/[escript]/trunk/finley/test/python/AdvectivePDETest.py
ViewVC logotype

Annotation of /trunk/finley/test/python/AdvectivePDETest.py

Parent Directory Parent Directory | Revision Log Revision Log


Revision 617 - (hide annotations)
Wed Mar 22 02:58:17 2006 UTC (13 years, 7 months ago) by elspeth
File MIME type: text/x-python
File size: 4556 byte(s)
More copyright.

1 jgs 108 # $Id$
2    
3     # Test for the AdvectivePDE class
4     #
5     # for a single equation the test problem is
6     #
7     # -(K_{ij}u_{,j})_{,i} - (w_i u)_{,i} + v_j u_{,j} =0
8     #
9     # + constraints on the surface
10     #
11     # for system of two equation the test problem is
12     #
13     # -(K_{milj}u_{l,j})_{,i} - (w_{mil} u_l)_{,i} + v_{mlj} u_{l,j} =0
14     #
15     # + constraints on the surface
16     #
17     # K,w and v are constant (we will set v=0 or w=0)
18     #
19     # the test solution is u(x)=e^{z_i*x_i} and u_l(x)=e^{z_{li}*x_i}
20     #
21     # an easy caculation shows that
22     #
23     # z_i*K_{ij}*z_j=(v_i-w_i)*z_i and z_{li}*K_{milj}*z_{lj}=(v_{mjl}-w_{mlj})*z_{lj}
24     #
25     # obviously one can choose: v_i-w_i=K_{ji}z_j and v_{mjl}-w_{mlj}=z_{li}*K_{milj} (no summation over l)
26     #
27    
28 elspeth 617 __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
29     http://www.access.edu.au
30     Primary Business: Queensland, Australia"""
31     __license__="""Licensed under the Open Software License version 3.0
32     http://www.opensource.org/licenses/osl-3.0.php"""
33 jgs 108 from esys.escript import *
34 gross 423 from esys.escript.linearPDEs import AdvectivePDE,LinearPDE
35 jgs 108 from esys import finley
36     from random import random
37    
38     def printError(u,u_ex):
39     if u.getRank()==0:
40     out=" error = %e range = [%e:%e] [%e:%e]"%(Lsup(u-u_ex)/Lsup(u_ex),sup(u),inf(u),sup(u_ex),inf(u_ex))
41     else:
42     out="\n"
43     for i in range(u.getShape()[0]):
44     out+=" %d error = %e range = [%e:%e] [%e:%e]\n"%(i,Lsup(u[i]-u_ex[i])/Lsup(u_ex[i]),sup(u[i]),inf(u[i]),sup(u_ex[i]),inf(u_ex[i]))
45     return out
46    
47    
48     def makeRandomFloats(n,val_low=0.,val_up=1.):
49     out=[]
50     for i in range(n):
51     out.append((val_up-val_low)*random()+val_low)
52     return out
53    
54     def makeRandomFloatMatrix(m,n,val_low=0.,val_up=1.):
55     out=[]
56     for i in range(m):
57     out.append(makeRandomFloats(n,val_low,val_up))
58     return out
59    
60     def makeRandomFloatTensor(l,k,m,n,val_low=0.,val_up=1.):
61     out=[]
62     for j in range(l):
63     out2=[]
64     for i in range(k): out2.append(makeRandomFloatMatrix(m,n,val_low,val_up))
65     out.append(out2)
66     return out
67    
68     ne=20
69 jgs 110 # for d in [2,3]:
70     for d in [3]:
71 jgs 108 # create domain:
72     if d==2:
73     mydomain=finley.Rectangle(ne,ne,1)
74     x=mydomain.getX()
75 gross 423 msk=whereZero(x[0])+whereZero(x[0]-1.)+whereZero(x[1])+whereZero(x[1]-1.)
76 jgs 108 else:
77     mydomain=finley.Brick(ne,ne,ne,1)
78     x=mydomain.getX()
79 gross 423 msk=whereZero(x[0])+whereZero(x[0]-1.)+whereZero(x[1])+whereZero(x[1]-1.)+whereZero(x[2])+whereZero(x[2]-1.)
80 jgs 108 print "@ generated %d-dimension mesh with %d elements in each direction"%(d,ne)
81     # for ncomp in [1,2]:
82 jgs 110 for ncomp in [2]:
83 jgs 108 if ncomp==1:
84     maskf=1.
85     Z=makeRandomFloats(d,-1.,0.)
86     K_sup=makeRandomFloatMatrix(d,d,-1.,1.)
87     K=numarray.identity(d)*1.
88     else:
89     maskf=numarray.ones(ncomp)
90     Z=makeRandomFloatMatrix(ncomp,d,-1.,0.)
91     K_sup=makeRandomFloatTensor(ncomp,d,ncomp,d,-1.,1.)
92     K=numarray.zeros([ncomp,d,ncomp,d])*0.
93     for i in range(ncomp):
94     K[i,:,i,:]=numarray.identity(d)*1.
95 jgs 110 K_sup=numarray.array(K_sup)
96 jgs 108 Z=numarray.array(Z)
97     Z/=length(Z)
98     if ncomp==1:
99     Zx=Z[0]*x[0]
100     for j in range(1,d):
101     Zx+=Z[j]*x[j]
102     else:
103     Zx=x[0]*Z[:,0]
104     for j in range(1,d):
105     Zx+=x[j]*Z[:,j]
106 jgs 110 K+=0.02*K_sup/length(K_sup)
107 jgs 108 K/=length(K)
108     if ncomp==1:
109     U=numarray.matrixmultiply(numarray.transpose(K),Z)
110     else:
111 jgs 110 U=numarray.zeros([ncomp,d,ncomp])*1.
112 jgs 108 for m in range(ncomp):
113     for l in range(ncomp):
114     for j in range(d):
115     for i in range(d):
116     U[m,j,l]+=K[m,i,l,j]*Z[l,i]
117    
118     # create domain:
119     mypde=AdvectivePDE(mydomain)
120     # mypde.setSolverMethod(mypde.DIRECT)
121 gross 423 print K
122     mypde.setValue(q=msk*maskf)
123     mypde.setValue(A=K)
124     mypde.setValue(A=K,q=msk*maskf)
125 jgs 110 mypde.checkSymmetry()
126 jgs 108 # run Peclet
127 jgs 110 for Pe in [0.001,1.,1.,10.,100,1000.,10000.,100000.,1000000.,10000000.]:
128     peclet=Pe*length(U)/2./length(K)/ne
129     print "@@@ Peclet Number :",peclet
130 jgs 108 u_ex=exp(Pe*Zx)
131     mypde.setValue(r=u_ex)
132 jgs 110 # mypde.setValue(B=Data(),C=Pe*U)
133     # u=mypde.getSolution()
134     # print "@@@@ C=U: Pe = ",peclet,printError(u,u_ex)
135 jgs 108 mypde.setValue(C=Data(),B=-Pe*U)
136     u=mypde.getSolution()
137 jgs 110 print "@@@@ B=-U: Pe = ",peclet,printError(u,u_ex)

Properties

Name Value
svn:eol-style native
svn:keywords Author Date Id Revision

  ViewVC Help
Powered by ViewVC 1.1.26