/[escript]/trunk/finley/test/python/AdvectivePDETest.py
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Contents of /trunk/finley/test/python/AdvectivePDETest.py

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Revision 108 - (show annotations)
Thu Jan 27 06:21:59 2005 UTC (15 years, 6 months ago) by jgs
Original Path: trunk/esys2/finley/test/python/AdvectivePDETest.py
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1 # $Id$
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 from esys.escript import *
29 from esys.linearPDEs import AdvectivePDE,LinearPDE
30 from esys import finley
31 from random import random
32
33 def printError(u,u_ex):
34 if u.getRank()==0:
35 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))
36 else:
37 out="\n"
38 for i in range(u.getShape()[0]):
39 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]))
40 return out
41
42
43 def makeRandomFloats(n,val_low=0.,val_up=1.):
44 out=[]
45 for i in range(n):
46 out.append((val_up-val_low)*random()+val_low)
47 return out
48
49 def makeRandomFloatMatrix(m,n,val_low=0.,val_up=1.):
50 out=[]
51 for i in range(m):
52 out.append(makeRandomFloats(n,val_low,val_up))
53 return out
54
55 def makeRandomFloatTensor(l,k,m,n,val_low=0.,val_up=1.):
56 out=[]
57 for j in range(l):
58 out2=[]
59 for i in range(k): out2.append(makeRandomFloatMatrix(m,n,val_low,val_up))
60 out.append(out2)
61 return out
62
63 ne=20
64 for d in [2,3]:
65 # create domain:
66 if d==2:
67 mydomain=finley.Rectangle(ne,ne,1)
68 x=mydomain.getX()
69 msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero()
70 else:
71 mydomain=finley.Brick(ne,ne,ne,1)
72 x=mydomain.getX()
73 msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero()+x[2].whereZero()+(x[2]-1.).whereZero()
74 print "@ generated %d-dimension mesh with %d elements in each direction"%(d,ne)
75 # for ncomp in [1,2]:
76 for ncomp in [1,2]:
77 if ncomp==1:
78 maskf=1.
79 Z=makeRandomFloats(d,-1.,0.)
80 K_sup=makeRandomFloatMatrix(d,d,-1.,1.)
81 K=numarray.identity(d)*1.
82 else:
83 maskf=numarray.ones(ncomp)
84 Z=makeRandomFloatMatrix(ncomp,d,-1.,0.)
85 K_sup=makeRandomFloatTensor(ncomp,d,ncomp,d,-1.,1.)
86 K=numarray.zeros([ncomp,d,ncomp,d])*0.
87 for i in range(ncomp):
88 K[i,:,i,:]=numarray.identity(d)*1.
89 Z=numarray.array(Z)
90 Z/=length(Z)
91 if ncomp==1:
92 Zx=Z[0]*x[0]
93 for j in range(1,d):
94 Zx+=Z[j]*x[j]
95 else:
96 Zx=x[0]*Z[:,0]
97 for j in range(1,d):
98 Zx+=x[j]*Z[:,j]
99 K_sup=numarray.array(makeRandomFloatMatrix(d,d,-1.,1.))
100 K+=0.05*K_sup/length(K_sup)
101 K/=length(K)
102 if ncomp==1:
103 U=numarray.matrixmultiply(numarray.transpose(K),Z)
104 else:
105 U=numarray.zeros([ncomp,d,ncomp])*0.
106 for m in range(ncomp):
107 for l in range(ncomp):
108 for j in range(d):
109 for i in range(d):
110 U[m,j,l]+=K[m,i,l,j]*Z[l,i]
111
112 # create domain:
113 mypde=AdvectivePDE(mydomain)
114 # mypde.setSolverMethod(mypde.DIRECT)
115 mypde.setValue(q=msk*maskf,A=K)
116 # run Peclet
117 for Pe in [0.001,1.,1.,10.,100,1000.,10000.,100000.,1000000.]:
118 print "@@@ Peclet Number :",Pe*length(U)/length(K)
119 u_ex=exp(Pe*Zx)
120 mypde.setValue(r=u_ex)
121 mypde.setValue(B=Data(),C=Pe*U)
122 u=mypde.getSolution()
123 print "@@@@ C=U: Pe = ",Pe,printError(u,u_ex)
124 mypde.setValue(C=Data(),B=-Pe*U)
125 u=mypde.getSolution()
126 print "@@@@ B=-U: Pe = ",Pe,printError(u,u_ex)

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