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

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Revision 1661 - (show annotations)
Mon Jul 21 22:08:27 2008 UTC (11 years, 2 months ago) by gross
File MIME type: text/x-python
File size: 9259 byte(s)
some improvements on level set
1 # $Id:$
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 from pdetools import HomogeneousSaddlePointProblem,Projector
40
41 class StokesProblemCartesian_DC(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 # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0)
67
68 # self.__pde_proj=LinearPDE(domain,numEquations=1,numSolutions=1)
69 # self.__pde_proj.setReducedOrderOn()
70 # self.__pde_proj.setSymmetryOn()
71 # self.__pde_proj.setSolverMethod(LinearPDE.LUMPING)
72
73 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()):
74 self.eta=eta
75 A =self.__pde_u.createCoefficientOfGeneralPDE("A")
76 self.__pde_u.setValue(A=Data())
77 for i in range(self.domain.getDim()):
78 for j in range(self.domain.getDim()):
79 A[i,j,j,i] += 1.
80 A[i,j,i,j] += 1.
81 # self.__inv_eta=util.interpolate(self.eta,ReducedFunction(self.domain))
82 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress)
83
84 # self.__pde_proj.setValue(D=1/eta)
85 # self.__pde_proj.setValue(Y=1.)
86 # self.__inv_eta=util.interpolate(self.__pde_proj.getSolution(),ReducedFunction(self.domain))
87 self.__inv_eta=util.interpolate(self.eta,ReducedFunction(self.domain))
88
89 def B(self,arg):
90 a=util.div(arg, ReducedFunction(self.domain))
91 return a-util.integrate(a)/self.vol
92
93 def inner(self,p0,p1):
94 return util.integrate(p0*p1)
95
96 def getStress(self,u):
97 mg=util.grad(u)
98 return 2.*self.eta*util.symmetric(mg)
99 def getEtaEffective(self):
100 return self.eta
101
102 def solve_A(self,u,p):
103 """
104 solves Av=f-Au-B^*p (v=0 on fixed_u_mask)
105 """
106 self.__pde_u.setTolerance(self.getSubProblemTolerance())
107 self.__pde_u.setValue(X=-self.getStress(u),X_reduced=-p*util.kronecker(self.domain))
108 return self.__pde_u.getSolution(verbose=self.show_details)
109
110
111 def solve_prec(self,p):
112 a=self.__inv_eta*p
113 return a-util.integrate(a)/self.vol
114
115 def stoppingcriterium(self,Bv,v,p):
116 n_r=util.sqrt(self.inner(Bv,Bv))
117 n_v=util.sqrt(util.integrate(util.length(util.grad(v))**2))
118 if self.verbose: print "PCG step %s: L2(div(v)) = %s, L2(grad(v))=%s"%(self.iter,n_r,n_v) , util.Lsup(v)
119 if self.iter == 0: self.__n_v=n_v;
120 self.__n_v, n_v_old =n_v, self.__n_v
121 self.iter+=1
122 if self.iter>1 and n_r <= n_v*self.getTolerance() and abs(n_v_old-self.__n_v) <= n_v * self.getTolerance():
123 if self.verbose: print "PCG terminated after %s steps."%self.iter
124 return True
125 else:
126 return False
127
128
129 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
130 """
131 solves
132
133 -(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i
134 u_{i,i}=0
135
136 u=0 where fixed_u_mask>0
137 eta*(u_{i,j}+u_{j,i})*n_j=surface_stress
138
139 if surface_stress is not give 0 is assumed.
140
141 typical usage:
142
143 sp=StokesProblemCartesian(domain)
144 sp.setTolerance()
145 sp.initialize(...)
146 v,p=sp.solve(v0,p0)
147 """
148 def __init__(self,domain,**kwargs):
149 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
150 self.domain=domain
151 self.vol=util.integrate(1.,Function(self.domain))
152 self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
153 self.__pde_u.setSymmetryOn()
154 # self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0)
155
156 self.__pde_prec=LinearPDE(domain)
157 self.__pde_prec.setReducedOrderOn()
158 self.__pde_prec.setSymmetryOn()
159
160 self.__pde_proj=LinearPDE(domain)
161 self.__pde_proj.setReducedOrderOn()
162 self.__pde_proj.setSymmetryOn()
163 self.__pde_proj.setValue(D=1.)
164
165 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()):
166 self.eta=eta
167 A =self.__pde_u.createCoefficientOfGeneralPDE("A")
168 self.__pde_u.setValue(A=Data())
169 for i in range(self.domain.getDim()):
170 for j in range(self.domain.getDim()):
171 A[i,j,j,i] += 1.
172 A[i,j,i,j] += 1.
173 self.__pde_prec.setValue(D=1/self.eta)
174 self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress)
175
176 def B(self,arg):
177 d=util.div(arg)
178 self.__pde_proj.setValue(Y=d)
179 self.__pde_proj.setTolerance(self.getSubProblemTolerance())
180 return self.__pde_proj.getSolution(verbose=self.show_details)
181
182 def inner(self,p0,p1):
183 s0=util.interpolate(p0,Function(self.domain))
184 s1=util.interpolate(p1,Function(self.domain))
185 return util.integrate(s0*s1)
186
187 def inner_a(self,a0,a1):
188 p0=util.interpolate(a0[1],Function(self.domain))
189 p1=util.interpolate(a1[1],Function(self.domain))
190 alfa=(1/self.vol)*util.integrate(p0)
191 beta=(1/self.vol)*util.integrate(p1)
192 v0=util.grad(a0[0])
193 v1=util.grad(a1[0])
194 return util.integrate((p0-alfa)*(p1-beta)+((1/self.eta)**2)*util.inner(v0,v1))
195
196
197 def getStress(self,u):
198 mg=util.grad(u)
199 return 2.*self.eta*util.symmetric(mg)
200 def getEtaEffective(self):
201 return self.eta
202
203 def solve_A(self,u,p):
204 """
205 solves Av=f-Au-B^*p (v=0 on fixed_u_mask)
206 """
207 self.__pde_u.setTolerance(self.getSubProblemTolerance())
208 self.__pde_u.setValue(X=-self.getStress(u)-p*util.kronecker(self.domain))
209 return self.__pde_u.getSolution(verbose=self.show_details)
210
211
212 def solve_prec(self,p):
213 #proj=Projector(domain=self.domain, reduce = True, fast=False)
214 self.__pde_prec.setTolerance(self.getSubProblemTolerance())
215 self.__pde_prec.setValue(Y=p)
216 q=self.__pde_prec.getSolution(verbose=self.show_details)
217 return q
218
219 def solve_prec1(self,p):
220 #proj=Projector(domain=self.domain, reduce = True, fast=False)
221 self.__pde_prec.setTolerance(self.getSubProblemTolerance())
222 self.__pde_prec.setValue(Y=p)
223 q=self.__pde_prec.getSolution(verbose=self.show_details)
224 q0=util.interpolate(q,Function(self.domain))
225 print util.inf(q*q0),util.sup(q*q0)
226 q-=(1/self.vol)*util.integrate(q0)
227 print util.inf(q*q0),util.sup(q*q0)
228 return q
229
230 def stoppingcriterium(self,Bv,v,p):
231 n_r=util.sqrt(self.inner(Bv,Bv))
232 n_v=util.sqrt(util.integrate(util.length(util.grad(v))**2))
233 if self.verbose: print "PCG step %s: L2(div(v)) = %s, L2(grad(v))=%s"%(self.iter,n_r,n_v)
234 if self.iter == 0: self.__n_v=n_v;
235 self.__n_v, n_v_old =n_v, self.__n_v
236 self.iter+=1
237 if self.iter>1 and n_r <= n_v*self.getTolerance() and abs(n_v_old-self.__n_v) <= n_v * self.getTolerance():
238 if self.verbose: print "PCG terminated after %s steps."%self.iter
239 return True
240 else:
241 return False
242 def stoppingcriterium2(self,norm_r,norm_b,solver='GMRES',TOL=None):
243 if TOL==None:
244 TOL=self.getTolerance()
245 if self.verbose: print "%s step %s: L2(r) = %s, L2(b)*TOL=%s"%(solver,self.iter,norm_r,norm_b*TOL)
246 self.iter+=1
247
248 if norm_r <= norm_b*TOL:
249 if self.verbose: print "%s terminated after %s steps."%(solver,self.iter)
250 return True
251 else:
252 return False
253
254

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