSolverOptionsFlux(self):     def getSolverOptionsFlux(self):
209        """        """
210        Returns the solver options used to solve the flux problems        Returns the solver options used to solve the flux problems
         
       *K^{-1} u=F*  
         
211        :return: `SolverOptions`        :return: `SolverOptions`
212        """        """
213        return self.__pde_k.getSolverOptions()        if self.__pde_v == None:
214              return None
215          else:
216              return self.__pde_v.getSolverOptions()
217                
218     def setSolverOptionsFlux(self, options=None):     def setSolverOptionsFlux(self, options=None):
219        """        """
220        Sets the solver options used to solve the flux problems        Sets the solver options used to solve the flux problems
         
       *K^{-1}u=F*  
         
221        If ``options`` is not present, the options are reset to default        If ``options`` is not present, the options are reset to default
         
222        :param options: `SolverOptions`        :param options: `SolverOptions`
       :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.  
223        """        """
224        return self.__pde_v.setSolverOptions(options)        if not self.__pde_v == None:
225              self.__pde_v.setSolverOptions(options)
226            
227     def getSolverOptionsPressure(self):     def getSolverOptionsPressure(self):
228        """        """
229        Returns the solver options used to solve the pressure problems        Returns the solver options used to solve the pressure problems
         
       *(Q^* K Q)p=-Q^*G*  
         
230        :return: `SolverOptions`        :return: `SolverOptions`
231        """        """
232        return self.__pde_p.getSolverOptions()        return self.__pde_p.getSolverOptions()
# Line 119  class DarcyFlow(object): Line 234  class DarcyFlow(object):
234     def setSolverOptionsPressure(self, options=None):     def setSolverOptionsPressure(self, options=None):
235        """        """
236        Sets the solver options used to solve the pressure problems        Sets the solver options used to solve the pressure problems
         
       *(Q^* K Q)p=-Q^*G*  
         
237        If ``options`` is not present, the options are reset to default        If ``options`` is not present, the options are reset to default
238                
239        :param options: `SolverOptions`        :param options: `SolverOptions`
240        :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.        :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
241        """        """
242        return self.__pde_p.setSolverOptions(options)        return self.__pde_p.setSolverOptions(options)
   
    def getSolverOptionsWeighting(self):  
       """  
       Returns the solver options used to solve the pressure problems  
   
       *(D K D^*)p=-D F*  
   
       :return: `SolverOptions`  
       """  
       return self.__pde_l.getSolverOptions()  
   
    def setSolverOptionsWeighting(self, options=None):  
       """  
       Sets the solver options used to solve the pressure problems  
   
       *(D K D^*)p=-D F*  
   
       If ``options`` is not present, the options are reset to default  
   
       :param options: `SolverOptions`  
       :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.  
       """  
       return self.__pde_l.setSolverOptions(options)  
   
   
    def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):  
       """  
       assigns values to model parameters  
   
       :param f: volumetic sources/sinks  
       :type f: scalar value on the domain (e.g. `Data`)  
       :param g: flux sources/sinks  
       :type g: vector values on the domain (e.g. `Data`)  
       :param location_of_fixed_pressure: mask for locations where pressure is fixed  
       :type location_of_fixed_pressure: scalar value on the domain (e.g. `Data`)  
       :param location_of_fixed_flux:  mask for locations where flux is fixed.  
       :type location_of_fixed_flux: vector values on the domain (e.g. `Data`)  
       :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.  
       :type permeability: scalar or tensor values on the domain (e.g. `Data`)  
   
       :note: the values of parameters which are not set by calling ``setValue`` are not altered.  
       :note: at any point on the boundary of the domain the pressure (``location_of_fixed_pressure`` >0)  
       or the normal component of the flux (``location_of_fixed_flux[i]>0``) if direction of the normal is along the *x_i* axis.  
   
       """  
       if f !=None:  
      f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("X"))  
      if f.isEmpty():  
         f=Scalar(0,self.__pde_p.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_p.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)  
            #self.__pde_l.setValue(q=location_of_fixed_pressure)  
       if location_of_fixed_flux!=None:  
            self.__pde_k.setValue(q=location_of_fixed_flux)  
               
       if permeability!=None:  
      perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))  
      if perm.getRank()==0:  
         perm_inv=(1./perm)*util.kronecker(self.domain.getDim())  
         perm=perm*util.kronecker(self.domain.getDim())  
      elif perm.getRank()==2:  
         perm_inv=util.inverse(perm)  
      else:  
         raise ValueError,"illegal rank of permeability."  
   
      self.__permeability=perm  
      self.__permeability_inv=perm_inv  
      self.__l =(util.longestEdge(self.domain)**2*util.length(self.__permeability_inv))/10  
      #self.__l =(self.domain.getSize()**2*util.length(self.__permeability_inv))/10  
      if  self.solveForFlux:  
         self.__pde_k.setValue(D=self.__permeability_inv)  
      else:  
         self.__pde_k.setValue(D=self.__permeability_inv, A=self.__l*util.outer(util.kronecker(self.domain),util.kronecker(self.domain)))  
      self.__pde_p.setValue(A=self.__permeability)  
      #self.__pde_l.setValue(D=1/self.__l)  
          #self.__pde_l.setValue(A=self.__permeability)  
   
    def __applWeight(self, v, f=None):  
       # solves L p = f-Dv with p = 0  
       if self.getSolverOptionsWeighting().isVerbose() or self.verbose: print "DarcyFlux: Applying weighting operator"  
       if f == None:  
      return -util.div(v)*self.__l  
       else:  
      return (f-util.div(v))*self.__l  
       # if f == None:  
       #      self.__pde_l.setValue(Y=-util.div(v))    
       # else:  
       #      return (f-util.div(v))/self.__l  
       # return self.__pde_l.getSolution()  
         
    def __getPressure(self, v, p0, g=None):  
       # solves (G*KG)p = G^(g-v) with p = p0 where location_of_fixed_pressure>0  
       if self.getSolverOptionsPressure().isVerbose() or self.verbose: print "DarcyFlux: Pressure update"  
       if g == None:  
      self.__pde_p.setValue(X=-v, r=p0)  
       else:  
      self.__pde_p.setValue(X=g-v, r=p0)        
       p=self.__pde_p.getSolution()  
       return p  
   
    def __Aprod_v(self,dv):  
       # calculates: (a,b,c) = (K^{-1}(dv + KG * dp), L^{-1}Ddv, dp)  with (G*KG)dp = - G^*dv    
       dp=self.__getPressure(dv, p0=Data()) # dp = (G*KG)^{-1} (0-G^*dv)  
       a=util.tensor_mult(self.__permeability_inv,dv)+util.grad(dp) # a= K^{-1}u+G*dp  
       b= - self.__applWeight(dv) # b = - (D K D^*)^{-1} (0-Dv)  
       return ArithmeticTuple(a,b,-dp)  
   
    def __Msolve_PCG_v(self,r):  
       # K^{-1} u = r[0] + D^*r[1] = K^{-1}(dv + KG * dp) + D^*L^{-1}Ddv  
       if self.getSolverOptionsFlux().isVerbose() or self.verbose: print "DarcyFlux: Applying preconditioner"  
       self.__pde_k.setValue(X=r[1]*util.kronecker(self.domain), Y=r[0], r=Data())  
       # self.__pde_p.getOperator().saveMM("prec.mm")  
       return self.__pde_k.getSolution()  
   
    def __inner_PCG_v(self,v,r):  
       return util.integrate(util.inner(v,r[0])+util.div(v)*r[1])  
         
    def __Aprod_p(self,dp):  
       if self.getSolverOptionsFlux().isVerbose(): print "DarcyFlux: Applying operator"  
       Gdp=util.grad(dp)  
       self.__pde_k.setValue(Y=-Gdp,X=Data(), r=Data())  
       du=self.__pde_k.getSolution()  
       # self.__pde_v.getOperator().saveMM("proj.mm")  
       return ArithmeticTuple(util.tensor_mult(self.__permeability,Gdp),-du)  
   
    def __getFlux(self,p, v0, f=None, g=None):  
       # solves (K^{-1}+D^*L^{-1} D) v = D^*L^{-1}f + K^{-1}g - Gp  
       if f!=None:  
      self.__pde_k.setValue(X=self.__applWeight(v0*0,self.__f)*util.kronecker(self.domain))  
       self.__pde_k.setValue(r=v0)  
       g2=util.tensor_mult(self.__permeability_inv,g)  
       if p == None:  
      self.__pde_k.setValue(Y=g2)  
       else:  
      self.__pde_k.setValue(Y=g2-util.grad(p))  
       return self.__pde_k.getSolution()    
243                
244        #v=self.__getFlux(p, u0, f=self.__f, g=g2)           def solve(self, u0, p0):
    def __Msolve_PCG_p(self,r):  
       if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"  
       self.__pde_p.setValue(X=r[0]-r[1], Y=Data(), r=Data(), y=Data())  
       # self.__pde_p.getOperator().saveMM("prec.mm")  
       return self.__pde_p.getSolution()  
           
    def __inner_PCG_p(self,p,r):  
        return util.integrate(util.inner(util.grad(p), r[0]-r[1]))  
   
    def __L2(self,v):  
       return util.sqrt(util.integrate(util.length(util.interpolate(v,Function(self.domain)))**2))  
   
    def solve(self,u0,p0, max_iter=100, verbose=False, max_num_corrections=10):  
245        """        """
246        solves the problem.        solves the problem.
247                
       The iteration is terminated if the residual norm is less then self.getTolerance().  
   
248        :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.        :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.
249        :type u0: vector value on the domain (e.g. `Data`).        :type u0: vector value on the domain (e.g. `escript.Data`).
250        :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.        :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.
251        :type p0: scalar value on the domain (e.g. `Data`).        :type p0: scalar value on the domain (e.g. `escript.Data`).
       :param verbose: if set some information on iteration progress are printed  
       :type verbose: ``bool``  
252        :return: flux and pressure        :return: flux and pressure
253        :rtype: ``tuple`` of `Data`.        :rtype: ``tuple`` of `escript.Data`.
254    
       :note: The problem is solved as a least squares form  
       *(K^[-1]+D^* (DKD^*)^[-1] D)u+G p=D^* (DKD^*)^[-1] f + K^[-1]g*  
       *G^*u+*G^* K Gp=G^*g*  
       where *D* is the *div* operator and *(Gp)_i=p_{,i}* for the permeability *K=k_{ij}*.  
255        """        """
256        self.verbose=verbose        p0=util.interpolate(p0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
257        rtol=self.getTolerance()        if self.ref_point_id == None:
258        atol=self.getAbsoluteTolerance()            p_ref=0
       self.setSubProblemTolerance()  
       num_corrections=0  
       converged=False  
       norm_r=None  
         
       # Eliminate the hydrostatic pressure:  
       if self.verbose: print "DarcyFlux: calculate hydrostatic pressure component."  
       self.__pde_p.setValue(X=self.__g, r=p0, y=-util.inner(self.domain.getNormal(),u0))          
       p0=self.__pde_p.getSolution()  
       g2=self.__g - util.tensor_mult(self.__permeability, util.grad(p0))  
       norm_g2=util.integrate(util.inner(g2,util.tensor_mult(self.__permeability_inv,g2)))**0.5      
   
       p=p0*0  
       if self.solveForFlux:  
      v=u0.copy()  
259        else:        else:
260       v=self.__getFlux(p, u0, f=self.__f, g=g2)            p_ref=p0.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
261          p0_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
262        while not converged and norm_g2 > 0:        g_2=self.__g - util.tensor_mult(self.__permeability, self.__permeability_invXg_ref * self.perm_scale)
263       Gp=util.grad(p)        self.__pde_p.setValue(X=g_2 * 1./self.perm_scale,
264       KGp=util.tensor_mult(self.__permeability,Gp)                              Y=self.__f * 1./self.perm_scale,
265       if self.verbose:                              y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux * 1./self.perm_scale ),
266          def_p=g2-(v+KGp)                              r=p0 - p0_hydrostatic)
267          def_v=self.__f-util.div(v)        pp=self.__pde_p.getSolution()
268          print "DarcyFlux: L2: g-v-K*grad(p) = %e (v = %e)."%(self.__L2(def_p),self.__L2(v))        u = self._getFlux(pp, u0)
269          print "DarcyFlux: L2: f-div(v) = %e (grad(v) = %e)."%(self.__L2(def_v),self.__L2(util.grad(v)))        return u,pp + p0_hydrostatic
         print "DarcyFlux: K^{-1}-norm of v = %e."%util.integrate(util.inner(v,util.tensor_mult(self.__permeability_inv,v)))**0.5  
         print "DarcyFlux: K^{-1}-norm of g2 = %e."%norm_g2  
         print "DarcyFlux: K-norm of grad(dp) = %e."%util.integrate(util.inner(Gp,KGp))**0.5  
      ATOL=atol+rtol*norm_g2  
      if self.verbose: 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."  
         
         if self.solveForFlux:  
            # initial residual is r=K^{-1}*(g-v-K*Gp)+D^*L^{-1}(f-Du)  
            v,r, norm_r=PCG(ArithmeticTuple(util.tensor_mult(self.__permeability_inv,g2-v)-Gp,self.__applWeight(v,self.__f),p),  
                self.__Aprod_v,  
                v,  
                self.__Msolve_PCG_v,  
                self.__inner_PCG_v,  
                atol=ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
            p=r[2]  
         else:  
            # initial residual is r=G^*(g2-KGp - v)  
            p,r, norm_r=PCG(ArithmeticTuple(g2-KGp,v),  
                  self.__Aprod_p,  
                  p,  
                  self.__Msolve_PCG_p,  
                  self.__inner_PCG_p,  
                  atol=ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
            v=r[1]  
         if self.verbose: print "DarcyFlux: residual norm = %e."%norm_r  
         num_corrections+=1  
      else:  
         if self.verbose: print "DarcyFlux: stopping criterium reached."  
         converged=True  
       return v,p+p0  
    def setTolerance(self,rtol=1e-4):  
       """  
       sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if  
   
       *|g-v-K gard(p)|_PCG <= atol + rtol * |K^{1/2}g2|_0*  
270                
271        where ``atol`` is an absolut tolerance (see `setAbsoluteTolerance`).     def getFlux(self,p, u0=None):
         
       :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-K gard(p)|_PCG <= atol + rtol * |K^{1/2}g2|_0*  
   
   
       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**(0.5),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.)  
      self.getSolverOptionsWeighting().setTolerance(sub_tol)  
      self.getSolverOptionsWeighting().setAbsoluteTolerance(0.)  
      if self.verbose: print "DarcyFlux: relative subtolerance is set to %e."%sub_tol  
   
   
 class DarcyFlowOld(object):  
     """  
     solves the problem  
   
     *u_i+k_{ij}*p_{,j} = g_i*  
     *u_{i,i} = f*  
   
     where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,  
   
     :note: The problem is solved in a least squares formulation.  
     """  
   
     def __init__(self, domain, weight=None, useReduced=False, adaptSubTolerance=True):  
         """  
         initializes the Darcy flux problem  
         :param domain: domain of the problem  
         :type domain: `Domain`  
     :param useReduced: uses reduced oreder on flux and pressure  
     :type useReduced: ``bool``  
     :param adaptSubTolerance: switches on automatic subtolerance selection  
     :type adaptSubTolerance: ``bool``    
         """  
         self.domain=domain  
         if weight == None:  
            s=self.domain.getSize()  
            self.__l=(3.*util.longestEdge(self.domain)*s/util.sup(s))**2  
            # self.__l=(3.*util.longestEdge(self.domain))**2  
            #self.__l=(0.1*util.longestEdge(self.domain)*s/util.sup(s))**2  
         else:  
            self.__l=weight  
         self.__pde_v=LinearPDESystem(domain)  
         if useReduced: self.__pde_v.setReducedOrderOn()  
         self.__pde_v.setSymmetryOn()  
         self.__pde_v.setValue(D=util.kronecker(domain), A=self.__l*util.outer(util.kronecker(domain),util.kronecker(domain)))  
         self.__pde_p=LinearSinglePDE(domain)  
         self.__pde_p.setSymmetryOn()  
         if useReduced: self.__pde_p.setReducedOrderOn()  
         self.__f=Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))  
         self.__g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))  
         self.setTolerance()  
         self.setAbsoluteTolerance()  
     self.__adaptSubTolerance=adaptSubTolerance  
     self.verbose=False  
     def getSolverOptionsFlux(self):  
     """  
     Returns the solver options used to solve the flux problems  
       
     *(I+D^*D)u=F*  
       
     :return: `SolverOptions`  
     """  
     return self.__pde_v.getSolverOptions()  
     def setSolverOptionsFlux(self, options=None):  
     """  
     Sets the solver options used to solve the flux problems  
       
     *(I+D^*D)u=F*  
       
     If ``options`` is not present, the options are reset to default  
     :param options: `SolverOptions`  
     :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.  
     """  
     return self.__pde_v.setSolverOptions(options)  
     def getSolverOptionsPressure(self):  
     """  
     Returns the solver options used to solve the pressure problems  
       
     *(Q^*Q)p=Q^*G*  
       
     :return: `SolverOptions`  
     """  
     return self.__pde_p.getSolverOptions()  
     def setSolverOptionsPressure(self, options=None):  
     """  
     Sets the solver options used to solve the pressure problems  
       
     *(Q^*Q)p=Q^*G*  
       
     If ``options`` is not present, the options are reset to default  
     :param options: `SolverOptions`  
     :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.  
     """  
     return self.__pde_p.setSolverOptions(options)  
   
     def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):  
         """  
         assigns values to model parameters  
   
         :param f: volumetic sources/sinks  
         :type f: scalar value on the domain (e.g. `Data`)  
         :param g: flux sources/sinks  
         :type g: vector values on the domain (e.g. `Data`)  
         :param location_of_fixed_pressure: mask for locations where pressure is fixed  
         :type location_of_fixed_pressure: scalar value on the domain (e.g. `Data`)  
         :param location_of_fixed_flux:  mask for locations where flux is fixed.  
         :type location_of_fixed_flux: vector values on the domain (e.g. `Data`)  
         :param permeability: permeability tensor. If scalar ``s`` is given the tensor with  
                              ``s`` on the main diagonal is used. If vector ``v`` is given the tensor with  
                              ``v`` on the main diagonal is used.  
         :type permeability: scalar, vector or tensor values on the domain (e.g. `Data`)  
   
         :note: the values of parameters which are not set by calling ``setValue`` are not altered.  
         :note: at any point on the boundary of the domain the pressure (``location_of_fixed_pressure`` >0)  
                or the normal component of the flux (``location_of_fixed_flux[i]>0`` if direction of the normal  
                is along the *x_i* axis.  
         """  
         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):  
272          """          """
273          sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if          returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
   
         *|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.util.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()  
   
     def getFlux(self,p=None, fixed_flux=Data()):  
         """  
         returns the flux for a given pressure ``p`` where the flux is equal to ``fixed_flux``  
274          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
275          Note that ``g`` and ``f`` are used, see `setValue`.          Notice that ``g`` is used, see `setValue`.
276    
277          :param p: pressure.          :param p: pressure.
278          :type p: scalar value on the domain (e.g. `Data`).          :type p: scalar value on the domain (e.g. `escript.Data`).
279          :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``.
280          :type fixed_flux: vector values on the domain (e.g. `Data`).          :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
281          :return: flux          :return: flux
282          :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}*  
283          """          """
284      self.setSubProblemTolerance()          p=util.interpolate(p, self.__pde_p.getFunctionSpaceForCoefficient("q"))
285          g=self.__g          if self.ref_point_id == None:
286          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)  
287          else:          else:
288             self.__pde_v.setValue(Y=g-self.__Q(p))              p_ref=p.getTupleForGlobalDataPoint(*self.ref_point_id)[0]
289          return self.__pde_v.getSolution()          p_hydrostatic=p_ref+util.inner(self.__permeability_invXg_ref, self.__pde_p.getFunctionSpaceForCoefficient("q").getX() - self.ref_point)
290            return self._getFlux(p-p_hydrostatic, u0)
291    
292       def _getFlux(self, pp, u0=None):
293            """
294            returns the flux for a given pressure ``pp`` where the flux is equal to
295            ``u0`` on locations where ``location_of_fixed_flux`` is positive (see
296            `setValue`). Notice that ``g`` is used, see `setValue`.
297    
298            :param pp: pressure.
299            :type pp: scalar value on the domain (i.e. `escript.Data`).
300            :param u0: flux on the locations of the domain marked in ``location_of_fixed_flux``.
301            :type u0: vector values on the domain (i.e. `escript.Data`) or ``None``
302            :return: flux
303            :rtype: `escript.Data`
304            """
305            if self.solver  == self.EVAL:
306               u = self.__g - util.tensor_mult(self.__permeability, self.perm_scale * (util.grad(pp) + self.__permeability_invXg_ref))
307            elif self.solver  == self.POST or self.solver  == self.SMOOTH:
308                self.__pde_v.setValue(Y= self.__permeability_invXg - (util.grad(pp) + self.__permeability_invXg_ref))
309                print
310                if u0 == None:
311                   self.__pde_v.setValue(r=escript.Data())
312                else:
313                   if not isinstance(u0, escript.Data) : u0 = escript.Vector(u0, escript.Solution(self.domain))
314                   self.__pde_v.setValue(r=1./self.perm_scale * u0)
315                u= self.__pde_v.getSolution() * self.perm_scale
316            return u
317          
318  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  class StokesProblemCartesian(HomogeneousSaddlePointProblem):
319       """       """
320       solves       solves
# Line 777  class StokesProblemCartesian(Homogeneous Line 333  class StokesProblemCartesian(Homogeneous
333              sp.setTolerance()              sp.setTolerance()
334              sp.initialize(...)              sp.initialize(...)
335              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
336                sp.setStokesEquation(...) # new values for some parameters
337                v1,p1=sp.solve(v,p)
338       """       """
339       def __init__(self,domain,**kwargs):       def __init__(self,domain,**kwargs):
340           """           """
# Line 791  class StokesProblemCartesian(Homogeneous Line 349  class StokesProblemCartesian(Homogeneous
349           """           """
350           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
351           self.domain=domain           self.domain=domain
352           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())
353           self.__pde_u.setSymmetryOn()           self.__pde_v.setSymmetryOn()
354            
355           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
356           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
# Line 800  class StokesProblemCartesian(Homogeneous Line 358  class StokesProblemCartesian(Homogeneous
358    
359           self.__pde_proj=LinearPDE(domain)           self.__pde_proj=LinearPDE(domain)
360           self.__pde_proj.setReducedOrderOn()           self.__pde_proj.setReducedOrderOn()
361       self.__pde_proj.setValue(D=1)           self.__pde_proj.setValue(D=1)
362           self.__pde_proj.setSymmetryOn()           self.__pde_proj.setSymmetryOn()
363    
364       def getSolverOptionsVelocity(self):       def getSolverOptionsVelocity(self):
# Line 809  class StokesProblemCartesian(Homogeneous Line 367  class StokesProblemCartesian(Homogeneous
367            
368       :rtype: `SolverOptions`       :rtype: `SolverOptions`
369       """       """
370       return self.__pde_u.getSolverOptions()           return self.__pde_v.getSolverOptions()
371       def setSolverOptionsVelocity(self, options=None):       def setSolverOptionsVelocity(self, options=None):
372           """           """
373       set the solver options for solving the equation for velocity.       set the solver options for solving the equation for velocity.
# Line 817  class StokesProblemCartesian(Homogeneous Line 375  class StokesProblemCartesian(Homogeneous
375       :param options: new solver  options       :param options: new solver  options
376       :type options: `SolverOptions`       :type options: `SolverOptions`
377       """       """
378           self.__pde_u.setSolverOptions(options)           self.__pde_v.setSolverOptions(options)
379       def getSolverOptionsPressure(self):       def getSolverOptionsPressure(self):
380           """           """
381       returns the solver options used  solve the equation for pressure.       returns the solver options used  solve the equation for pressure.
382       :rtype: `SolverOptions`       :rtype: `SolverOptions`
383       """       """
384       return self.__pde_prec.getSolverOptions()           return self.__pde_prec.getSolverOptions()
385       def setSolverOptionsPressure(self, options=None):       def setSolverOptionsPressure(self, options=None):
386           """           """
387       set the solver options for solving the equation for pressure.       set the solver options for solving the equation for pressure.
388       :param options: new solver  options       :param options: new solver  options
389       :type options: `SolverOptions`       :type options: `SolverOptions`
390       """       """
391       self.__pde_prec.setSolverOptions(options)           self.__pde_prec.setSolverOptions(options)
392    
393       def setSolverOptionsDiv(self, options=None):       def setSolverOptionsDiv(self, options=None):
394           """           """
# Line 840  class StokesProblemCartesian(Homogeneous Line 398  class StokesProblemCartesian(Homogeneous
398       :param options: new solver options       :param options: new solver options
399       :type options: `SolverOptions`       :type options: `SolverOptions`
400       """       """
401       self.__pde_proj.setSolverOptions(options)           self.__pde_proj.setSolverOptions(options)
402       def getSolverOptionsDiv(self):       def getSolverOptionsDiv(self):
403           """           """
404       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 848  class StokesProblemCartesian(Homogeneous Line 406  class StokesProblemCartesian(Homogeneous
406            
407       :rtype: `SolverOptions`       :rtype: `SolverOptions`
408       """       """
409       return self.__pde_proj.getSolverOptions()           return self.__pde_proj.getSolverOptions()
410    
411       def updateStokesEquation(self, v, p):       def updateStokesEquation(self, v, p):
412           """           """
413           updates the Stokes equation to consider dependencies from ``v`` and ``p``           updates the Stokes equation to consider dependencies from ``v`` and ``p``
414           :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values.           :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
415           """           """
416           pass           pass
417       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 874  class StokesProblemCartesian(Homogeneous Line 432  class StokesProblemCartesian(Homogeneous
432          if eta !=None:          if eta !=None:
433              k=util.kronecker(self.domain.getDim())              k=util.kronecker(self.domain.getDim())
434              kk=util.outer(k,k)              kk=util.outer(k,k)
435              self.eta=util.interpolate(eta, Function(self.domain))              self.eta=util.interpolate(eta, escript.Function(self.domain))
436          self.__pde_prec.setValue(D=1/self.eta)              self.__pde_prec.setValue(D=1/self.eta)
437              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)))
438          if restoration_factor!=None:          if restoration_factor!=None:
439              n=self.domain.getNormal()              n=self.domain.getNormal()
440              self.__pde_u.setValue(d=restoration_factor*util.outer(n,n))              self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
441          if fixed_u_mask!=None:          if fixed_u_mask!=None:
442              self.__pde_u.setValue(q=fixed_u_mask)              self.__pde_v.setValue(q=fixed_u_mask)
443          if f!=None: self.__f=f          if f!=None: self.__f=f
444          if surface_stress!=None: self.__surface_stress=surface_stress          if surface_stress!=None: self.__surface_stress=surface_stress
445          if stress!=None: self.__stress=stress          if stress!=None: self.__stress=stress
446    
447       def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data(), restoration_factor=0):       def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
448          """          """
449          assigns values to the model parameters          assigns values to the model parameters
450    
# Line 899  class StokesProblemCartesian(Homogeneous Line 457  class StokesProblemCartesian(Homogeneous
457          :param surface_stress: normal surface stress          :param surface_stress: normal surface stress
458          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
459          :param stress: initial stress          :param stress: initial stress
460      :type stress: `Tensor` object on `FunctionSpace` `Function` or similar          :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
461          """          """
462          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
463    
# Line 912  class StokesProblemCartesian(Homogeneous Line 470  class StokesProblemCartesian(Homogeneous
470           :rtype: ``float``           :rtype: ``float``
471           """           """
472           self.__pde_proj.setValue(Y=-util.div(v))           self.__pde_proj.setValue(Y=-util.div(v))
473       self.getSolverOptionsDiv().setTolerance(tol)           self.getSolverOptionsDiv().setTolerance(tol)
474       self.getSolverOptionsDiv().setAbsoluteTolerance(0.)           self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
475           out=self.__pde_proj.getSolution()           out=self.__pde_proj.getSolution()
476           return out           return out
477    
# Line 926  class StokesProblemCartesian(Homogeneous Line 484  class StokesProblemCartesian(Homogeneous
484           :return: inner product of element p and Bv=-div(v)           :return: inner product of element p and Bv=-div(v)
485           :rtype: ``float``           :rtype: ``float``
486           """           """
487           return util.integrate(util.interpolate(p,Function(self.domain))*util.interpolate(Bv,Function(self.domain)))           return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
488    
489       def inner_p(self,p0,p1):       def inner_p(self,p0,p1):
490           """           """
# Line 937  class StokesProblemCartesian(Homogeneous Line 495  class StokesProblemCartesian(Homogeneous
495           :return: inner product of p0 and p1           :return: inner product of p0 and p1
496           :rtype: ``float``           :rtype: ``float``
497           """           """
498           s0=util.interpolate(p0,Function(self.domain))           s0=util.interpolate(p0, escript.Function(self.domain))
499           s1=util.interpolate(p1,Function(self.domain))           s1=util.interpolate(p1, escript.Function(self.domain))
500           return util.integrate(s0*s1)           return util.integrate(s0*s1)
501    
502       def norm_v(self,v):       def norm_v(self,v):
# Line 954  class StokesProblemCartesian(Homogeneous Line 512  class StokesProblemCartesian(Homogeneous
512    
513       def getDV(self, p, v, tol):       def getDV(self, p, v, tol):
514           """           """
515           return the value for v for a given p (overwrite)           return the value for v for a given p
516    
517           :param p: a pressure           :param p: a pressure
518           :param v: a initial guess for the value v to return.           :param v: a initial guess for the value v to return.
519           :return: dv given as *Adv=(f-Av-B^*p)*           :return: dv given as *Adv=(f-Av-B^*p)*
520           """           """
521           self.updateStokesEquation(v,p)           self.updateStokesEquation(v,p)
522           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
523       self.getSolverOptionsVelocity().setTolerance(tol)           self.getSolverOptionsVelocity().setTolerance(tol)
524       self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)           self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
525           if self.__stress.isEmpty():           if self.__stress.isEmpty():
526              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)))
527           else:           else:
528              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)))
529           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
530           return  out           return  out
531    
532       def norm_Bv(self,Bv):       def norm_Bv(self,Bv):
# Line 978  class StokesProblemCartesian(Homogeneous Line 536  class StokesProblemCartesian(Homogeneous
536          :rtype: equal to the type of p          :rtype: equal to the type of p
537          :note: boundary conditions on p should be zero!          :note: boundary conditions on p should be zero!
538          """          """
539          return util.sqrt(util.integrate(util.interpolate(Bv,Function(self.domain))**2))          return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
540    
541       def solve_AinvBt(self,p, tol):       def solve_AinvBt(self,p, tol):
542           """           """
# Line 988  class StokesProblemCartesian(Homogeneous Line 546  class StokesProblemCartesian(Homogeneous
546           :return: the solution of *Av=B^*p*           :return: the solution of *Av=B^*p*
547           :note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
548           """           """
549           self.__pde_u.setValue(Y=Data(), y=Data(), X=-p*util.kronecker(self.domain))           self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
550           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
551           return  out           return  out
552    
553       def solve_prec(self,Bv, tol):       def solve_prec(self,Bv, tol):
554           """           """
555           applies preconditioner for for *BA^{-1}B^** to *Bv*           applies preconditioner for for *BA^{-1}B^** to *Bv*
556           with accuracy `self.getSubProblemTolerance()`           with accuracy ``self.getSubProblemTolerance()``
557    
558           :param Bv: velocity increment           :param Bv: velocity increment
559           :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^ * )*
560           :note: boundary conditions on p are zero.           :note: boundary conditions on p are zero.
561           """           """
562           self.__pde_prec.setValue(Y=Bv)           self.__pde_prec.setValue(Y=Bv)
563       self.getSolverOptionsPressure().setTolerance(tol)           self.getSolverOptionsPressure().setTolerance(tol)
564       self.getSolverOptionsPressure().setAbsoluteTolerance(0.)           self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
565           out=self.__pde_prec.getSolution()           out=self.__pde_prec.getSolution()
566           return out           return out

Legend:
Removed from v.3360  
changed lines
  Added in v.3990

  ViewVC Help
Powered by ViewVC 1.1.26