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

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Revision 4576 - (show annotations)
Mon Dec 9 23:35:30 2013 UTC (4 years, 8 months ago) by sshaw
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python3ified things, replaced mixed whitespace and xrange calls
1
2 ##############################################################################
3 #
4 # Copyright (c) 2009-2013 by University of Queensland
5 # http://www.uq.edu.au
6 #
7 # Primary Business: Queensland, Australia
8 # Licensed under the Open Software License version 3.0
9 # http://www.opensource.org/licenses/osl-3.0.php
10 #
11 # Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12 # Development since 2012 by School of Earth Sciences
13 #
14 ##############################################################################
15
16 __copyright__="""Copyright (c) 2009-2013 by University of Queensland
17 http://www.uq.edu.au
18 Primary Business: Queensland, Australia"""
19 __license__="""Licensed under the Open Software License version 3.0
20 http://www.opensource.org/licenses/osl-3.0.php"""
21 __url__="https://launchpad.net/escript-finley"
22
23 ############################################################FILE HEADER
24 # example08b.py
25 # Antony Hallam
26 # Seismic Wave Equation Simulation using acceleration solution.
27 # Extend the solution in example 08a to use absorbing boundary
28 # conditions.
29
30 #######################################################EXTERNAL MODULES
31 import matplotlib
32 matplotlib.use('agg') #It's just here for automated testing
33 from esys.escript import *
34 from esys.finley import Rectangle
35 from esys.weipa import saveVTK
36 import os
37 # smoothing operator
38 from esys.escript.pdetools import Projector, Locator
39 from esys.escript.unitsSI import *
40 import numpy as np
41
42 import pylab as pl
43 import matplotlib.cm as cm
44 from esys.escript.linearPDEs import LinearPDE
45
46 ########################################################MPI WORLD CHECK
47 if getMPISizeWorld() > 1:
48 import sys
49 print("This example will not run in an MPI world.")
50 sys.exit(0)
51
52 #################################################ESTABLISHING VARIABLES
53 # where to save output data
54 savepath = "data/example08b"
55 mkDir(savepath)
56 #Geometric and material property related variables.
57 mx = 1000. # model lenght
58 my = 1000. # model width
59 ndx = 300 # steps in x direction
60 ndy = 300 # steps in y direction
61 xstep=mx/ndx # calculate the size of delta x
62 ystep=abs(my/ndy) # calculate the size of delta y
63 lam=3.462e9 #lames constant
64 mu=3.462e9 #bulk modulus
65 rho=1154. #density
66 # Time related variables.
67 testing=True
68 if testing:
69 print('The testing end time is currently selected. This severely limits the number of time iterations.')
70 print("Try changing testing to False for more iterations.")
71 tend=0.001
72 else:
73 tend=0.5 # end time
74
75 h=0.0001 # time step
76 # data recording times
77 rtime=0.0 # first time to record
78 rtime_inc=tend/50.0 # time increment to record
79 #Check to make sure number of time steps is not too large.
80 print("Time step size= ",h, "Expected number of outputs= ",tend/h)
81
82 U0=0.1 # amplitude of point source
83 ls=500 # length of the source
84 source=np.zeros(ls,'float') # source array
85 decay1=np.zeros(ls,'float') # decay curve one
86 decay2=np.zeros(ls,'float') # decay curve two
87 time=np.zeros(ls,'float') # time values
88 g=np.log(0.01)/ls
89
90 dfeq=50 #Dominant Frequency
91 a = 2.0 * (np.pi * dfeq)**2.0
92 t0 = 5.0 / (2.0 * np.pi * dfeq)
93 srclength = 5. * t0
94 ls = int(srclength/h)
95 print('source length',ls)
96 source=np.zeros(ls,'float') # source array
97 ampmax=0
98 for it in range(0,ls):
99 t = it*h
100 tt = t-t0
101 dum1 = np.exp(-a * tt * tt)
102 source[it] = -2. * a * tt * dum1
103 # source[it] = exp(-a * tt * tt) !gaussian
104 if (abs(source[it]) > ampmax):
105 ampmax = abs(source[it])
106 #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
107 #decay1[t]=np.exp(g*t)
108 #decay2[t]=(np.exp(-.1*g*t)-1)
109 time[t]=t*h
110 #tdecay=decay1*decay2*U0
111 #decay1=decay1*U0; decay2=decay2*U0
112 pl.clf();
113 pl.plot(source)
114 #pl.plot(time,decay1);pl.plot(time,decay2);
115 #pl.plot(time,tdecay)
116 pl.savefig(os.path.join(savepath,'source.png'))
117
118 # will introduce a spherical source at middle left of bottom face
119 xc=[mx/2,0]
120
121 ####################################################DOMAIN CONSTRUCTION
122 domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain
123 x=domain.getX() # get the locations of the nodes in the domani
124
125 ##########################################################ESTABLISH PDE
126 mypde=LinearPDE(domain) # create pde
127 mypde.setSymmetryOn() # turn symmetry on
128 # turn lumping on for more efficient solving
129 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
130 kmat = kronecker(domain) # create the kronecker delta function of the domain
131 mypde.setValue(D=kmat*rho) #set the general form value D
132
133 ##########################################################ESTABLISH ABC
134 # Define where the boundary decay will be applied.
135 bn=50.
136 bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
137 # btop=ystep*bn # don't apply to force boundary!!!
138
139 # locate these points in the domain
140 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
141
142 tgamma=0.85 # decay value for exponential function
143 def calc_gamma(G,npts):
144 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
145 return func
146
147 gleft = calc_gamma(tgamma,bleft)
148 gright = calc_gamma(tgamma,bleft)
149 gbottom= calc_gamma(tgamma,ystep*bn)
150
151 print('gamma', gleft,gright,gbottom)
152
153 # calculate decay functions
154 def abc_bfunc(gamma,loc,x,G):
155 func=exp(-1.*(gamma*abs(loc-x))**2.)
156 return func
157
158 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
159 fright=abc_bfunc(gright,bright,x[0],tgamma)
160 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
161 # apply these functions only where relevant
162 abcleft=fleft*whereNegative(left)
163 abcright=fright*wherePositive(right)
164 abcbottom=fbottom*wherePositive(bottom)
165 # make sure the inside of the abc is value 1
166 abcleft=abcleft+whereZero(abcleft)
167 abcright=abcright+whereZero(abcright)
168 abcbottom=abcbottom+whereZero(abcbottom)
169 # multiply the conditions together to get a smooth result
170 abc=abcleft*abcright*abcbottom
171
172 #visualise the boundary function
173 #abcT=abc.toListOfTuples()
174 #abcT=np.reshape(abcT,(ndx+1,ndy+1))
175 #pl.clf(); pl.imshow(abcT); pl.colorbar();
176 #pl.savefig(os.path.join(savepath,"abc.png"))
177
178
179 ############################################FIRST TIME STEPS AND SOURCE
180 # define small radius around point xc
181 src_length = 40; print("src_length = ",src_length)
182 # set initial values for first two time steps with source terms
183 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
184 src_dir=numpy.array([0.,1.]) # defines direction of point source as down
185 y=y*src_dir
186 mypde.setValue(y=y) #set the source as a function on the boundary
187 # turn lumping on for more efficient solving
188 mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().HRZ_LUMPING)
189 # for first two time steps
190 u=[0.0,0.0]*wherePositive(x)
191 u_m1=u
192
193 ####################################################ITERATION VARIABLES
194 n=0 # iteration counter
195 t=0 # time counter
196 ##############################################################ITERATION
197 while t<tend:
198 # get current stress
199 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
200 mypde.setValue(X=-stress*abc) # set PDE values
201 accel = mypde.getSolution() #get PDE solution for accelleration
202 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
203 u_p1=u_p1*abc # apply boundary conditions
204 u_m1=u; u=u_p1 # shift values by 1
205 # save current displacement, acceleration and pressure
206 if (t >= rtime):
207 saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
208 acceleration=length(accel),tensor=stress)
209 rtime=rtime+rtime_inc #increment data save time
210 # increment loop values
211 t=t+h; n=n+1
212 if (n < ls):
213 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
214 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
215 print("time step %d, t=%s"%(n,t))

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