/[escript]/trunk/doc/examples/cookbook/example08b.py
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Contents of /trunk/doc/examples/cookbook/example08b.py

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Revision 3055 - (show annotations)
Sun Jul 4 21:52:36 2010 UTC (11 years, 5 months ago) by ahallam
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3d wave equation and ABC
1
2 ########################################################
3 #
4 # Copyright (c) 2009-2010 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) 2009-2010 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 ############################################################FILE HEADER
23 # example08b.py
24 # Antony Hallam
25 # Seismic Wave Equation Simulation using acceleration solution.
26 # Extend the solution in example 08a to use absorbing boundary
27 # conditions.
28
29 #######################################################EXTERNAL MODULES
30 from esys.escript import *
31 from esys.finley import Rectangle
32 import sys
33 import os
34 # smoothing operator
35 from esys.escript.pdetools import Projector, Locator
36 from esys.escript.unitsSI import *
37 import numpy as np
38 import pylab as pl
39 import matplotlib.cm as cm
40 from esys.escript.linearPDEs import LinearPDE
41
42 #################################################ESTABLISHING VARIABLES
43 # where to save output data
44 savepath = "data/example08b"
45 mkDir(savepath)
46 #Geometric and material property related variables.
47 mx = 1000. # model lenght
48 my = 1000. # model width
49 ndx = 1000 # steps in x direction
50 ndy = 1000 # steps in y direction
51 xstep=mx/ndx # calculate the size of delta x
52 ystep=abs(my/ndy) # calculate the size of delta y
53 lam=3.462e9 #lames constant
54 mu=3.462e9 #bulk modulus
55 rho=1154. #density
56 # Time related variables.
57 tend=0.5 # end time
58 h=0.0001 # time step
59 # data recording times
60 rtime=0.0 # first time to record
61 rtime_inc=tend/50.0 # time increment to record
62 #Check to make sure number of time steps is not too large.
63 print "Time step size= ",h, "Expected number of outputs= ",tend/h
64
65 U0=0.1 # amplitude of point source
66 ls=500 # length of the source
67 source=np.zeros(ls,'float') # source array
68 decay1=np.zeros(ls,'float') # decay curve one
69 decay2=np.zeros(ls,'float') # decay curve two
70 time=np.zeros(ls,'float') # time values
71 g=np.log(0.01)/ls
72
73 dfeq=50 #Dominant Frequency
74 a = 2.0 * (np.pi * dfeq)**2.0
75 t0 = 5.0 / (2.0 * np.pi * dfeq)
76 srclength = 5. * t0
77 ls = srclength/h
78 print 'source length',ls
79 source=np.zeros(ls,'float') # source array
80 ampmax=0
81 for it in range(0,ls):
82 t = it*h
83 tt = t-t0
84 dum1 = np.exp(-a * tt * tt)
85 source[it] = -2. * a * tt * dum1
86 # source[it] = exp(-a * tt * tt) !gaussian
87 if (abs(source[it]) > ampmax):
88 ampmax = abs(source[it])
89 #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
90 #decay1[t]=np.exp(g*t)
91 #decay2[t]=(np.exp(-.1*g*t)-1)
92 time[t]=t*h
93 #tdecay=decay1*decay2*U0
94 #decay1=decay1*U0; decay2=decay2*U0
95 pl.clf();
96 pl.plot(source)
97 #pl.plot(time,decay1);pl.plot(time,decay2);
98 #pl.plot(time,tdecay)
99 pl.savefig(os.path.join(savepath,'source.png'))
100
101 # will introduce a spherical source at middle left of bottom face
102 xc=[mx/2,0]
103
104 ####################################################DOMAIN CONSTRUCTION
105 domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy) # create the domain
106 x=domain.getX() # get the locations of the nodes in the domani
107
108 ##########################################################ESTABLISH PDE
109 mypde=LinearPDE(domain) # create pde
110 mypde.setSymmetryOn() # turn symmetry on
111 # turn lumping on for more efficient solving
112 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
113 kmat = kronecker(domain) # create the kronecker delta function of the domain
114 mypde.setValue(D=kmat*rho) #set the general form value D
115
116 ##########################################################ESTABLISH ABC
117 # Define where the boundary decay will be applied.
118 bn=50.
119 bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
120 # btop=ystep*bn # don't apply to force boundary!!!
121
122 # locate these points in the domain
123 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
124
125 tgamma=0.99 # decay value for exponential function
126 def calc_gamma(G,npts):
127 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
128 return func
129
130 gleft = calc_gamma(tgamma,bleft)
131 gright = calc_gamma(tgamma,bleft)
132 gbottom= calc_gamma(tgamma,ystep*bn)
133
134 print 'gamma', gleft,gright,gbottom
135
136 # calculate decay functions
137 def abc_bfunc(gamma,loc,x,G):
138 func=exp(-1.*(gamma*abs(loc-x))**2.)
139 return func
140
141 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
142 fright=abc_bfunc(gright,bright,x[0],tgamma)
143 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
144 # apply these functions only where relevant
145 abcleft=fleft*whereNegative(left)
146 abcright=fright*wherePositive(right)
147 abcbottom=fbottom*wherePositive(bottom)
148 # make sure the inside of the abc is value 1
149 abcleft=abcleft+whereZero(abcleft)
150 abcright=abcright+whereZero(abcright)
151 abcbottom=abcbottom+whereZero(abcbottom)
152 # multiply the conditions together to get a smooth result
153 abc=abcleft*abcright*abcbottom
154
155 #visualise the boundary function
156 abcT=abc.toListOfTuples()
157 abcT=np.reshape(abcT,(ndx+1,ndy+1))
158 pl.clf(); pl.imshow(abcT); pl.colorbar();
159 pl.savefig(os.path.join(savepath,"abc.png"))
160
161
162 ############################################FIRST TIME STEPS AND SOURCE
163 # define small radius around point xc
164 src_length = 40; print "src_length = ",src_length
165 # set initial values for first two time steps with source terms
166 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
167 src_dir=numpy.array([0.,-1.]) # defines direction of point source as down
168 y=y*src_dir
169 mypde.setValue(y=y) #set the source as a function on the boundary
170 # initial value of displacement at point source is constant (U0=0.01)
171 # for first two time steps
172 u=[0.0,0.0]*whereNegative(x)
173 u_m1=u
174
175 ####################################################ITERATION VARIABLES
176 n=0 # iteration counter
177 t=0 # time counter
178 ##############################################################ITERATION
179 while t<tend:
180 # get current stress
181 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
182 mypde.setValue(X=-stress) # set PDE values
183 accel = mypde.getSolution() #get PDE solution for accelleration
184 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
185 u_p1=u_p1*abc # apply boundary conditions
186 u_m1=u; u=u_p1 # shift values by 1
187 # save current displacement, acceleration and pressure
188 if (t >= rtime):
189 saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
190 acceleration=length(accel),tensor=stress)
191 rtime=rtime+rtime_inc #increment data save time
192 # increment loop values
193 t=t+h; n=n+1
194 if (n < ls):
195 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
196 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
197 print n,"-th time step t ",t

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