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

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Revision 3075 - (show annotations)
Wed Jul 28 02:51:20 2010 UTC (9 years, 4 months ago) by ahallam
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Updates to cookbook example. Lumping turned off for order 2 models until bug resolves.
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 os
33 # smoothing operator
34 from esys.escript.pdetools import Projector, Locator
35 from esys.escript.unitsSI import *
36 import numpy as np
37 import pylab as pl
38 import matplotlib.cm as cm
39 from esys.escript.linearPDEs import LinearPDE
40
41 ########################################################MPI WORLD CHECK
42 if getMPISizeWorld() > 1:
43 import sys
44 print "This example will not run in an MPI world."
45 sys.exit(0)
46
47 #################################################ESTABLISHING VARIABLES
48 # where to save output data
49 savepath = "data/example08b"
50 mkDir(savepath)
51 #Geometric and material property related variables.
52 mx = 1000. # model lenght
53 my = 1000. # model width
54 ndx = 500 # steps in x direction
55 ndy = 500 # steps in y direction
56 xstep=mx/ndx # calculate the size of delta x
57 ystep=abs(my/ndy) # calculate the size of delta y
58 lam=3.462e9 #lames constant
59 mu=3.462e9 #bulk modulus
60 rho=1154. #density
61 # Time related variables.
62 tend=0.5 # end time
63 h=0.0005 # time step
64 # data recording times
65 rtime=0.0 # first time to record
66 rtime_inc=tend/50.0 # time increment to record
67 #Check to make sure number of time steps is not too large.
68 print "Time step size= ",h, "Expected number of outputs= ",tend/h
69
70 U0=0.1 # amplitude of point source
71 ls=500 # length of the source
72 source=np.zeros(ls,'float') # source array
73 decay1=np.zeros(ls,'float') # decay curve one
74 decay2=np.zeros(ls,'float') # decay curve two
75 time=np.zeros(ls,'float') # time values
76 g=np.log(0.01)/ls
77
78 dfeq=50 #Dominant Frequency
79 a = 2.0 * (np.pi * dfeq)**2.0
80 t0 = 5.0 / (2.0 * np.pi * dfeq)
81 srclength = 5. * t0
82 ls = int(srclength/h)
83 print 'source length',ls
84 source=np.zeros(ls,'float') # source array
85 ampmax=0
86 for it in range(0,ls):
87 t = it*h
88 tt = t-t0
89 dum1 = np.exp(-a * tt * tt)
90 source[it] = -2. * a * tt * dum1
91 # source[it] = exp(-a * tt * tt) !gaussian
92 if (abs(source[it]) > ampmax):
93 ampmax = abs(source[it])
94 #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
95 #decay1[t]=np.exp(g*t)
96 #decay2[t]=(np.exp(-.1*g*t)-1)
97 time[t]=t*h
98 #tdecay=decay1*decay2*U0
99 #decay1=decay1*U0; decay2=decay2*U0
100 pl.clf();
101 pl.plot(source)
102 #pl.plot(time,decay1);pl.plot(time,decay2);
103 #pl.plot(time,tdecay)
104 pl.savefig(os.path.join(savepath,'source.png'))
105
106 # will introduce a spherical source at middle left of bottom face
107 xc=[mx/2,0]
108
109 ####################################################DOMAIN CONSTRUCTION
110 domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain
111 x=domain.getX() # get the locations of the nodes in the domani
112
113 ##########################################################ESTABLISH PDE
114 mypde=LinearPDE(domain) # create pde
115 mypde.setSymmetryOn() # turn symmetry on
116 # turn lumping on for more efficient solving
117 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
118 kmat = kronecker(domain) # create the kronecker delta function of the domain
119 mypde.setValue(D=kmat*rho) #set the general form value D
120
121 ##########################################################ESTABLISH ABC
122 # Define where the boundary decay will be applied.
123 bn=50.
124 bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
125 # btop=ystep*bn # don't apply to force boundary!!!
126
127 # locate these points in the domain
128 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
129
130 tgamma=0.85 # decay value for exponential function
131 def calc_gamma(G,npts):
132 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
133 return func
134
135 gleft = calc_gamma(tgamma,bleft)
136 gright = calc_gamma(tgamma,bleft)
137 gbottom= calc_gamma(tgamma,ystep*bn)
138
139 print 'gamma', gleft,gright,gbottom
140
141 # calculate decay functions
142 def abc_bfunc(gamma,loc,x,G):
143 func=exp(-1.*(gamma*abs(loc-x))**2.)
144 return func
145
146 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
147 fright=abc_bfunc(gright,bright,x[0],tgamma)
148 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
149 # apply these functions only where relevant
150 abcleft=fleft*whereNegative(left)
151 abcright=fright*wherePositive(right)
152 abcbottom=fbottom*wherePositive(bottom)
153 # make sure the inside of the abc is value 1
154 abcleft=abcleft+whereZero(abcleft)
155 abcright=abcright+whereZero(abcright)
156 abcbottom=abcbottom+whereZero(abcbottom)
157 # multiply the conditions together to get a smooth result
158 abc=abcleft*abcright*abcbottom
159
160 #visualise the boundary function
161 #abcT=abc.toListOfTuples()
162 #abcT=np.reshape(abcT,(ndx+1,ndy+1))
163 #pl.clf(); pl.imshow(abcT); pl.colorbar();
164 #pl.savefig(os.path.join(savepath,"abc.png"))
165
166
167 ############################################FIRST TIME STEPS AND SOURCE
168 # define small radius around point xc
169 src_length = 40; print "src_length = ",src_length
170 # set initial values for first two time steps with source terms
171 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
172 src_dir=numpy.array([0.,-1.]) # defines direction of point source as down
173 y=y*src_dir
174 mypde.setValue(y=y) #set the source as a function on the boundary
175 # initial value of displacement at point source is constant (U0=0.01)
176 # for first two time steps
177 u=[0.0,0.0]*whereNegative(x)
178 u_m1=u
179
180 ####################################################ITERATION VARIABLES
181 n=0 # iteration counter
182 t=0 # time counter
183 ##############################################################ITERATION
184 while t<tend:
185 # get current stress
186 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))*abc
187 mypde.setValue(X=-stress) # set PDE values
188 accel = mypde.getSolution() #get PDE solution for accelleration
189 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
190 u_p1=u_p1*abc # apply boundary conditions
191 u_m1=u; u=u_p1 # shift values by 1
192 # save current displacement, acceleration and pressure
193 if (t >= rtime):
194 saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
195 acceleration=length(accel),tensor=stress)
196 rtime=rtime+rtime_inc #increment data save time
197 # increment loop values
198 t=t+h; n=n+1
199 if (n < ls):
200 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
201 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
202 print n,"-th time step t ",t

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