/[escript]/trunk/escript/py_src/flows.py
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revision 2208 by gross, Mon Jan 12 06:37:07 2009 UTC revision 3619 by gross, Wed Oct 5 03:53:34 2011 UTC
# Line 1  Line 1 
1    # -*- coding: utf-8 -*-
2  ########################################################  ########################################################
3  #  #
4  # Copyright (c) 2003-2008 by University of Queensland  # Copyright (c) 2003-2010 by University of Queensland
5  # Earth Systems Science Computational Center (ESSCC)  # Earth Systems Science Computational Center (ESSCC)
6  # http://www.uq.edu.au/esscc  # http://www.uq.edu.au/esscc
7  #  #
# Line 10  Line 11 
11  #  #
12  ########################################################  ########################################################
13    
14  __copyright__="""Copyright (c) 2003-2008 by University of Queensland  __copyright__="""Copyright (c) 2003-2010 by University of Queensland
15  Earth Systems Science Computational Center (ESSCC)  Earth Systems Science Computational Center (ESSCC)
16  http://www.uq.edu.au/esscc  http://www.uq.edu.au/esscc
17  Primary Business: Queensland, Australia"""  Primary Business: Queensland, Australia"""
18  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
19  http://www.opensource.org/licenses/osl-3.0.php"""  http://www.opensource.org/licenses/osl-3.0.php"""
20  __url__="http://www.uq.edu.au/esscc/escript-finley"  __url__="https://launchpad.net/escript-finley"
21    
22  """  """
23  Some models for flow  Some models for flow
24    
25  @var __author__: name of author  :var __author__: name of author
26  @var __copyright__: copyrights  :var __copyright__: copyrights
27  @var __license__: licence agreement  :var __license__: licence agreement
28  @var __url__: url entry point on documentation  :var __url__: url entry point on documentation
29  @var __version__: version  :var __version__: version
30  @var __date__: date of the version  :var __date__: date of the version
31  """  """
32    
33  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
34    
35  from escript import *  import escript
36  import util  import util
37  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE  from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
38  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm  from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
39    
40  class DarcyFlow(object):  class DarcyFlow(object):
41      """     """
42      solves the problem     solves the problem
   
     M{u_i+k_{ij}*p_{,j} = g_i}  
     M{u_{i,i} = f}  
   
     where M{p} represents the pressure and M{u} the Darcy flux. M{k} represents the permeability,  
   
     @note: The problem is solved in a least squares formulation.  
     """  
   
     def __init__(self, domain,useReduced=False):  
         """  
         initializes the Darcy flux problem  
         @param domain: domain of the problem  
         @type domain: L{Domain}  
         """  
         self.domain=domain  
         self.__pde_v=LinearPDESystem(domain)  
         if useReduced: self.__pde_v.setReducedOrderOn()  
         self.__pde_v.setSymmetryOn()  
         self.__pde_v.setValue(D=util.kronecker(domain), A=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.__ATOL= None  
   
     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. L{Data})  
         @param g: flux sources/sinks  
         @type g: vector values on the domain (e.g. L{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. L{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. L{Data})  
         @param permeability: permeability tensor. If scalar C{s} is given the tensor with  
                              C{s} on the main diagonal is used. If vector C{v} is given the tensor with  
                              C{v} on the main diagonal is used.  
         @type permeability: scalar, vector or tensor values on the domain (e.g. L{Data})  
   
         @note: the values of parameters which are not set by calling C{setValue} are not altered.  
         @note: at any point on the boundary of the domain the pressure (C{location_of_fixed_pressure} >0)  
                or the normal component of the flux (C{location_of_fixed_flux[i]>0} if direction of the normal  
                is along the M{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 getFlux(self,p=None, fixed_flux=Data(),tol=1.e-8, show_details=False):  
         """  
         returns the flux for a given pressure C{p} where the flux is equal to C{fixed_flux}  
         on locations where C{location_of_fixed_flux} is positive (see L{setValue}).  
         Note that C{g} and C{f} are used, see L{setValue}.  
           
         @param p: pressure.  
         @type p: scalar value on the domain (e.g. L{Data}).  
         @param fixed_flux: flux on the locations of the domain marked be C{location_of_fixed_flux}.  
         @type fixed_flux: vector values on the domain (e.g. L{Data}).  
         @param tol: relative tolerance to be used.  
         @type tol: positive C{float}.  
         @return: flux  
         @rtype: L{Data}  
         @note: the method uses the least squares solution M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}}  
                for the permeability M{k_{ij}}  
         """  
         self.__pde_v.setTolerance(tol)  
         g=self.__g  
         f=self.__f  
         self.__pde_v.setValue(X=f*util.kronecker(self.domain), r=fixed_flux)  
         if p == None:  
            self.__pde_v.setValue(Y=g)  
         else:  
            self.__pde_v.setValue(Y=g-util.tensor_mult(self.__permeability,util.grad(p)))  
         return self.__pde_v.getSolution(verbose=show_details)  
   
     def getPressure(self,v=None, fixed_pressure=Data(),tol=1.e-8, show_details=False):  
         """  
         returns the pressure for a given flux C{v} where the pressure is equal to C{fixed_pressure}  
         on locations where C{location_of_fixed_pressure} is positive (see L{setValue}).  
         Note that C{g} is used, see L{setValue}.  
           
         @param v: flux.  
         @type v: vector-valued on the domain (e.g. L{Data}).  
         @param fixed_pressure: pressure on the locations of the domain marked be C{location_of_fixed_pressure}.  
         @type fixed_pressure: vector values on the domain (e.g. L{Data}).  
         @param tol: relative tolerance to be used.  
         @type tol: positive C{float}.  
         @return: pressure  
         @rtype: L{Data}  
         @note: the method uses the least squares solution M{p=(Q^*Q)^{-1}Q^*(g-u)} where and M{(Qp)_i=k_{ij}p_{,j}}  
                for the permeability M{k_{ij}}  
         """  
         self.__pde_v.setTolerance(tol)  
         g=self.__g  
         self.__pde_p.setValue(r=fixed_pressure)  
         if v == None:  
            self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,g-v))  
         else:  
            self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,g))  
         return self.__pde_p.getSolution(verbose=show_details)  
   
     def setTolerance(self,atol=0,rtol=1e-8,p_ref=None,v_ref=None):  
         """  
         set the tolerance C{ATOL} used to terminate the solution process. It is used  
   
         M{ATOL = atol + rtol * max( |g-v_ref|, |Qp_ref| )}  
   
         where M{|f|^2 = integrate(length(f)^2)} and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}. If C{v_ref} or C{p_ref} is not present zero is assumed.  
   
         The iteration is terminated if for the current approximation C{p}, flux C{v=(I+D^*D)^{-1}(D^*f-g-Qp)} and their residual  
   
         M{r=Q^*(g-Qp-v)}  
   
         the condition  
   
         M{<(Q^*Q)^{-1} r,r> <= ATOL}  
   
         holds. M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}  
   
         @param atol: absolute tolerance for the pressure  
         @type atol: non-negative C{float}  
         @param rtol: relative tolerance for the pressure  
         @type rtol: non-negative C{float}  
         @param p_ref: reference pressure. If not present zero is used. You may use physical arguments to set a resonable value for C{p_ref}, use the  
         L{getPressure} method or use  the value from a previous time step.  
         @type p_ref: scalar value on the domain (e.g. L{Data}).  
         @param v_ref: reference velocity.  If not present zero is used. You may use physical arguments to set a resonable value for C{v_ref}, use the  
         L{getFlux} method or use  the value from a previous time step.  
         @type v_ref: vector-valued on the domain (e.g. L{Data}).  
         @return: used absolute tolerance.  
         @rtype: positive C{float}  
         """  
         g=self.__g  
         if not v_ref == None:  
            f1=util.integrate(util.length(util.interpolate(g-v_ref,Function(self.domain)))**2)  
         else:  
            f1=util.integrate(util.length(util.interpolate(g))**2)  
         if not p_ref == None:  
            f2=util.integrate(util.length(util.tensor_mult(self.__permeability,util.grad(p_ref)))**2)  
         else:  
            f2=0  
         self.__ATOL= atol + rtol * util.sqrt(max(f1,f2))  
         if self.__ATOL<=0:  
            raise ValueError,"Positive tolerance (=%e) is expected."%self.__ATOL  
         return self.__ATOL  
           
     def getTolerance(self):  
         """  
         returns the current tolerance.  
43        
44          @return: used absolute tolerance.     *u_i+k_{ij}*p_{,j} = g_i*
45          @rtype: positive C{float}     *u_{i,i} = f*
46          """    
47          if self.__ATOL==None:     where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
48             raise ValueError,"no tolerance is defined."    
49          return self.__ATOL     :cvar EVAL: direct pressure gradient evaluation for flux
50       :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*
51      def solve(self,u0,p0, max_iter=100, verbose=False, show_details=False, sub_rtol=1.e-8):                 where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
52           """     :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
53           solves the problem.     """
54       EVAL="EVAL"
55           The iteration is terminated if the residual norm is less then self.getTolerance().     SIMPLE="EVAL"
56       POST="POST"
57           @param u0: initial guess for the flux. At locations in the domain marked by C{location_of_fixed_flux} the value of C{u0} is kept unchanged.     SMOOTH="SMOOTH"
58           @type u0: vector value on the domain (e.g. L{Data}).     def __init__(self, domain, useReduced=False, solver="EVAL", verbose=False, w=1.):
59           @param p0: initial guess for the pressure. At locations in the domain marked by C{location_of_fixed_pressure} the value of C{p0} is kept unchanged.        """
60           @type p0: scalar value on the domain (e.g. L{Data}).        initializes the Darcy flux problem
61           @param sub_rtol: tolerance to be used in the sub iteration. It is recommended that M{sub_rtol<rtol*5.e-3}        :param domain: domain of the problem
62           @type sub_rtol: positive-negative C{float}        :type domain: `Domain`
63           @param verbose: if set some information on iteration progress are printed        :param useReduced: uses reduced oreder on flux and pressure
64           @type verbose: C{bool}        :type useReduced: ``bool``
65           @param show_details:  if set information on the subiteration process are printed.        :param solver: solver method
66           @type show_details: C{bool}        :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST',  `DarcyFlow.SMOOTH' ]
67           @return: flux and pressure        :param verbose: if ``True`` some information on the iteration progress are printed.
68           @rtype: C{tuple} of L{Data}.        :type verbose: ``bool``
69          :param w: weighting factor for `DarcyFlow.POST` solver
70           @note: The problem is solved as a least squares form        :type w: ``float``
71          
72           M{(I+D^*D)u+Qp=D^*f+g}        """
73           M{Q^*u+Q^*Qp=Q^*g}        if not solver in [DarcyFlow.EVAL, DarcyFlow.POST,  DarcyFlow.SMOOTH ] :
74              raise ValueError,"unknown solver %d."%solver
75    
76           where M{D} is the M{div} operator and M{(Qp)_i=k_{ij}p_{,j}} for the permeability M{k_{ij}}.        self.domain=domain
77           We eliminate the flux form the problem by setting        self.solver=solver
78          self.useReduced=useReduced
79          self.verbose=verbose
80          self.l=None
81          self.w=None
82        
83          self.__pde_p=LinearSinglePDE(domain)
84          self.__pde_p.setSymmetryOn()
85          if self.useReduced: self.__pde_p.setReducedOrderOn()
86    
87          if self.solver  == self.EVAL:
88             self.__pde_v=None
89         if self.verbose: print "DarcyFlow: simple solver is used."
90    
91          elif self.solver  == self.POST:
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             self.__pde_v=LinearPDESystem(domain)
96             self.__pde_v.setSymmetryOn()
97             if self.useReduced: self.__pde_v.setReducedOrderOn()
98         self.w=w
99             self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
100    
101          elif self.solver  == self.SMOOTH:
102             self.__pde_v=LinearPDESystem(domain)
103             self.__pde_v.setSymmetryOn()
104             if self.useReduced: self.__pde_v.setReducedOrderOn()
105         if self.verbose: print "DarcyFlow: flux smoothing is used."
106         self.w=0
107    
108          self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
109          self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
110          self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
111          self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
112          self.perm_scale=1.
113        
114            
115       def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
116          """
117          assigns values to model parameters
118    
119           M{u=(I+D^*D)^{-1}(D^*f-g-Qp)} with u=u0 on location_of_fixed_flux        :param f: volumetic sources/sinks
120          :type f: scalar value on the domain (e.g. `escript.Data`)
121          :param g: flux sources/sinks
122          :type g: vector values on the domain (e.g. `escript.Data`)
123          :param location_of_fixed_pressure: mask for locations where pressure is fixed
124          :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
125          :param location_of_fixed_flux:  mask for locations where flux is fixed.
126          :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
127          :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
128          :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
129    
130          :note: the values of parameters which are not set by calling ``setValue`` are not altered.
131          :note: at any point on the boundary of the domain the pressure
132                 (``location_of_fixed_pressure`` >0) or the normal component of the
133                 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
134                 is along the *x_i* axis.
135    
136           form the first equation. Inserted into the second equation we get        """
137          if location_of_fixed_pressure!=None:
138               self.location_of_fixed_pressure=util.wherePositive(location_of_fixed_pressure)
139               self.__pde_p.setValue(q=self.location_of_fixed_pressure)
140          if location_of_fixed_flux!=None:
141              self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
142              if not self.__pde_v == None: self.__pde_v.setValue(q=self.location_of_fixed_flux)
143                
144          if permeability!=None:
145        
146         perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
147             self.perm_scale=util.Lsup(util.length(perm))
148             perm=perm*(1./self.perm_scale)
149            
150         if perm.getRank()==0:
151    
152           M{Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g))} with p=p0  on location_of_fixed_pressure          perm_inv=(1./perm)
153            perm_inv=perm_inv*util.kronecker(self.domain.getDim())
154            perm=perm*util.kronecker(self.domain.getDim())
155            
156            
157         elif perm.getRank()==2:
158            perm_inv=util.inverse(perm)
159         else:
160            raise ValueError,"illegal rank of permeability."
161                    
162           which is solved using the PCG method (precondition is M{Q^*Q}). In each iteration step       self.__permeability=perm
163           PDEs with operator M{I+D^*D} and with M{Q^*Q} needs to be solved using a sub iteration scheme.       self.__permeability_inv=perm_inv
164           """      
165           self.verbose=verbose           #====================
166           self.show_details= show_details and self.verbose       self.__pde_p.setValue(A=self.__permeability)
167           self.__pde_v.setTolerance(sub_rtol)           if self.solver  == self.EVAL:
168           self.__pde_p.setTolerance(sub_rtol)                pass # no extra work required
169           ATOL=self.getTolerance()           elif self.solver  == self.POST:
170           if self.verbose: print "DarcyFlux: absolute tolerance = %e"%ATOL          k=util.kronecker(self.domain.getDim())
171           #########################################################################################################################          self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
172           #          self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
173           #   we solve:           elif self.solver  == self.SMOOTH:
174           #            self.__pde_v.setValue(D=self.__permeability_inv)
175           #      Q^*(I-(I+D^*D)^{-1})Q dp =  Q^* (g-u0-Qp0 - (I+D^*D)^{-1} ( D^*(f-Du0)+g-u0-Qp0) )  
176           #        if g != None:
177           #   residual is      g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
178           #      if g.isEmpty():
179           #    r=  Q^* (g-u0-Qp0 - (I+D^*D)^{-1} ( D^*(f-Du0)+g-u0-Qp0) - Q dp +(I+D^*D)^{-1})Q dp ) = Q^* (g - Qp - v)            g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
180           #      else:
181           #        with v = (I+D^*D)^{-1} (D^*f+g-Qp) including BC          if not g.getShape()==(self.domain.getDim(),): raise ValueError,"illegal shape of g"
182           #      self.__g=g
183           #    we use (g - Qp, v) to represent the residual. not that        if f !=None:
184           #       f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
185           #    dr(dp)=( -Q(dp), dv) with dv = - (I+D^*D)^{-1} Q(dp)       if f.isEmpty():      
186           #            f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
187           #   while the initial residual is       else:
188           #           if f.getRank()>0: raise ValueError,"illegal rank of f."
189           #      r0=( g - Qp0, v00) with v00=(I+D^*D)^{-1} (D^*f+g-Qp0) including BC       self.__f=f
          #    
          d0=self.__g-util.tensor_mult(self.__permeability,util.grad(p0))  
          self.__pde_v.setValue(Y=d0, X=self.__f*util.kronecker(self.domain), r=u0)  
          v00=self.__pde_v.getSolution(verbose=show_details)  
          if self.verbose: print "DarcyFlux: range of initial flux = ",util.inf(v00), util.sup(v00)  
          self.__pde_v.setValue(r=Data())  
          # start CG  
          r=ArithmeticTuple(d0, v00)  
          p,r=PCG(r,self.__Aprod_PCG,p0,self.__Msolve_PCG,self.__inner_PCG,atol=ATOL, rtol=0.,iter_max=max_iter, verbose=self.verbose)  
          return r[1],p  
   
     def __Aprod_PCG(self,dp):  
           if self.show_details: print "DarcyFlux: Applying operator"  
           #  -dr(dp) = (Qdp,du) where du = (I+D^*D)^{-1} (Qdp)  
           mQdp=util.tensor_mult(self.__permeability,util.grad(dp))  
           self.__pde_v.setValue(Y=mQdp,X=Data(), r=Data())  
           du=self.__pde_v.getSolution(verbose=self.show_details)  
           return ArithmeticTuple(mQdp,du)  
   
     def __inner_PCG(self,p,r):  
          a=util.tensor_mult(self.__permeability,util.grad(p))  
          f0=util.integrate(util.inner(a,r[0]))  
          f1=util.integrate(util.inner(a,r[1]))  
          # print "__inner_PCG:",f0,f1,"->",f0-f1  
          return f0-f1  
   
     def __Msolve_PCG(self,r):  
           if self.show_details: print "DarcyFlux: Applying preconditioner"  
           self.__pde_p.setValue(X=util.transposed_tensor_mult(self.__permeability,r[0]-r[1]), r=Data())  
           return self.__pde_p.getSolution(verbose=self.show_details)  
190    
191  class StokesProblemCartesian(HomogeneousSaddlePointProblem):     def getSolverOptionsFlux(self):
192          """
193          Returns the solver options used to solve the flux problems
194          :return: `SolverOptions`
195          """
196          if self.__pde_v == None:
197              return None
198          else:
199              return self.__pde_v.getSolverOptions()
200          
201       def setSolverOptionsFlux(self, options=None):
202          """
203          Sets the solver options used to solve the flux problems
204          If ``options`` is not present, the options are reset to default
205          :param options: `SolverOptions`
206          """
207          if not self.__pde_v == None:
208              self.__pde_v.setSolverOptions(options)
209        
210       def getSolverOptionsPressure(self):
211          """
212          Returns the solver options used to solve the pressure problems
213          :return: `SolverOptions`
214          """
215          return self.__pde_p.getSolverOptions()
216          
217       def setSolverOptionsPressure(self, options=None):
218          """
219          Sets the solver options used to solve the pressure problems
220          If ``options`` is not present, the options are reset to default
221          
222          :param options: `SolverOptions`
223          :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
224        """        """
225        solves        return self.__pde_p.setSolverOptions(options)
226          
227       def solve(self, u0, p0):
228          """
229          solves the problem.
230          
231          :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.
232          :type u0: vector value on the domain (e.g. `escript.Data`).
233          :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.
234          :type p0: scalar value on the domain (e.g. `escript.Data`).
235          :return: flux and pressure
236          :rtype: ``tuple`` of `escript.Data`.
237    
238          """
239          self.__pde_p.setValue(X=self.__g * 1./self.perm_scale,
240                                Y=self.__f,
241                                y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux),
242                                r=p0)
243          p=self.__pde_p.getSolution()
244          u = self.getFlux(p, u0)
245          return u,p
246          
247       def getFlux(self,p, u0=None):
248            """
249            returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
250            on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
251            Notice that ``g`` is used, see `setValue`.
252    
253            :param p: pressure.
254            :type p: scalar value on the domain (e.g. `escript.Data`).
255            :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
256            :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
257            :return: flux
258            :rtype: `escript.Data`
259            """
260            if self.solver  == self.EVAL:
261               u = self.__g-self.perm_scale * util.tensor_mult(self.__permeability,util.grad(p))
262            elif self.solver  == self.POST or self.solver  == self.SMOOTH:
263                self.__pde_v.setValue(Y=util.tensor_mult(self.__permeability_inv,self.__g * 1./self.perm_scale)-util.grad(p))
264                if u0 == None:
265               self.__pde_v.setValue(r=escript.Data())
266            else:
267               self.__pde_v.setValue(r=u0)
268                u= self.__pde_v.getSolution() * self.perm_scale
269        return u
270          
271    class StokesProblemCartesian(HomogeneousSaddlePointProblem):
272         """
273         solves
274    
275            -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}            -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
276                  u_{i,i}=0                  u_{i,i}=0
# Line 333  class StokesProblemCartesian(Homogeneous Line 278  class StokesProblemCartesian(Homogeneous
278            u=0 where  fixed_u_mask>0            u=0 where  fixed_u_mask>0
279            eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j            eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
280    
281        if surface_stress is not given 0 is assumed.       if surface_stress is not given 0 is assumed.
282    
283        typical usage:       typical usage:
284    
285              sp=StokesProblemCartesian(domain)              sp=StokesProblemCartesian(domain)
286              sp.setTolerance()              sp.setTolerance()
287              sp.initialize(...)              sp.initialize(...)
288              v,p=sp.solve(v0,p0)              v,p=sp.solve(v0,p0)
289        """              sp.setStokesEquation(...) # new values for some parameters
290        def __init__(self,domain,**kwargs):              v1,p1=sp.solve(v,p)
291         """
292         def __init__(self,domain,**kwargs):
293           """           """
294           initialize the Stokes Problem           initialize the Stokes Problem
295    
296           @param domain: domain of the problem. The approximation order needs to be two.           The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be
297           @type domain: L{Domain}           LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
298           @warning: The apprximation order needs to be two otherwise you may see oscilations in the pressure.           with macro elements for the pressure.
299    
300             :param domain: domain of the problem.
301             :type domain: `Domain`
302           """           """
303           HomogeneousSaddlePointProblem.__init__(self,**kwargs)           HomogeneousSaddlePointProblem.__init__(self,**kwargs)
304           self.domain=domain           self.domain=domain
305           self.vol=util.integrate(1.,Function(self.domain))           self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
306           self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())           self.__pde_v.setSymmetryOn()
307           self.__pde_u.setSymmetryOn()      
          # self.__pde_u.setSolverMethod(self.__pde_u.DIRECT)  
          # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.RILU)  
               
308           self.__pde_prec=LinearPDE(domain)           self.__pde_prec=LinearPDE(domain)
309           self.__pde_prec.setReducedOrderOn()           self.__pde_prec.setReducedOrderOn()
          # self.__pde_prec.setSolverMethod(self.__pde_prec.LUMPING)  
310           self.__pde_prec.setSymmetryOn()           self.__pde_prec.setSymmetryOn()
311    
312           self.__pde_proj=LinearPDE(domain)           self.__pde_proj=LinearPDE(domain)
313           self.__pde_proj.setReducedOrderOn()           self.__pde_proj.setReducedOrderOn()
314         self.__pde_proj.setValue(D=1)
315           self.__pde_proj.setSymmetryOn()           self.__pde_proj.setSymmetryOn()
          self.__pde_proj.setValue(D=1.)  
316    
317        def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data(),stress=Data()):       def getSolverOptionsVelocity(self):
318             """
319         returns the solver options used  solve the equation for velocity.
320        
321         :rtype: `SolverOptions`
322         """
323         return self.__pde_v.getSolverOptions()
324         def setSolverOptionsVelocity(self, options=None):
325             """
326         set the solver options for solving the equation for velocity.
327        
328         :param options: new solver  options
329         :type options: `SolverOptions`
330         """
331             self.__pde_v.setSolverOptions(options)
332         def getSolverOptionsPressure(self):
333             """
334         returns the solver options used  solve the equation for pressure.
335         :rtype: `SolverOptions`
336         """
337         return self.__pde_prec.getSolverOptions()
338         def setSolverOptionsPressure(self, options=None):
339             """
340         set the solver options for solving the equation for pressure.
341         :param options: new solver  options
342         :type options: `SolverOptions`
343         """
344         self.__pde_prec.setSolverOptions(options)
345    
346         def setSolverOptionsDiv(self, options=None):
347             """
348         set the solver options for solving the equation to project the divergence of
349         the velocity onto the function space of presure.
350        
351         :param options: new solver options
352         :type options: `SolverOptions`
353         """
354         self.__pde_proj.setSolverOptions(options)
355         def getSolverOptionsDiv(self):
356             """
357         returns the solver options for solving the equation to project the divergence of
358         the velocity onto the function space of presure.
359        
360         :rtype: `SolverOptions`
361         """
362         return self.__pde_proj.getSolverOptions()
363    
364         def updateStokesEquation(self, v, p):
365             """
366             updates the Stokes equation to consider dependencies from ``v`` and ``p``
367             :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
368             """
369             pass
370         def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
371            """
372            assigns new values to the model parameters.
373    
374            :param f: external force
375            :type f: `Vector` object in `FunctionSpace` `Function` or similar
376            :param fixed_u_mask: mask of locations with fixed velocity.
377            :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
378            :param eta: viscosity
379            :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
380            :param surface_stress: normal surface stress
381            :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
382            :param stress: initial stress
383        :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
384            """
385            if eta !=None:
386                k=util.kronecker(self.domain.getDim())
387                kk=util.outer(k,k)
388                self.eta=util.interpolate(eta, escript.Function(self.domain))
389            self.__pde_prec.setValue(D=1/self.eta)
390                self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
391            if restoration_factor!=None:
392                n=self.domain.getNormal()
393                self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
394            if fixed_u_mask!=None:
395                self.__pde_v.setValue(q=fixed_u_mask)
396            if f!=None: self.__f=f
397            if surface_stress!=None: self.__surface_stress=surface_stress
398            if stress!=None: self.__stress=stress
399    
400         def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
401          """          """
402          assigns values to the model parameters          assigns values to the model parameters
403    
404          @param f: external force          :param f: external force
405          @type f: L{Vector} object in L{FunctionSpace} L{Function} or similar          :type f: `Vector` object in `FunctionSpace` `Function` or similar
406          @param fixed_u_mask: mask of locations with fixed velocity.          :param fixed_u_mask: mask of locations with fixed velocity.
407          @type fixed_u_mask: L{Vector} object on L{FunctionSpace} L{Solution} or similar          :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
408          @param eta: viscosity          :param eta: viscosity
409          @type eta: L{Scalar} object on L{FunctionSpace} L{Function} or similar          :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
410          @param surface_stress: normal surface stress          :param surface_stress: normal surface stress
411          @type eta: L{Vector} object on L{FunctionSpace} L{FunctionOnBoundary} or similar          :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
412          @param stress: initial stress          :param stress: initial stress
413      @type stress: L{Tensor} object on L{FunctionSpace} L{Function} or similar      :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
         @note: All values needs to be set.  
   
414          """          """
415          self.eta=eta          self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
         A =self.__pde_u.createCoefficient("A")  
     self.__pde_u.setValue(A=Data())  
         for i in range(self.domain.getDim()):  
         for j in range(self.domain.getDim()):  
             A[i,j,j,i] += 1.  
             A[i,j,i,j] += 1.  
     self.__pde_prec.setValue(D=1/self.eta)  
         self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress)  
         self.__stress=stress  
416    
417        def B(self,v):       def Bv(self,v,tol):
418          """           """
419          returns div(v)           returns inner product of element p and div(v)
         @rtype: equal to the type of p  
420    
421          @note: boundary conditions on p should be zero!           :param v: a residual
422          """           :return: inner product of element p and div(v)
423          if self.show_details: print "apply divergence:"           :rtype: ``float``
424          self.__pde_proj.setValue(Y=-util.div(v))           """
425          self.__pde_proj.setTolerance(self.getSubProblemTolerance())           self.__pde_proj.setValue(Y=-util.div(v))
426          return self.__pde_proj.getSolution(verbose=self.show_details)       self.getSolverOptionsDiv().setTolerance(tol)
427         self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
428             out=self.__pde_proj.getSolution()
429             return out
430    
431        def inner_pBv(self,p,Bv):       def inner_pBv(self,p,Bv):
432           """           """
433           returns inner product of element p and Bv  (overwrite)           returns inner product of element p and Bv=-div(v)
           
          @type p: equal to the type of p  
          @type Bv: equal to the type of result of operator B  
          @rtype: C{float}  
434    
435           @rtype: equal to the type of p           :param p: a pressure increment
436             :param Bv: a residual
437             :return: inner product of element p and Bv=-div(v)
438             :rtype: ``float``
439           """           """
440           s0=util.interpolate(p,Function(self.domain))           return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
          s1=util.interpolate(Bv,Function(self.domain))  
          return util.integrate(s0*s1)  
441    
442        def inner_p(self,p0,p1):       def inner_p(self,p0,p1):
443           """           """
444           returns inner product of element p0 and p1  (overwrite)           Returns inner product of p0 and p1
           
          @type p0: equal to the type of p  
          @type p1: equal to the type of p  
          @rtype: C{float}  
445    
446           @rtype: equal to the type of p           :param p0: a pressure
447             :param p1: a pressure
448             :return: inner product of p0 and p1
449             :rtype: ``float``
450           """           """
451           s0=util.interpolate(p0/self.eta,Function(self.domain))           s0=util.interpolate(p0, escript.Function(self.domain))
452           s1=util.interpolate(p1/self.eta,Function(self.domain))           s1=util.interpolate(p1, escript.Function(self.domain))
453           return util.integrate(s0*s1)           return util.integrate(s0*s1)
454    
455        def inner_v(self,v0,v1):       def norm_v(self,v):
456           """           """
457           returns inner product of two element v0 and v1  (overwrite)           returns the norm of v
           
          @type v0: equal to the type of v  
          @type v1: equal to the type of v  
          @rtype: C{float}  
458    
459           @rtype: equal to the type of v           :param v: a velovity
460             :return: norm of v
461             :rtype: non-negative ``float``
462           """           """
463       gv0=util.grad(v0)           return util.sqrt(util.integrate(util.length(util.grad(v))**2))
464       gv1=util.grad(v1)  
          return util.integrate(util.inner(gv0,gv1))  
465    
466        def solve_A(self,u,p):       def getDV(self, p, v, tol):
467           """           """
468           solves Av=f-Au-B^*p (v=0 on fixed_u_mask)           return the value for v for a given p
469    
470             :param p: a pressure
471             :param v: a initial guess for the value v to return.
472             :return: dv given as *Adv=(f-Av-B^*p)*
473           """           """
474           if self.show_details: print "solve for velocity:"           self.updateStokesEquation(v,p)
475           self.__pde_u.setTolerance(self.getSubProblemTolerance())           self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
476         self.getSolverOptionsVelocity().setTolerance(tol)
477         self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
478           if self.__stress.isEmpty():           if self.__stress.isEmpty():
479              self.__pde_u.setValue(X=-2*self.eta*util.symmetric(util.grad(u))+p*util.kronecker(self.domain))              self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
480           else:           else:
481              self.__pde_u.setValue(X=self.__stress-2*self.eta*util.symmetric(util.grad(u))+p*util.kronecker(self.domain))              self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
482           out=self.__pde_u.getSolution(verbose=self.show_details)           out=self.__pde_v.getSolution()
483           return  out           return  out
484    
485        def solve_prec(self,p):       def norm_Bv(self,Bv):
486           if self.show_details: print "apply preconditioner:"          """
487           self.__pde_prec.setTolerance(self.getSubProblemTolerance())          Returns Bv (overwrite).
488           self.__pde_prec.setValue(Y=p)  
489           q=self.__pde_prec.getSolution(verbose=self.show_details)          :rtype: equal to the type of p
490           return q          :note: boundary conditions on p should be zero!
491            """
492            return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
493    
494         def solve_AinvBt(self,p, tol):
495             """
496             Solves *Av=B^*p* with accuracy `tol`
497    
498             :param p: a pressure increment
499             :return: the solution of *Av=B^*p*
500             :note: boundary conditions on v should be zero!
501             """
502             self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
503             out=self.__pde_v.getSolution()
504             return  out
505    
506         def solve_prec(self,Bv, tol):
507             """
508             applies preconditioner for for *BA^{-1}B^** to *Bv*
509             with accuracy `self.getSubProblemTolerance()`
510    
511             :param Bv: velocity increment
512             :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
513             :note: boundary conditions on p are zero.
514             """
515             self.__pde_prec.setValue(Y=Bv)
516         self.getSolverOptionsPressure().setTolerance(tol)
517         self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
518             out=self.__pde_prec.getSolution()
519             return out

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