/[escript]/trunk/escript/py_src/flows.py
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Annotation of /trunk/escript/py_src/flows.py

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Revision 1554 - (hide annotations)
Fri May 9 02:50:49 2008 UTC (11 years, 4 months ago) by artak
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1 gross 1414 # $Id:$
2     #
3     #######################################################
4     #
5     # Copyright 2008 by University of Queensland
6     #
7     # http://esscc.uq.edu.au
8     # Primary Business: Queensland, Australia
9     # Licensed under the Open Software License version 3.0
10     # http://www.opensource.org/licenses/osl-3.0.php
11     #
12     #######################################################
13     #
14    
15     """
16     Some models for flow
17    
18     @var __author__: name of author
19     @var __copyright__: copyrights
20     @var __license__: licence agreement
21     @var __url__: url entry point on documentation
22     @var __version__: version
23     @var __date__: date of the version
24     """
25    
26     __author__="Lutz Gross, l.gross@uq.edu.au"
27     __copyright__=""" Copyright (c) 2008 by ACcESS MNRF
28     http://www.access.edu.au
29     Primary Business: Queensland, Australia"""
30     __license__="""Licensed under the Open Software License version 3.0
31     http://www.opensource.org/licenses/osl-3.0.php"""
32     __url__="http://www.iservo.edu.au/esys"
33     __version__="$Revision:$"
34     __date__="$Date:$"
35    
36     from escript import *
37     import util
38     from linearPDEs import LinearPDE
39 artak 1550 from pdetools import HomogeneousSaddlePointProblem,Projector
40 gross 1414
41     class StokesProblemCartesian(HomogeneousSaddlePointProblem):
42     """
43     solves
44    
45     -(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i
46     u_{i,i}=0
47    
48     u=0 where fixed_u_mask>0
49     eta*(u_{i,j}+u_{j,i})*n_j=surface_stress
50    
51     if surface_stress is not give 0 is assumed.
52    
53     typical usage:
54    
55     sp=StokesProblemCartesian(domain)
56     sp.setTolerance()
57     sp.initialize(...)
58     v,p=sp.solve(v0,p0)
59     """
60     def __init__(self,domain,**kwargs):
61     HomogeneousSaddlePointProblem.__init__(self,**kwargs)
62     self.domain=domain
63     self.vol=util.integrate(1.,Function(self.domain))
64     self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
65     self.__pde_u.setSymmetryOn()
66 artak 1551 self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0)
67 gross 1414
68     self.__pde_prec=LinearPDE(domain)
69     self.__pde_prec.setReducedOrderOn()
70     self.__pde_prec.setSymmetryOn()
71    
72     self.__pde_proj=LinearPDE(domain)
73     self.__pde_proj.setReducedOrderOn()
74     self.__pde_proj.setSymmetryOn()
75     self.__pde_proj.setValue(D=1.)
76    
77     def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()):
78     self.eta=eta
79     A =self.__pde_u.createCoefficientOfGeneralPDE("A")
80     self.__pde_u.setValue(A=Data())
81     for i in range(self.domain.getDim()):
82     for j in range(self.domain.getDim()):
83     A[i,j,j,i] += 1.
84     A[i,j,i,j] += 1.
85 artak 1554 self.__pde_prec.setValue(D=1/self.eta)
86 gross 1414 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress)
87    
88     def B(self,arg):
89     d=util.div(arg)
90     self.__pde_proj.setValue(Y=d)
91     self.__pde_proj.setTolerance(self.getSubProblemTolerance())
92     return self.__pde_proj.getSolution(verbose=self.show_details)
93    
94     def inner(self,p0,p1):
95     s0=util.interpolate(p0,Function(self.domain))
96     s1=util.interpolate(p1,Function(self.domain))
97     return util.integrate(s0*s1)
98    
99 artak 1550 def inner_a(self,a0,a1):
100     p0=util.interpolate(a0[1],Function(self.domain))
101     p1=util.interpolate(a1[1],Function(self.domain))
102     alfa=(1/self.vol)*util.integrate(p0)
103     beta=(1/self.vol)*util.integrate(p1)
104     v0=util.grad(a0[0])
105     v1=util.grad(a1[0])
106     #print "NORM",alfa,beta,util.integrate((p0-alfa)*(p1-beta))+util.integrate(util.inner(v0,v1))
107     return util.integrate((p0-alfa)*(p1-beta)+((1/self.eta)**2)*util.inner(v0,v1))
108    
109    
110 gross 1414 def getStress(self,u):
111     mg=util.grad(u)
112     return 2.*self.eta*util.symmetric(mg)
113    
114     def solve_A(self,u,p):
115     """
116     solves Av=f-Au-B^*p (v=0 on fixed_u_mask)
117     """
118     self.__pde_u.setTolerance(self.getSubProblemTolerance())
119 gross 1470 self.__pde_u.setValue(X=-self.getStress(u)-p*util.kronecker(self.domain))
120 gross 1414 return self.__pde_u.getSolution(verbose=self.show_details)
121    
122 artak 1550
123 gross 1414 def solve_prec(self,p):
124 artak 1550 #proj=Projector(domain=self.domain, reduce = True, fast=False)
125 gross 1414 self.__pde_prec.setTolerance(self.getSubProblemTolerance())
126     self.__pde_prec.setValue(Y=p)
127     q=self.__pde_prec.getSolution(verbose=self.show_details)
128 artak 1554 return q
129    
130     def solve_prec1(self,p):
131     #proj=Projector(domain=self.domain, reduce = True, fast=False)
132     self.__pde_prec.setTolerance(self.getSubProblemTolerance())
133     self.__pde_prec.setValue(Y=p)
134     q=self.__pde_prec.getSolution(verbose=self.show_details)
135 artak 1550 q0=util.interpolate(q,Function(self.domain))
136     q-=(1/self.vol)*util.integrate(q0)
137 gross 1414 return q
138 artak 1550
139 gross 1414 def stoppingcriterium(self,Bv,v,p):
140     n_r=util.sqrt(self.inner(Bv,Bv))
141 gross 1552 n_v=util.sqrt(util.integrate(util.length(util.grad(v))**2))
142     if self.verbose: print "PCG step %s: L2(div(v)) = %s, L2(grad(v))=%s"%(self.iter,n_r,n_v)
143     if self.iter == 0: self.__n_v=n_v;
144     self.__n_v, n_v_old =n_v, self.__n_v
145 gross 1414 self.iter+=1
146 gross 1552 print abs(n_v_old-self.__n_v), n_v, self.getTolerance()
147     if self.iter>1 and n_r <= n_v*self.getTolerance() and abs(n_v_old-self.__n_v) <= n_v * self.getTolerance():
148 gross 1414 if self.verbose: print "PCG terminated after %s steps."%self.iter
149     return True
150     else:
151     return False
152 artak 1519 def stoppingcriterium2(self,norm_r,norm_b,solver='GMRES',TOL=None):
153     if TOL==None:
154     TOL=self.getTolerance()
155     if self.verbose: print "%s step %s: L2(r) = %s, L2(b)*TOL=%s"%(solver,self.iter,norm_r,norm_b*TOL)
156 artak 1465 self.iter+=1
157 artak 1519
158     if norm_r <= norm_b*TOL:
159 artak 1517 if self.verbose: print "%s terminated after %s steps."%(solver,self.iter)
160 artak 1465 return True
161     else:
162     return False
163 artak 1481
164 artak 1517

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