/[escript]/trunk/esys2/finley/test/python/AdvectivePDETest.py
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Mon Feb 14 04:14:42 2005 UTC (14 years, 2 months ago) by jgs
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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 for d in [3]:
66 # create domain:
67 if d==2:
68 mydomain=finley.Rectangle(ne,ne,1)
69 x=mydomain.getX()
70 msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero()
71 else:
72 mydomain=finley.Brick(ne,ne,ne,1)
73 x=mydomain.getX()
74 msk=x[0].whereZero()+(x[0]-1.).whereZero()+x[1].whereZero()+(x[1]-1.).whereZero()+x[2].whereZero()+(x[2]-1.).whereZero()
75 print "@ generated %d-dimension mesh with %d elements in each direction"%(d,ne)
76 # for ncomp in [1,2]:
77 for ncomp in [2]:
78 if ncomp==1:
79 maskf=1.
80 Z=makeRandomFloats(d,-1.,0.)
81 K_sup=makeRandomFloatMatrix(d,d,-1.,1.)
82 K=numarray.identity(d)*1.
83 else:
84 maskf=numarray.ones(ncomp)
85 Z=makeRandomFloatMatrix(ncomp,d,-1.,0.)
86 K_sup=makeRandomFloatTensor(ncomp,d,ncomp,d,-1.,1.)
87 K=numarray.zeros([ncomp,d,ncomp,d])*0.
88 for i in range(ncomp):
89 K[i,:,i,:]=numarray.identity(d)*1.
90 K_sup=numarray.array(K_sup)
91 Z=numarray.array(Z)
92 Z/=length(Z)
93 if ncomp==1:
94 Zx=Z[0]*x[0]
95 for j in range(1,d):
96 Zx+=Z[j]*x[j]
97 else:
98 Zx=x[0]*Z[:,0]
99 for j in range(1,d):
100 Zx+=x[j]*Z[:,j]
101 K+=0.02*K_sup/length(K_sup)
102 K/=length(K)
103 if ncomp==1:
104 U=numarray.matrixmultiply(numarray.transpose(K),Z)
105 else:
106 U=numarray.zeros([ncomp,d,ncomp])*1.
107 for m in range(ncomp):
108 for l in range(ncomp):
109 for j in range(d):
110 for i in range(d):
111 U[m,j,l]+=K[m,i,l,j]*Z[l,i]
112
113 # create domain:
114 mypde=AdvectivePDE(mydomain)
115 # mypde.setSolverMethod(mypde.DIRECT)
116 mypde.setValue(q=msk*maskf,A=K)
117 mypde.checkSymmetry()
118 # run Peclet
119 for Pe in [0.001,1.,1.,10.,100,1000.,10000.,100000.,1000000.,10000000.]:
120 peclet=Pe*length(U)/2./length(K)/ne
121 print "@@@ Peclet Number :",peclet
122 u_ex=exp(Pe*Zx)
123 mypde.setValue(r=u_ex)
124 # mypde.setValue(B=Data(),C=Pe*U)
125 # u=mypde.getSolution()
126 # print "@@@@ C=U: Pe = ",peclet,printError(u,u_ex)
127 mypde.setValue(C=Data(),B=-Pe*U)
128 u=mypde.getSolution()
129 print "@@@@ B=-U: Pe = ",peclet,printError(u,u_ex)

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