/[escript]/trunk/doc/examples/usersguide/wave.py
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Contents of /trunk/doc/examples/usersguide/wave.py

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Revision 2580 - (show annotations)
Tue Aug 4 08:24:12 2009 UTC (9 years, 6 months ago) by gross
File MIME type: text/x-python
File size: 4138 byte(s)
another example for the usage of matplot lib added to users guide.
1
2 ########################################################
3 #
4 # Copyright (c) 2003-2009 by University of Queensland
5 # Earth Systems Science Computational Center (ESSCC)
6 # http://www.uq.edu.au/esscc
7 #
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 __copyright__="""Copyright (c) 2003-2009 by University of Queensland
15 Earth Systems Science Computational Center (ESSCC)
16 http://www.uq.edu.au/esscc
17 Primary Business: Queensland, Australia"""
18 __license__="""Licensed under the Open Software License version 3.0
19 http://www.opensource.org/licenses/osl-3.0.php"""
20 __url__="https://launchpad.net/escript-finley"
21
22 from esys.escript import *
23 from esys.escript.pdetools import Locator
24 from esys.escript.linearPDEs import LinearPDE
25 from esys.finley import Brick
26 from numpy import identity,zeros,ones
27 import matplotlib.pyplot as plt
28
29
30 ne=32 # number of cells in x_0 and x_1 directions
31 width=10000. # length in x_0 and x_1 directions
32 lam=3.462e9
33 mu=3.462e9
34 rho=1154.
35 tend=10. # to ran a full simulation change tend to 60.
36 alpha=0.7
37 t0=3.
38
39
40 U0=1. # maximum displacement
41 mkDir("data") # create directory data if it does not exist already.
42
43 def wavePropagation(domain,h,tend,lam,mu,rho, xc, src_radius, U0):
44 # lists to collect displacement at point source
45 ts, u_pc0,u_pc1,u_pc2=[], [], [], []
46 x=domain.getX()
47 # ... open new PDE ...
48 mypde=LinearPDE(domain)
49 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
50 kronecker=identity(mypde.getDim())
51
52 dunit=numpy.array([1.,0.,0.]) # defines direction of point source
53
54 mypde.setValue(D=kronecker*rho, q=whereNegative(length(x-xc)-src_radius)*dunit)
55 # ... set initial values ....
56 n=0
57 # for first two time steps
58 u=Vector(0.,Solution(domain))
59 u_last=Vector(0.,Solution(domain))
60 t=0
61
62 # define the location of the point source
63 L=Locator(domain,xc)
64 # find potential at point source
65 u_pc=L.getValue(u)
66 print "u at point charge=",u_pc
67 ts.append(t); u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2])
68
69 while t<tend:
70 t+=h
71 # ... get current stress ....
72 g=grad(u)
73 stress=lam*trace(g)*kronecker+mu*(g+transpose(g))
74 # ... get new acceleration ....
75 amplitude=U0*(4*(t-t0)**3/alpha**3-6*(t-t0)/alpha)*sqrt(2.)/alpha**2*exp(1./2.-(t-t0)**2/alpha**2)
76 mypde.setValue(X=-stress, r=dunit*amplitude)
77 a=mypde.getSolution()
78 # ... get new displacement ...
79 u_new=2*u-u_last+h**2*a
80 # ... shift displacements ....
81 u_last=u
82 u=u_new
83 n+=1
84 print n,"-th time step t ",t
85 u_pc=L.getValue(u)
86 print "u at point charge=",u_pc
87 ts.append(t); u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2])
88
89 # ... save current acceleration in units of gravity and displacements
90 if n==1 or n%10==0: saveVTK("./data/usoln.%i.vtu"%(n/10),acceleration=length(a)/9.81,
91 displacement = length(u), tensor = stress, Ux = u[0] )
92 return ts, u_pc0,u_pc1,u_pc2
93
94 #
95 # create domain:
96 #
97 mydomain=Brick(ne,ne,10,l0=width,l1=width,l2=10.*width/ne)
98 #
99 # sety time step size:
100 #
101 h=inf(1./5.)*inf(sqrt(rho/(lam+2*mu))*mydomain.getSize())
102 print "time step size = ",h
103 #
104 # spherical source at middle of bottom face
105 #
106 xc=[width/2.,width/2.,0.]
107 # define small radius around point xc
108 src_radius = 0.03*width
109 print "src_radius = ",src_radius
110 #
111 # run it
112 #
113 ts, u_pc0,u_pc1,u_pc2 = wavePropagation(mydomain,h,tend,lam,mu,rho, xc, src_radius, U0)
114 #
115 # create a plot:
116 #
117 if getMPIRankWorld() == 0:
118 plt.title("Displacement at Point Source")
119 plt.plot(ts, u_pc0, '-', label="x_0", linewidth=1)
120 plt.plot(ts, u_pc1, '-', label="x_1", linewidth=1)
121 plt.plot(ts, u_pc2, '-', label="x_2", linewidth=1)
122 plt.xlabel('time')
123 plt.ylabel('displacement')
124 plt.legend()
125 plt.savefig('u_pc.png', format='png')
126 # or save displacement
127 u_pc_data=FileWriter('./data/U_pc.out')
128 for i in xrange(len(ts)) :
129 u_pc_data.write("%f %f %f %f\n"%(ts[i],u_pc0[i],u_pc1[i],u_pc2[i]))
130 u_pc_data.close()
131

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