/[escript]/trunk/escript/py_src/flows.py
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revision 3452 by caltinay, Tue Jan 25 01:53:57 2011 UTC revision 3510 by gross, Fri May 13 06:09:49 2011 UTC
# Line 37  import util Line 37  import util
37  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
38  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
39    
 print dir(escript)  
   
40  class DarcyFlow(object):  class DarcyFlow(object):
41     """     """
42     solves the problem     solves the problem
# Line 48  class DarcyFlow(object): Line 46  class DarcyFlow(object):
46        
47     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,
48        
49     :note: The problem is solved in a least squares formulation.     :cvar SIMPLE: simple solver
50       :cvar POST: solver using global postprocessing of flux
51       :cvar STAB: solver uses (non-symmetric) stabilization
52       :cvar SYMSTAB: solver uses symmetric stabilization
53     """     """
54         SIMPLE="SIMPLE"
55     def __init__(self, domain, useReduced=False, adaptSubTolerance=True, solveForFlux=False, useVPIteration=True, weighting_scale=0.1):     POST="POST"
56       STAB="STAB"
57       SYMSTAB="SYMSTAB"
58       def __init__(self, domain, useReduced=False, solver="SYMSTAB", verbose=False, w=1.):
59        """        """
60        initializes the Darcy flux problem        initializes the Darcy flux problem
61        :param domain: domain of the problem        :param domain: domain of the problem
62        :type domain: `Domain`        :type domain: `Domain`
63        :param useReduced: uses reduced oreder on flux and pressure        :param useReduced: uses reduced oreder on flux and pressure
64        :type useReduced: ``bool``        :type useReduced: ``bool``
65        :param adaptSubTolerance: switches on automatic subtolerance selection        :param solver: solver method
66        :type adaptSubTolerance: ``bool``        :type solver: in [`DarcyFlow.SIMPLE`, `DarcyFlow.POST', `DarcyFlow.STAB`, `DarcyFlow.SYMSTAB` ]
67        :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.
68        :type solveForFlux: ``bool``          :type verbose: ``bool``
69        :param useVPIteration: if True altenative iteration over v and p is performed. Otherwise V and P are calculated in a single PDE.        :param w: weighting factor for `DarcyFlow.POST` solver
70        :type useVPIteration: ``bool``            :type w: ``float``
71          
72        """        """
73        self.domain=domain        self.domain=domain
74        self.useVPIteration=useVPIteration        self.solver=solver
75        self.useReduced=useReduced        self.useReduced=useReduced
76        self.weighting_scale=weighting_scale        self.verbose=verbose
77        if self.useVPIteration:        self.scale=1.
          self.solveForFlux=solveForFlux  
          self.__adaptSubTolerance=adaptSubTolerance  
          self.verbose=False  
           
          self.__pde_k=LinearPDESystem(domain)  
          self.__pde_k.setSymmetryOn()  
          if self.useReduced: self.__pde_k.setReducedOrderOn()  
     
          self.__pde_p=LinearSinglePDE(domain)  
          self.__pde_p.setSymmetryOn()  
          if self.useReduced: self.__pde_p.setReducedOrderOn()  
          self.setTolerance()  
          self.setAbsoluteTolerance()  
       else:  
          self.__pde_k=LinearPDE(self.domain, numEquations=self.domain.getDim()+1)  
          self.__pde_k.setSymmetryOn()  
          if self.useReduced: self.__pde_k.setReducedOrderOn()  
          C=self.__pde_k.createCoefficient("C")  
          B=self.__pde_k.createCoefficient("B")  
          for i in range(self.domain.getDim()):  
             C[i,self.domain.getDim(),i]=1  
             B[self.domain.getDim(),i,i]=1  
          self.__pde_k.setValue(C=C, B=B)  
       self.__f=escript.Scalar(0,self.__pde_k.getFunctionSpaceForCoefficient("X"))  
       self.__g=escript.Vector(0,self.__pde_k.getFunctionSpaceForCoefficient("Y"))  
         
    def getSolverOptionsFlux(self):  
       """  
       Returns the solver options used to solve the flux problems  
         
       *K^{-1} u=F*  
         
       :return: `SolverOptions`  
       """  
       return self.__pde_k.getSolverOptions()  
         
    def setSolverOptionsFlux(self, options=None):  
       """  
       Sets the solver options used to solve the flux problems  
         
       *K^{-1}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^* K 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^* K Q)p=-Q^*G*  
78                
       If ``options`` is not present, the options are reset to default  
79                
80        :param options: `SolverOptions`        self.__pde_v=LinearPDESystem(domain)
81        :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.        self.__pde_v.setSymmetryOn()
82        """        if self.useReduced: self.__pde_v.setReducedOrderOn()
83        return self.__pde_p.setSolverOptions(options)        self.__pde_p=LinearSinglePDE(domain)
84          self.__pde_p.setSymmetryOn()
85          if self.useReduced: self.__pde_p.setReducedOrderOn()
86          
87          if self.solver  == self.SIMPLE:
88         if self.verbose: print "DarcyFlow: simple solver is used."
89             self.__pde_v.setValue(D=util.kronecker(self.domain.getDim()))
90          elif self.solver  == self.POST:
91         self.w=w
92         if util.inf(w)<0.:
93            raise ValueError,"Weighting factor must be non-negative."
94         if self.verbose: print "DarcyFlow: global postprocessing of flux is used."
95          elif self.solver  == self.STAB:
96          if self.verbose: print "DarcyFlow: (non-symmetric) stabilization is used."
97          elif  self.solver  == self.SYMSTAB:
98          if self.verbose: print "DarcyFlow: symmetric stabilization is used."
99          else:
100        raise ValueError,"unknown solver %s"%self.solver
101          self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
102          self.__g=escript.Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
103          self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
104          self.location_of_fixed_flux = escript.Vector(0, self.__pde_v.getFunctionSpaceForCoefficient("q"))
105          self.setTolerance()
106        
107            
108     def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):     def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
109        """        """
110        assigns values to model parameters        assigns values to model parameters
# Line 156  class DarcyFlow(object): Line 118  class DarcyFlow(object):
118        :param location_of_fixed_flux:  mask for locations where flux is fixed.        :param location_of_fixed_flux:  mask for locations where flux is fixed.
119        :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)        :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
120        :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.        :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
121        :type permeability: scalar or tensor values on the domain (e.g. `escript.Data`)        :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
122    
123        :note: the values of parameters which are not set by calling ``setValue`` are not altered.        :note: the values of parameters which are not set by calling ``setValue`` are not altered.
124        :note: at any point on the boundary of the domain the pressure        :note: at any point on the boundary of the domain the pressure
# Line 165  class DarcyFlow(object): Line 127  class DarcyFlow(object):
127               is along the *x_i* axis.               is along the *x_i* axis.
128    
129        """        """
130        if self.useVPIteration:        if location_of_fixed_pressure!=None:
131           if location_of_fixed_pressure!=None: self.__pde_p.setValue(q=location_of_fixed_pressure)             self.location_of_fixed_pressure=util.wherePositive(location_of_fixed_pressure)
132           if location_of_fixed_flux!=None: self.__pde_k.setValue(q=location_of_fixed_flux)             self.__pde_p.setValue(q=self.location_of_fixed_pressure)
133        else:        if location_of_fixed_flux!=None:
134           q=self.__pde_k.getCoefficient("q")            self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
135           if q.isEmpty(): q=self.__pde_k.createCoefficient("q")            self.__pde_v.setValue(q=self.location_of_fixed_flux)
136           if location_of_fixed_pressure!=None: q[self.domain.getDim()]=location_of_fixed_pressure        
          if location_of_fixed_flux!=None: q[:self.domain.getDim()]=location_of_fixed_flux  
          self.__pde_k.setValue(q=q)  
137                            
138        # flux is rescaled by the factor mean value(perm_inv)*length where length**self.domain.getDim()=vol(self.domain)        # pressure  is rescaled by the factor 1/self.scale
139        if permeability!=None:        if permeability!=None:
140       perm=util.interpolate(permeability,self.__pde_k.getFunctionSpaceForCoefficient("A"))      
141         perm=util.interpolate(permeability,self.__pde_v.getFunctionSpaceForCoefficient("A"))
142           V=util.vol(self.domain)           V=util.vol(self.domain)
143             l=V**(1./self.domain.getDim())
144            
145       if perm.getRank()==0:       if perm.getRank()==0:
146          perm_inv=(1./perm)          perm_inv=(1./perm)
147              if self.useVPIteration:              self.scale=util.integrate(perm_inv)/V*l
               self.scale=1.  
             else:  
               self.scale=util.integrate(perm_inv)*V**(1./self.domain.getDim()-1.)  
   
148          perm_inv=perm_inv*((1./self.scale)*util.kronecker(self.domain.getDim()))          perm_inv=perm_inv*((1./self.scale)*util.kronecker(self.domain.getDim()))
149          perm=perm*(self.scale*util.kronecker(self.domain.getDim()))          perm=perm*(self.scale*util.kronecker(self.domain.getDim()))
150            
151            
152       elif perm.getRank()==2:       elif perm.getRank()==2:
153          perm_inv=util.inverse(perm)          perm_inv=util.inverse(perm)
154              if self.useVPIteration:              self.scale=util.sqrt(util.integrate(util.length(perm_inv)**2)/V)*l
155                self.scale=1.          perm_inv*=(1./self.scale)
156              else:          perm=perm*self.scale
               self.scale=util.sqrt(util.integrate(util.length(perm_inv)**2)*V**(2./self.domain.getDim()-1.)/self.domain.getDim())  
           perm_inv*=(1./self.scale)  
           perm=perm*self.scale  
157       else:       else:
158          raise ValueError,"illegal rank of permeability."          raise ValueError,"illegal rank of permeability."
159            
160       self.__permeability=perm       self.__permeability=perm
161       self.__permeability_inv=perm_inv       self.__permeability_inv=perm_inv
162         if self.verbose: print "DarcyFlow: scaling factor for pressure is %e."%self.scale
163       self.__l2 =(util.longestEdge(self.domain)**2*util.length(self.__permeability_inv))*self.weighting_scale      
164           if self.useVPIteration:       if self.solver  == self.SIMPLE:
         if  self.solveForFlux:  
            self.__pde_k.setValue(D=self.__permeability_inv)  
         else:  
            self.__pde_k.setValue(D=self.__permeability_inv, A=self.__l2*util.outer(util.kronecker(self.domain),util.kronecker(self.domain)))  
165          self.__pde_p.setValue(A=self.__permeability)          self.__pde_p.setValue(A=self.__permeability)
166           else:       elif self.solver  == self.POST:
167              D=self.__pde_k.createCoefficient("D")          self.__pde_p.setValue(A=self.__permeability)
168              A=self.__pde_k.createCoefficient("A")          k=util.kronecker(self.domain.getDim())
169              D[:self.domain.getDim(),:self.domain.getDim()]=self.__permeability_inv          self.lamb = self.w*util.length(perm_inv)*l
170              for i in range(self.domain.getDim()):          self.__pde_v.setValue(D=self.__permeability_inv, A=self.lamb*self.domain.getSize()*util.outer(k,k))
171                 for j in range(self.domain.getDim()):       elif self.solver  == self.STAB:
172                   A[i,i,j,j]=self.__l2          self.__pde_p.setValue(A=0.5*self.__permeability)
173              A[self.domain.getDim(),:,self.domain.getDim(),:]=self.__permeability          self.__pde_v.setValue(D=0.5*self.__permeability_inv)
174              self.__pde_k.setValue(A=A, D=D)       elif  self.solver  == self.SYMSTAB:
175        if g !=None:          self.__pde_p.setValue(A=0.5*self.__permeability)
176       g=util.interpolate(g, self.__pde_k.getFunctionSpaceForCoefficient("Y"))          self.__pde_v.setValue(D=0.5*self.__permeability_inv)
177       if g.isEmpty():  
178            g=Vector(0,self.__pde_k.getFunctionSpaceForCoefficient("Y"))        if g != None:
179       else:      g=util.interpolate(g, self.__pde_v.getFunctionSpaceForCoefficient("Y"))
180          if not g.getShape()==(self.domain.getDim(),):      if g.isEmpty():
181                raise ValueError,"illegal shape of g"            g=Vector(0,self.__pde_v.getFunctionSpaceForCoefficient("Y"))
182          self.__g=g      else:
183        elif permeability!=None:          if not g.getShape()==(self.domain.getDim(),): raise ValueError,"illegal shape of g"
184               X      self.__g=g
185        if f !=None:        if f !=None:
186       f=util.interpolate(f, self.__pde_k.getFunctionSpaceForCoefficient("X"))       f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
187       if f.isEmpty():       if f.isEmpty():      
188            f=Scalar(0,self.__pde_k.getFunctionSpaceForCoefficient("X"))            f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
189       else:       else:
190           if f.getRank()>0: raise ValueError,"illegal rank of f."           if f.getRank()>0: raise ValueError,"illegal rank of f."
191           self.__f=f       self.__f=f
192       def getSolverOptionsFlux(self):
         
    def solve(self,u0,p0, max_iter=100, verbose=False, max_num_corrections=10):  
193        """        """
194        solves the problem.        Returns the solver options used to solve the flux problems
195          :return: `SolverOptions`
196          """
197          return self.__pde_v.getSolverOptions()
198                
199        The iteration is terminated if the residual norm is less then self.getTolerance().     def setSolverOptionsFlux(self, options=None):
   
       :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. `escript.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. `escript.Data`).  
       :param verbose: if set some information on iteration progress are printed  
       :type verbose: ``bool``  
       :return: flux and pressure  
       :rtype: ``tuple`` of `escript.Data`.  
   
       :note: The problem is solved as a least squares form  
              *(K^[-1]+D^* l2 D)u+G p=D^* l2 * 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}*.  
200        """        """
201        self.verbose=verbose        Sets the solver options used to solve the flux problems
202        if self.useVPIteration:        If ``options`` is not present, the options are reset to default
203            return self.__solveVP(u0,p0,max_iter,max_num_corrections)        :param options: `SolverOptions`
       else:  
           X=self.__pde_k.createCoefficient("X")  
           Y=self.__pde_k.createCoefficient("Y")  
           Y[:self.domain.getDim()]=self.scale*util.tensor_mult(self.__permeability_inv,self.__g)  
           rtmp=self.__f * self.__l2 * self.scale  
           for i in range(self.domain.getDim()): X[i,i]=rtmp  
           X[self.domain.getDim(),:]=self.__g*self.scale  
           r=self.__pde_k.createCoefficient("r")  
           r[:self.domain.getDim()]=u0*self.scale  
           r[self.domain.getDim()]=p0  
           self.__pde_k.setValue(X=X, Y=Y, r=r)  
           self.__pde_k.getSolverOptions().setVerbosity(self.verbose)  
           #self.__pde_k.getSolverOptions().setPreconditioner(self.__pde_k.getSolverOptions().AMG)  
           self.__pde_k.getSolverOptions().setSolverMethod(self.__pde_k.getSolverOptions().DIRECT)  
           U=self.__pde_k.getSolution()  
           # self.__pde_k.getOperator().saveMM("k.mm")  
           u=U[:self.domain.getDim()]*(1./self.scale)  
           p=U[self.domain.getDim()]  
           if self.verbose:  
         KGp=util.tensor_mult(self.__permeability,util.grad(p)/self.scale)  
         def_p=self.__g-(u+KGp)  
         def_v=self.__f-util.div(u, self.__pde_k.getFunctionSpaceForCoefficient("X"))  
         print "DarcyFlux: L2: g-v-K*grad(p) = %e (v = %e)."%(self.__L2(def_p),self.__L2(u))  
         print "DarcyFlux: L2: f-div(v) = %e (grad(v) = %e)."%(self.__L2(def_v),self.__L2(util.grad(u)))  
           return u,p  
   
    def __solveVP(self,u0,p0, max_iter=100, max_num_corrections=10):  
204        """        """
205        solves the problem.        return self.__pde_v.setSolverOptions(options)
206        
207       def getSolverOptionsPressure(self):
208          """
209          Returns the solver options used to solve the pressure problems
210          :return: `SolverOptions`
211          """
212          return self.__pde_p.getSolverOptions()
213                
214        The iteration is terminated if the residual norm is less than self.getTolerance().     def setSolverOptionsPressure(self, options=None):
215          """
216        :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.        Sets the solver options used to solve the pressure problems
217        :type u0: vector value on the domain (e.g. `escript.Data`).        If ``options`` is not present, the options are reset to default
       :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. `escript.Data`).  
       :return: flux and pressure  
       :rtype: ``tuple`` of `escript.Data`.  
   
       :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}*.  
       """  
       rtol=self.getTolerance()  
       atol=self.getAbsoluteTolerance()  
       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()  
       else:  
      v=self.__getFlux(p, u0, f=self.__f, g=g2)  
   
       while not converged and norm_g2 > 0:  
      Gp=util.grad(p)  
      KGp=util.tensor_mult(self.__permeability,Gp)  
      if self.verbose:  
         def_p=g2-(v+KGp)  
         def_v=self.__f-util.div(v)  
         print "DarcyFlux: L2: g-v-K*grad(p) = %e (v = %e)."%(self.__L2(def_p),self.__L2(v))  
         print "DarcyFlux: L2: f-div(v) = %e (grad(v) = %e)."%(self.__L2(def_v),self.__L2(util.grad(v)))  
         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 __applWeight(self, v, f=None):  
       # solves L p = f-Dv with p = 0  
       if self.verbose: print "DarcyFlux: Applying weighting operator"  
       if f == None:  
      return -util.div(v)*self.__l2  
       else:  
      return (f-util.div(v))*self.__l2  
    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=escript.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=escript.Data())  
       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=escript.Data(), r=escript.Data())  
       du=self.__pde_k.getSolution()  
       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()    
218                
219        #v=self.__getFlux(p, u0, f=self.__f, g=g2)              :param options: `SolverOptions`
220     def __Msolve_PCG_p(self,r):        :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
       if self.getSolverOptionsPressure().isVerbose(): print "DarcyFlux: Applying preconditioner"  
       self.__pde_p.setValue(X=r[0]-r[1], Y=escript.Data(), r=escript.Data(), y=escript.Data())  
       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,escript.Function(self.domain)))**2))  
   
    def __L2_r(self,v):  
       return util.sqrt(util.integrate(util.length(util.interpolate(v,escript.ReducedFunction(self.domain)))**2))  
   
    def setTolerance(self,rtol=1e-4):  
221        """        """
222        sets the relative tolerance ``rtol`` used to terminate the solution process. The iteration is terminated if        return self.__pde_p.setSolverOptions(options)
   
       *|g-v-K gard(p)|_PCG <= atol + rtol * |K^{1/2}g2|_0*  
223                
224        where ``atol`` is an absolut tolerance (see `setAbsoluteTolerance`).     def setTolerance(self,rtol=1e-4):
225          """
226          sets the relative tolerance ``rtol`` for the pressure for the stabelized solvers.
227                
228        :param rtol: relative tolerance for the pressure        :param rtol: relative tolerance for the pressure
229        :type rtol: non-negative ``float``        :type rtol: non-negative ``float``
# Line 447  class DarcyFlow(object): Line 231  class DarcyFlow(object):
231        if rtol<0:        if rtol<0:
232       raise ValueError,"Relative tolerance needs to be non-negative."       raise ValueError,"Relative tolerance needs to be non-negative."
233        self.__rtol=rtol        self.__rtol=rtol
234          
235     def getTolerance(self):     def getTolerance(self):
236        """        """
237        returns the relative tolerance        returns the relative tolerance
# Line 454  class DarcyFlow(object): Line 239  class DarcyFlow(object):
239        :rtype: ``float``        :rtype: ``float``
240        """        """
241        return self.__rtol        return self.__rtol
242          
243     def setAbsoluteTolerance(self,atol=0.):     def solve(self,u0,p0, max_iter=100, iter_restart=20):
244        """        """
245        sets the absolute tolerance ``atol`` used to terminate the solution process. The iteration is terminated if        solves the problem.
246                
247        *|g-v-K gard(p)|_PCG <= atol + rtol * |K^{1/2}g2|_0*        The iteration is terminated if the residual norm is less then self.getTolerance().
   
   
       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}*.  
248    
249        :param atol: absolute tolerance for the pressure        :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.
250        :type atol: non-negative ``float``        :type u0: vector value on the domain (e.g. `escript.Data`).
251        """        :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.
252        if atol<0:        :type p0: scalar value on the domain (e.g. `escript.Data`).
253       raise ValueError,"Absolute tolerance needs to be non-negative."        :param max_iter: maximum number of (outer) iteration steps for the stabilization solvers,
254        self.__atol=atol        :type max_iter: ``int``
255     def getAbsoluteTolerance(self):        :param iter_restart: number of steps after which the iteration is restarted. The larger ``iter_restart`` the larger the required memory.
256        """                             A small value for ``iter_restart`` may require a large number of iteration steps or may even lead to a failure
257        returns the absolute tolerance                             of the iteration. ``iter_restart`` is relevant for the stabilization solvers only.
258        :return: current absolute tolerance        :type iter_restart: ``int``
259        :rtype: ``float``        :return: flux and pressure
260        """        :rtype: ``tuple`` of `escript.Data`.
       return self.__atol  
    def getSubProblemTolerance(self):  
       """  
       Returns a suitable subtolerance  
       :type: ``float``  
       """  
       return max(util.EPSILON**(0.5),self.getTolerance()**2)  
261    
    def setSubProblemTolerance(self):  
       """  
       Sets the relative tolerance to solve the subproblem(s) if subtolerance adaption is selected.  
262        """        """
263        if self.__adaptSubTolerance:        # rescale initial guess:
264       sub_tol=self.getSubProblemTolerance()        p0=p0/self.scale
265       self.getSolverOptionsFlux().setTolerance(sub_tol)        if self.solver  == self.SIMPLE or self.solver  == self.POST :
266       self.getSolverOptionsFlux().setAbsoluteTolerance(0.)          self.__pde_p.setValue(X=self.__g ,
267       self.getSolverOptionsPressure().setTolerance(sub_tol)                                Y=self.__f,
268       self.getSolverOptionsPressure().setAbsoluteTolerance(0.)                                y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux),
269       if self.verbose: print "DarcyFlux: relative subtolerance is set to %e."%sub_tol                                r=p0)
270            p=self.__pde_p.getSolution()
271            u = self.getFlux(p, u0)
272  class DarcyFlowOld(object):        elif  self.solver  == self.STAB:
273      """      u,p = self.__solve_STAB(u0,p0, max_iter, iter_restart)
274      solves the problem        elif  self.solver  == self.SYMSTAB:
275        u,p = self.__solve_SYMSTAB(u0,p0, max_iter, iter_restart)
     *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.__l2=(3.*util.longestEdge(self.domain)*s/util.sup(s))**2  
            # self.__l2=(3.*util.longestEdge(self.domain))**2  
            #self.__l2=(0.1*util.longestEdge(self.domain)*s/util.sup(s))**2  
         else:  
            self.__l2=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.__l2*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=escript.Scalar(0,self.__pde_v.getFunctionSpaceForCoefficient("X"))  
         self.__g=escript.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*  
276            
277      :return: `SolverOptions`        if self.verbose:
278      """          KGp=util.tensor_mult(self.__permeability,util.grad(p))
279      return self.__pde_p.getSolverOptions()          def_p=self.__g-(u+KGp)
280      def setSolverOptionsPressure(self, options=None):          def_v=self.__f-util.div(u, self.__pde_v.getFunctionSpaceForCoefficient("X"))
281      """          print "DarcyFlux: |g-u-K*grad(p)|_2 = %e (|u|_2 = %e)."%(self.__L2(def_p),self.__L2(u))
282      Sets the solver options used to solve the pressure problems          print "DarcyFlux: |f-div(u)|_2 = %e (|grad(u)|_2 = %e)."%(self.__L2(def_v),self.__L2(util.grad(u)))
283              #rescale result
284      *(Q^*Q)p=Q^*G*        p=p*self.scale
285              return u,p
286      If ``options`` is not present, the options are reset to default        
287      :param options: `SolverOptions`     def getFlux(self,p, u0=None):
     :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. `escript.Data`)  
         :param g: flux sources/sinks  
         :type g: vector values on the domain (e.g. `escript.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. `escript.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. `escript.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. `escript.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=escript.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=escript.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. `escript.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. `escript.Data`).  
          :param verbose: if set some information on iteration progress are printed  
          :type verbose: ``bool``  
          :return: flux and pressure  
          :rtype: ``tuple`` of `escript.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,escript.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,escript.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,escript.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=escript.Data(), r=escript.Data())  
           du=self.__pde_v.getSolution()  
           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=escript.Data(), r=escript.Data())  
           return self.__pde_p.getSolution()  
   
     def getFlux(self,p=None, fixed_flux=escript.Data()):  
288          """          """
289          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``
290          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).          on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
291          Note that ``g`` and ``f`` are used, see `setValue`.          Notice that ``g`` and ``f`` are used, see `setValue`.
292    
293          :param p: pressure.          :param p: pressure.
294          :type p: scalar value on the domain (e.g. `escript.Data`).          :type p: scalar value on the domain (e.g. `escript.Data`).
295          :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``.
296          :type fixed_flux: vector values on the domain (e.g. `escript.Data`).          :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
297          :return: flux          :return: flux
298          :rtype: `escript.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}*  
299          """          """
300      self.setSubProblemTolerance()          if self.solver  == self.SIMPLE or self.solver  == self.POST  :
301          g=self.__g              KGp=util.tensor_mult(self.__permeability,util.grad(p))
302          f=self.__f              self.__pde_v.setValue(Y=self.__g-KGp, X=escript.Data())
303          self.__pde_v.setValue(X=self.__l2*f*util.kronecker(self.domain), r=fixed_flux)              if u0 == None:
304          if p == None:             self.__pde_v.setValue(r=escript.Data())
305             self.__pde_v.setValue(Y=g)          else:
306          else:             self.__pde_v.setValue(r=u0)
307             self.__pde_v.setValue(Y=g-self.__Q(p))              u= self.__pde_v.getSolution()
308          return self.__pde_v.getSolution()      elif self.solver  == self.POST:
309                self.__pde_v.setValue(Y=util.tensor_mult(self.__permeability_inv,self.__g)-util.grad(p),
310                                      X=self.lamb * self.__f * util.kronecker(self.domain.getDim()))
311                if u0 == None:
312               self.__pde_v.setValue(r=escript.Data())
313            else:
314               self.__pde_v.setValue(r=u0)
315                u= self.__pde_v.getSolution()
316        elif self.solver  == self.STAB:
317             gp=util.grad(p)
318             self.__pde_v.setValue(Y=0.5*(util.tensor_mult(self.__permeability_inv,self.__g)+gp),
319                                   X= p * util.kronecker(self.domain.getDim()),
320                                   y= - p * self.domain.getNormal())                          
321             if u0 == None:
322               self.__pde_v.setValue(r=escript.Data())
323             else:
324               self.__pde_v.setValue(r=u0)
325             u= self.__pde_v.getSolution()
326        elif  self.solver  == self.SYMSTAB:
327             gp=util.grad(p)
328             self.__pde_v.setValue(Y=0.5*(util.tensor_mult(self.__permeability_inv,self.__g)-gp),
329                                   X= escript.Data() ,
330                                   y= escript.Data() )                          
331             if u0 == None:
332               self.__pde_v.setValue(r=escript.Data())
333             else:
334               self.__pde_v.setValue(r=u0)
335             u= self.__pde_v.getSolution()
336        return u
337          
338        
339       def __solve_STAB(self, u0, p0, max_iter, iter_restart):
340              # p0 is used as an initial guess
341          u=self.getFlux(p0, u0)  
342              self.__pde_p.setValue( Y=self.__f-util.div(u),
343                                     X=0.5*(self.__g - u - util.tensor_mult(self.__permeability,util.grad(p0)) ),
344                                     y= escript.Data(),
345                                     r=escript.Data())
346    
347          dp=self.__pde_p.getSolution()
348          p=GMRES(dp,
349                  self.__STAB_Aprod,
350              p0,
351              self.__inner,
352              atol=self.__norm(p0+dp)*self.getTolerance() ,
353              rtol=0.,
354              iter_max=max_iter,
355              iter_restart=iter_restart,
356              verbose=self.verbose,P_R=None)
357                
358              u=self.getFlux(p, u0)
359              return u,p
360    
361       def __solve_SYMSTAB(self, u0, p0, max_iter, iter_restart):
362              # p0 is used as an initial guess
363          u=self.getFlux(p0, u0)  
364              self.__pde_p.setValue( Y= self.__f,
365                                     X=  0.5*(self.__g + u - util.tensor_mult(self.__permeability,util.grad(p0)) ),
366                                     y=  -  util.inner(self.domain.getNormal(), u),
367                                     r=escript.Data())
368          dp=self.__pde_p.getSolution()
369          
370          print dp
371              print p0+dp
372              
373          p=GMRES(dp,
374                  self.__SYMSTAB_Aprod,
375              p0,
376              self.__inner,
377              atol=self.__norm(p0+dp)*self.getTolerance() ,
378              rtol=0.,
379              iter_max=max_iter,
380              iter_restart=iter_restart,
381              verbose=self.verbose,P_R=None)
382                
383              u=self.getFlux(p, u0)
384              return u,p
385    
386       def __L2(self,v):
387             return util.sqrt(util.integrate(util.length(util.interpolate(v,escript.Function(self.domain)))**2))      
388      
389       def __norm(self,r):
390             return util.sqrt(self.__inner(r,r))
391            
392       def __inner(self,r,s):
393             return util.integrate(util.inner(r,s), escript.Function(self.domain))
394            
395       def __STAB_Aprod(self,p):
396          gp=util.grad(p)
397          self.__pde_v.setValue(Y=-0.5*gp,
398                                X=-p*util.kronecker(self.__pde_v.getDomain()),
399                                y= p * self.domain.getNormal(),  
400                                r=escript.Data())
401          u = -self.__pde_v.getSolution()
402          self.__pde_p.setValue(Y=util.div(u),
403                                X=0.5*(u+util.tensor_mult(self.__permeability,gp)),
404                                y=escript.Data(),
405                                r=escript.Data())
406        
407          return  self.__pde_p.getSolution()
408      
409       def __SYMSTAB_Aprod(self,p):
410          gp=util.grad(p)
411          self.__pde_v.setValue(Y=0.5*gp ,
412                                X=escript.Data(),
413                                y=escript.Data(),  
414                                r=escript.Data())
415          u = -self.__pde_v.getSolution()
416          self.__pde_p.setValue(Y=escript.Data(),
417                                X=0.5*(-u+util.tensor_mult(self.__permeability,gp)),
418                                y=escript.Data(),
419                                r=escript.Data())
420        
421          return  self.__pde_p.getSolution()
422          
423    
424  class StokesProblemCartesian(HomogeneousSaddlePointProblem):  class StokesProblemCartesian(HomogeneousSaddlePointProblem):
425       """       """
# Line 849  class StokesProblemCartesian(Homogeneous Line 453  class StokesProblemCartesian(Homogeneous
453           """           """
454           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
455           self.domain=domain           self.domain=domain
456           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())
457           self.__pde_u.setSymmetryOn()           self.__pde_v.setSymmetryOn()
458            
459           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
460           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
# Line 867  class StokesProblemCartesian(Homogeneous Line 471  class StokesProblemCartesian(Homogeneous
471            
472       :rtype: `SolverOptions`       :rtype: `SolverOptions`
473       """       """
474       return self.__pde_u.getSolverOptions()       return self.__pde_v.getSolverOptions()
475       def setSolverOptionsVelocity(self, options=None):       def setSolverOptionsVelocity(self, options=None):
476           """           """
477       set the solver options for solving the equation for velocity.       set the solver options for solving the equation for velocity.
# Line 875  class StokesProblemCartesian(Homogeneous Line 479  class StokesProblemCartesian(Homogeneous
479       :param options: new solver  options       :param options: new solver  options
480       :type options: `SolverOptions`       :type options: `SolverOptions`
481       """       """
482           self.__pde_u.setSolverOptions(options)           self.__pde_v.setSolverOptions(options)
483       def getSolverOptionsPressure(self):       def getSolverOptionsPressure(self):
484           """           """
485       returns the solver options used  solve the equation for pressure.       returns the solver options used  solve the equation for pressure.
# Line 934  class StokesProblemCartesian(Homogeneous Line 538  class StokesProblemCartesian(Homogeneous
538              kk=util.outer(k,k)              kk=util.outer(k,k)
539              self.eta=util.interpolate(eta, escript.Function(self.domain))              self.eta=util.interpolate(eta, escript.Function(self.domain))
540          self.__pde_prec.setValue(D=1/self.eta)          self.__pde_prec.setValue(D=1/self.eta)
541              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)))
542          if restoration_factor!=None:          if restoration_factor!=None:
543              n=self.domain.getNormal()              n=self.domain.getNormal()
544              self.__pde_u.setValue(d=restoration_factor*util.outer(n,n))              self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
545          if fixed_u_mask!=None:          if fixed_u_mask!=None:
546              self.__pde_u.setValue(q=fixed_u_mask)              self.__pde_v.setValue(q=fixed_u_mask)
547          if f!=None: self.__f=f          if f!=None: self.__f=f
548          if surface_stress!=None: self.__surface_stress=surface_stress          if surface_stress!=None: self.__surface_stress=surface_stress
549          if stress!=None: self.__stress=stress          if stress!=None: self.__stress=stress
# Line 1019  class StokesProblemCartesian(Homogeneous Line 623  class StokesProblemCartesian(Homogeneous
623           :return: dv given as *Adv=(f-Av-B^*p)*           :return: dv given as *Adv=(f-Av-B^*p)*
624           """           """
625           self.updateStokesEquation(v,p)           self.updateStokesEquation(v,p)
626           self.__pde_u.setValue(Y=self.__f, y=self.__surface_stress)           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
627       self.getSolverOptionsVelocity().setTolerance(tol)       self.getSolverOptionsVelocity().setTolerance(tol)
628       self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)       self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
629           if self.__stress.isEmpty():           if self.__stress.isEmpty():
630              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)))
631           else:           else:
632              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)))
633           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
634           return  out           return  out
635    
636       def norm_Bv(self,Bv):       def norm_Bv(self,Bv):
# Line 1046  class StokesProblemCartesian(Homogeneous Line 650  class StokesProblemCartesian(Homogeneous
650           :return: the solution of *Av=B^*p*           :return: the solution of *Av=B^*p*
651           :note: boundary conditions on v should be zero!           :note: boundary conditions on v should be zero!
652           """           """
653           self.__pde_u.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))           self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
654           out=self.__pde_u.getSolution()           out=self.__pde_v.getSolution()
655           return  out           return  out
656    
657       def solve_prec(self,Bv, tol):       def solve_prec(self,Bv, tol):

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