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Contents of /trunk/doc/examples/cookbook/example08b.py

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Revision 3892 - (show annotations)
Tue Apr 10 08:57:23 2012 UTC (6 years, 11 months ago) by jfenwick
File MIME type: text/x-python
File size: 7656 byte(s)
Merged changes across from the attempt2 branch.
This version builds and passes python2 tests.
It also passes most python3 tests.



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 from esys.weipa import saveVTK
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 matplotlib
39 matplotlib.use('agg') #It's just here for automated testing
40
41 import pylab as pl
42 import matplotlib.cm as cm
43 from esys.escript.linearPDEs import LinearPDE
44
45 ########################################################MPI WORLD CHECK
46 if getMPISizeWorld() > 1:
47 import sys
48 print("This example will not run in an MPI world.")
49 sys.exit(0)
50
51 #################################################ESTABLISHING VARIABLES
52 # where to save output data
53 savepath = "data/example08b"
54 mkDir(savepath)
55 #Geometric and material property related variables.
56 mx = 1000. # model lenght
57 my = 1000. # model width
58 ndx = 300 # steps in x direction
59 ndy = 300 # steps in y direction
60 xstep=mx/ndx # calculate the size of delta x
61 ystep=abs(my/ndy) # calculate the size of delta y
62 lam=3.462e9 #lames constant
63 mu=3.462e9 #bulk modulus
64 rho=1154. #density
65 # Time related variables.
66 testing=True
67 if testing:
68 print('The testing end time is currently selected. This severely limits the number of time iterations.')
69 print("Try changing testing to False for more iterations.")
70 tend=0.001
71 else:
72 tend=0.5 # end time
73
74 h=0.0001 # time step
75 # data recording times
76 rtime=0.0 # first time to record
77 rtime_inc=tend/50.0 # time increment to record
78 #Check to make sure number of time steps is not too large.
79 print("Time step size= ",h, "Expected number of outputs= ",tend/h)
80
81 U0=0.1 # amplitude of point source
82 ls=500 # length of the source
83 source=np.zeros(ls,'float') # source array
84 decay1=np.zeros(ls,'float') # decay curve one
85 decay2=np.zeros(ls,'float') # decay curve two
86 time=np.zeros(ls,'float') # time values
87 g=np.log(0.01)/ls
88
89 dfeq=50 #Dominant Frequency
90 a = 2.0 * (np.pi * dfeq)**2.0
91 t0 = 5.0 / (2.0 * np.pi * dfeq)
92 srclength = 5. * t0
93 ls = int(srclength/h)
94 print('source length',ls)
95 source=np.zeros(ls,'float') # source array
96 ampmax=0
97 for it in range(0,ls):
98 t = it*h
99 tt = t-t0
100 dum1 = np.exp(-a * tt * tt)
101 source[it] = -2. * a * tt * dum1
102 # source[it] = exp(-a * tt * tt) !gaussian
103 if (abs(source[it]) > ampmax):
104 ampmax = abs(source[it])
105 #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
106 #decay1[t]=np.exp(g*t)
107 #decay2[t]=(np.exp(-.1*g*t)-1)
108 time[t]=t*h
109 #tdecay=decay1*decay2*U0
110 #decay1=decay1*U0; decay2=decay2*U0
111 pl.clf();
112 pl.plot(source)
113 #pl.plot(time,decay1);pl.plot(time,decay2);
114 #pl.plot(time,tdecay)
115 pl.savefig(os.path.join(savepath,'source.png'))
116
117 # will introduce a spherical source at middle left of bottom face
118 xc=[mx/2,0]
119
120 ####################################################DOMAIN CONSTRUCTION
121 domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain
122 x=domain.getX() # get the locations of the nodes in the domani
123
124 ##########################################################ESTABLISH PDE
125 mypde=LinearPDE(domain) # create pde
126 mypde.setSymmetryOn() # turn symmetry on
127 # turn lumping on for more efficient solving
128 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
129 kmat = kronecker(domain) # create the kronecker delta function of the domain
130 mypde.setValue(D=kmat*rho) #set the general form value D
131
132 ##########################################################ESTABLISH ABC
133 # Define where the boundary decay will be applied.
134 bn=50.
135 bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
136 # btop=ystep*bn # don't apply to force boundary!!!
137
138 # locate these points in the domain
139 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
140
141 tgamma=0.85 # decay value for exponential function
142 def calc_gamma(G,npts):
143 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
144 return func
145
146 gleft = calc_gamma(tgamma,bleft)
147 gright = calc_gamma(tgamma,bleft)
148 gbottom= calc_gamma(tgamma,ystep*bn)
149
150 print('gamma', gleft,gright,gbottom)
151
152 # calculate decay functions
153 def abc_bfunc(gamma,loc,x,G):
154 func=exp(-1.*(gamma*abs(loc-x))**2.)
155 return func
156
157 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
158 fright=abc_bfunc(gright,bright,x[0],tgamma)
159 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
160 # apply these functions only where relevant
161 abcleft=fleft*whereNegative(left)
162 abcright=fright*wherePositive(right)
163 abcbottom=fbottom*wherePositive(bottom)
164 # make sure the inside of the abc is value 1
165 abcleft=abcleft+whereZero(abcleft)
166 abcright=abcright+whereZero(abcright)
167 abcbottom=abcbottom+whereZero(abcbottom)
168 # multiply the conditions together to get a smooth result
169 abc=abcleft*abcright*abcbottom
170
171 #visualise the boundary function
172 #abcT=abc.toListOfTuples()
173 #abcT=np.reshape(abcT,(ndx+1,ndy+1))
174 #pl.clf(); pl.imshow(abcT); pl.colorbar();
175 #pl.savefig(os.path.join(savepath,"abc.png"))
176
177
178 ############################################FIRST TIME STEPS AND SOURCE
179 # define small radius around point xc
180 src_length = 40; print("src_length = ",src_length)
181 # set initial values for first two time steps with source terms
182 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
183 src_dir=numpy.array([0.,1.]) # defines direction of point source as down
184 y=y*src_dir
185 mypde.setValue(y=y) #set the source as a function on the boundary
186 # turn lumping on for more efficient solving
187 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
188 # for first two time steps
189 u=[0.0,0.0]*wherePositive(x)
190 u_m1=u
191
192 ####################################################ITERATION VARIABLES
193 n=0 # iteration counter
194 t=0 # time counter
195 ##############################################################ITERATION
196 while t<tend:
197 # get current stress
198 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
199 mypde.setValue(X=-stress*abc) # set PDE values
200 accel = mypde.getSolution() #get PDE solution for accelleration
201 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
202 u_p1=u_p1*abc # apply boundary conditions
203 u_m1=u; u=u_p1 # shift values by 1
204 # save current displacement, acceleration and pressure
205 if (t >= rtime):
206 saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
207 acceleration=length(accel),tensor=stress)
208 rtime=rtime+rtime_inc #increment data save time
209 # increment loop values
210 t=t+h; n=n+1
211 if (n < ls):
212 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
213 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
214 print(n,"-th time step t ",t)

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