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# $Id:$ |
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# |
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####################################################### |
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# |
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# Copyright 2008 by University of Queensland |
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# |
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# http://esscc.uq.edu.au |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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####################################################### |
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# |
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|
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""" |
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Some models for flow |
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|
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@var __author__: name of author |
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@var __copyright__: copyrights |
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@var __license__: licence agreement |
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@var __url__: url entry point on documentation |
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@var __version__: version |
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@var __date__: date of the version |
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""" |
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|
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__author__="Lutz Gross, l.gross@uq.edu.au" |
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__copyright__=""" Copyright (c) 2008 by ACcESS MNRF |
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http://www.access.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="http://www.iservo.edu.au/esys" |
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__version__="$Revision:$" |
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__date__="$Date:$" |
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|
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from escript import * |
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import util |
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from linearPDEs import LinearPDE |
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from pdetools import HomogeneousSaddlePointProblem,Projector |
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|
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class StokesProblemCartesian_DC(HomogeneousSaddlePointProblem): |
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""" |
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solves |
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|
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-(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i |
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u_{i,i}=0 |
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|
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u=0 where fixed_u_mask>0 |
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eta*(u_{i,j}+u_{j,i})*n_j=surface_stress |
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|
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if surface_stress is not give 0 is assumed. |
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|
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typical usage: |
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|
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sp=StokesProblemCartesian(domain) |
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sp.setTolerance() |
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sp.initialize(...) |
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v,p=sp.solve(v0,p0) |
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""" |
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def __init__(self,domain,**kwargs): |
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HomogeneousSaddlePointProblem.__init__(self,**kwargs) |
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self.domain=domain |
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self.vol=util.integrate(1.,Function(self.domain)) |
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self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim()) |
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self.__pde_u.setSymmetryOn() |
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# self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0) |
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|
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# self.__pde_proj=LinearPDE(domain,numEquations=1,numSolutions=1) |
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# self.__pde_proj.setReducedOrderOn() |
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# self.__pde_proj.setSymmetryOn() |
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# self.__pde_proj.setSolverMethod(LinearPDE.LUMPING) |
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|
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def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()): |
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self.eta=eta |
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A =self.__pde_u.createCoefficientOfGeneralPDE("A") |
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self.__pde_u.setValue(A=Data()) |
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for i in range(self.domain.getDim()): |
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for j in range(self.domain.getDim()): |
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A[i,j,j,i] += 1. |
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A[i,j,i,j] += 1. |
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# self.__inv_eta=util.interpolate(self.eta,ReducedFunction(self.domain)) |
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self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress) |
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|
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# self.__pde_proj.setValue(D=1/eta) |
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# self.__pde_proj.setValue(Y=1.) |
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# self.__inv_eta=util.interpolate(self.__pde_proj.getSolution(),ReducedFunction(self.domain)) |
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self.__inv_eta=util.interpolate(self.eta,ReducedFunction(self.domain)) |
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|
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def B(self,arg): |
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a=util.div(arg, ReducedFunction(self.domain)) |
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return a-util.integrate(a)/self.vol |
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|
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def inner(self,p0,p1): |
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return util.integrate(p0*p1) |
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|
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def getStress(self,u): |
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mg=util.grad(u) |
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return 2.*self.eta*util.symmetric(mg) |
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def getEtaEffective(self): |
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return self.eta |
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|
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def solve_A(self,u,p): |
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""" |
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solves Av=f-Au-B^*p (v=0 on fixed_u_mask) |
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""" |
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self.__pde_u.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_u.setValue(X=-self.getStress(u),X_reduced=-p*util.kronecker(self.domain)) |
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return self.__pde_u.getSolution(verbose=self.show_details) |
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|
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|
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def solve_prec(self,p): |
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a=self.__inv_eta*p |
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return a-util.integrate(a)/self.vol |
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|
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def stoppingcriterium(self,Bv,v,p): |
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n_r=util.sqrt(self.inner(Bv,Bv)) |
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n_v=util.sqrt(util.integrate(util.length(util.grad(v))**2)) |
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if self.verbose: print "PCG step %s: L2(div(v)) = %s, L2(grad(v))=%s"%(self.iter,n_r,n_v) , util.Lsup(v) |
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if self.iter == 0: self.__n_v=n_v; |
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self.__n_v, n_v_old =n_v, self.__n_v |
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self.iter+=1 |
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if self.iter>1 and n_r <= n_v*self.getTolerance() and abs(n_v_old-self.__n_v) <= n_v * self.getTolerance(): |
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if self.verbose: print "PCG terminated after %s steps."%self.iter |
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return True |
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else: |
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return False |
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|
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|
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class StokesProblemCartesian(HomogeneousSaddlePointProblem): |
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""" |
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solves |
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|
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-(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i |
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u_{i,i}=0 |
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|
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u=0 where fixed_u_mask>0 |
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eta*(u_{i,j}+u_{j,i})*n_j=surface_stress |
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|
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if surface_stress is not give 0 is assumed. |
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|
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typical usage: |
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|
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sp=StokesProblemCartesian(domain) |
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sp.setTolerance() |
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sp.initialize(...) |
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v,p=sp.solve(v0,p0) |
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""" |
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def __init__(self,domain,**kwargs): |
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HomogeneousSaddlePointProblem.__init__(self,**kwargs) |
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self.domain=domain |
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self.vol=util.integrate(1.,Function(self.domain)) |
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self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim()) |
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self.__pde_u.setSymmetryOn() |
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# self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0) |
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|
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self.__pde_prec=LinearPDE(domain) |
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self.__pde_prec.setReducedOrderOn() |
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self.__pde_prec.setSymmetryOn() |
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|
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self.__pde_proj=LinearPDE(domain) |
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self.__pde_proj.setReducedOrderOn() |
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self.__pde_proj.setSymmetryOn() |
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self.__pde_proj.setValue(D=1.) |
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|
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def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()): |
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self.eta=eta |
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A =self.__pde_u.createCoefficientOfGeneralPDE("A") |
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self.__pde_u.setValue(A=Data()) |
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for i in range(self.domain.getDim()): |
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for j in range(self.domain.getDim()): |
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A[i,j,j,i] += 1. |
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A[i,j,i,j] += 1. |
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self.__pde_prec.setValue(D=1/self.eta) |
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self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress) |
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|
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def B(self,arg): |
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d=util.div(arg) |
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self.__pde_proj.setValue(Y=d) |
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self.__pde_proj.setTolerance(self.getSubProblemTolerance()) |
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return self.__pde_proj.getSolution(verbose=self.show_details) |
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|
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def inner(self,p0,p1): |
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s0=util.interpolate(p0,Function(self.domain)) |
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s1=util.interpolate(p1,Function(self.domain)) |
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return util.integrate(s0*s1) |
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|
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def inner_a(self,a0,a1): |
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p0=util.interpolate(a0[1],Function(self.domain)) |
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p1=util.interpolate(a1[1],Function(self.domain)) |
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alfa=(1/self.vol)*util.integrate(p0) |
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beta=(1/self.vol)*util.integrate(p1) |
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v0=util.grad(a0[0]) |
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v1=util.grad(a1[0]) |
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return util.integrate((p0-alfa)*(p1-beta)+((1/self.eta)**2)*util.inner(v0,v1)) |
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|
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|
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def getStress(self,u): |
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mg=util.grad(u) |
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return 2.*self.eta*util.symmetric(mg) |
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def getEtaEffective(self): |
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return self.eta |
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|
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def solve_A(self,u,p): |
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""" |
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solves Av=f-Au-B^*p (v=0 on fixed_u_mask) |
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""" |
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self.__pde_u.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_u.setValue(X=-self.getStress(u)-p*util.kronecker(self.domain)) |
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return self.__pde_u.getSolution(verbose=self.show_details) |
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|
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|
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def solve_prec(self,p): |
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#proj=Projector(domain=self.domain, reduce = True, fast=False) |
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self.__pde_prec.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_prec.setValue(Y=p) |
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q=self.__pde_prec.getSolution(verbose=self.show_details) |
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return q |
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|
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def solve_prec1(self,p): |
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#proj=Projector(domain=self.domain, reduce = True, fast=False) |
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self.__pde_prec.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_prec.setValue(Y=p) |
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q=self.__pde_prec.getSolution(verbose=self.show_details) |
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q0=util.interpolate(q,Function(self.domain)) |
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print util.inf(q*q0),util.sup(q*q0) |
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q-=(1/self.vol)*util.integrate(q0) |
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print util.inf(q*q0),util.sup(q*q0) |
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return q |
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|
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def stoppingcriterium(self,Bv,v,p): |
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n_r=util.sqrt(self.inner(Bv,Bv)) |
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n_v=util.sqrt(util.integrate(util.length(util.grad(v))**2)) |
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if self.verbose: print "PCG step %s: L2(div(v)) = %s, L2(grad(v))=%s"%(self.iter,n_r,n_v) |
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if self.iter == 0: self.__n_v=n_v; |
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self.__n_v, n_v_old =n_v, self.__n_v |
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self.iter+=1 |
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if self.iter>1 and n_r <= n_v*self.getTolerance() and abs(n_v_old-self.__n_v) <= n_v * self.getTolerance(): |
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if self.verbose: print "PCG terminated after %s steps."%self.iter |
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return True |
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else: |
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return False |
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def stoppingcriterium2(self,norm_r,norm_b,solver='GMRES',TOL=None): |
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if TOL==None: |
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TOL=self.getTolerance() |
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if self.verbose: print "%s step %s: L2(r) = %s, L2(b)*TOL=%s"%(solver,self.iter,norm_r,norm_b*TOL) |
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self.iter+=1 |
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|
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if norm_r <= norm_b*TOL: |
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if self.verbose: print "%s terminated after %s steps."%(solver,self.iter) |
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return True |
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else: |
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return False |
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|
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