/[escript]/trunk/doc/examples/cookbook/example09a.py
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Revision 3069 - (hide annotations)
Wed Jul 21 03:24:48 2010 UTC (9 years, 2 months ago) by ahallam
Original Path: trunk/doc/examples/cookbook/example09.py
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File size: 7706 byte(s)
Updates to layer cake and cookbook as well as examples.
1 ahallam 3055
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     # example09.py
24     # Antony Hallam
25     # Seismic Wave Equation Simulation using acceleration solution.
26     # 3D model with multiple layers.
27    
28     #######################################################EXTERNAL MODULES
29     from esys.escript import *
30     from esys.finley import Rectangle
31     import os
32     # smoothing operator
33     from esys.escript.pdetools import Projector, Locator
34     from esys.escript.unitsSI import *
35     import numpy as np
36     import pylab as pl
37     import matplotlib.cm as cm
38     from esys.escript.linearPDEs import LinearPDE
39 ahallam 3069 from esys.finley import ReadMesh
40 ahallam 3055
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 ahallam 3069 savepath = "data/example09"
50 ahallam 3055 mkDir(savepath)
51     #Geometric and material property related variables.
52     mx = 1000. # model lenght
53     my = 1000. # model width
54 ahallam 3069 mz=200.0
55     step=5.0 # the element size
56     ndx = int(mx/step) # steps in x direction
57     ndy = int(my/step) # steps in y direction
58     ndz = int(mz/step)
59    
60     vel2=1800.; vel1=3000.
61     rho2=2300.; rho1=3100. #density
62     mu2=(vel2**2.)*rho2/8.; mu1=(vel1**2.)*rho1/8. #bulk modulus
63     lam2=mu2*6.; lam1=mu1*6. #lames constant
64    
65 ahallam 3055 # Time related variables.
66     tend=0.5 # end time
67     h=0.0005 # time step
68     # data recording times
69     rtime=0.0 # first time to record
70     rtime_inc=tend/50.0 # time increment to record
71     #Check to make sure number of time steps is not too large.
72     print "Time step size= ",h, "Expected number of outputs= ",tend/h
73    
74     U0=0.1 # amplitude of point source
75     ls=500 # length of the source
76     source=np.zeros(ls,'float') # source array
77     decay1=np.zeros(ls,'float') # decay curve one
78     decay2=np.zeros(ls,'float') # decay curve two
79     time=np.zeros(ls,'float') # time values
80     g=np.log(0.01)/ls
81    
82     dfeq=50 #Dominant Frequency
83     a = 2.0 * (np.pi * dfeq)**2.0
84     t0 = 5.0 / (2.0 * np.pi * dfeq)
85     srclength = 5. * t0
86     ls = int(srclength/h)
87     print 'source length',ls
88     source=np.zeros(ls,'float') # source array
89     ampmax=0
90     for it in range(0,ls):
91     t = it*h
92     tt = t-t0
93     dum1 = np.exp(-a * tt * tt)
94     source[it] = -2. * a * tt * dum1
95     # source[it] = exp(-a * tt * tt) !gaussian
96     if (abs(source[it]) > ampmax):
97     ampmax = abs(source[it])
98     #source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
99     #decay1[t]=np.exp(g*t)
100     #decay2[t]=(np.exp(-.1*g*t)-1)
101     time[t]=t*h
102     #tdecay=decay1*decay2*U0
103     #decay1=decay1*U0; decay2=decay2*U0
104     pl.clf();
105     pl.plot(source)
106     #pl.plot(time,decay1);pl.plot(time,decay2);
107     #pl.plot(time,tdecay)
108     pl.savefig(os.path.join(savepath,'source.png'))
109    
110     # will introduce a spherical source at middle left of bottom face
111 ahallam 3069 xc=[mx/2,my/2,0.]
112 ahallam 3055
113     ####################################################DOMAIN CONSTRUCTION
114 ahallam 3069 domain=ReadMesh(os.path.join(savepath,'example09m.fly')) # create the domain
115     x=domain.getX() # get the locations of the nodes in the domain
116 ahallam 3055
117 ahallam 3069 lam=Scalar(0,Function(domain))
118     lam.setTaggedValue("vintfa",lam1)
119     lam.setTaggedValue("vintfb",lam2)
120     mu=Scalar(0,Function(domain))
121     mu.setTaggedValue("vintfa",mu1)
122     mu.setTaggedValue("vintfb",mu2)
123     rho=Scalar(0,Function(domain))
124     rho.setTaggedValue("vintfa",rho1)
125     rho.setTaggedValue("vintfb",rho2)
126    
127 ahallam 3055 ##########################################################ESTABLISH PDE
128     mypde=LinearPDE(domain) # create pde
129     mypde.setSymmetryOn() # turn symmetry on
130     # turn lumping on for more efficient solving
131     mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
132     kmat = kronecker(domain) # create the kronecker delta function of the domain
133 ahallam 3069 mypde.setValue(D=rho*kmat) #set the general form value D
134 ahallam 3055
135 ahallam 3069
136    
137 ahallam 3055 ##########################################################ESTABLISH ABC
138     # Define where the boundary decay will be applied.
139 ahallam 3069 #bn=50.
140     #bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
141     ## btop=ystep*bn # don't apply to force boundary!!!
142 ahallam 3055
143 ahallam 3069 ## locate these points in the domain
144     #left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
145 ahallam 3055
146 ahallam 3069 #tgamma=0.85 # decay value for exponential function
147     #def calc_gamma(G,npts):
148     # func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
149     # return func
150 ahallam 3055
151 ahallam 3069 #gleft = calc_gamma(tgamma,bleft)
152     #gright = calc_gamma(tgamma,bleft)
153     #gbottom= calc_gamma(tgamma,ystep*bn)
154 ahallam 3055
155 ahallam 3069 #print 'gamma', gleft,gright,gbottom
156 ahallam 3055
157 ahallam 3069 ## calculate decay functions
158     #def abc_bfunc(gamma,loc,x,G):
159     # func=exp(-1.*(gamma*abs(loc-x))**2.)
160     # return func
161 ahallam 3055
162 ahallam 3069 #fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
163     #fright=abc_bfunc(gright,bright,x[0],tgamma)
164     #fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
165     ## apply these functions only where relevant
166     #abcleft=fleft*whereNegative(left)
167     #abcright=fright*wherePositive(right)
168     #abcbottom=fbottom*wherePositive(bottom)
169     ## make sure the inside of the abc is value 1
170     #abcleft=abcleft+whereZero(abcleft)
171     #abcright=abcright+whereZero(abcright)
172     #abcbottom=abcbottom+whereZero(abcbottom)
173     ## multiply the conditions together to get a smooth result
174     #abc=abcleft*abcright*abcbottom
175 ahallam 3055
176     #visualise the boundary function
177 ahallam 3069 #abcT=abc.toListOfTuples()
178     #abcT=np.reshape(abcT,(ndx+1,ndy+1))
179     #pl.clf(); pl.imshow(abcT); pl.colorbar();
180     #pl.savefig(os.path.join(savepath,"abc.png"))
181 ahallam 3055
182    
183     ############################################FIRST TIME STEPS AND SOURCE
184     # define small radius around point xc
185     src_length = 40; print "src_length = ",src_length
186     # set initial values for first two time steps with source terms
187 ahallam 3069 xb=FunctionOnBoundary(domain).getX()
188     y=source[0]*(cos(length(xb-xc)*3.1415/src_length)+1)*whereNegative(length(xb-src_length))
189     src_dir=numpy.array([0.,0.,1.0]) # defines direction of point source as down
190 ahallam 3055 y=y*src_dir
191     mypde.setValue(y=y) #set the source as a function on the boundary
192     # initial value of displacement at point source is constant (U0=0.01)
193     # for first two time steps
194 ahallam 3069 u=[0.0,0.0,0.0]*whereNegative(x)
195 ahallam 3055 u_m1=u
196    
197     ####################################################ITERATION VARIABLES
198     n=0 # iteration counter
199     t=0 # time counter
200     ##############################################################ITERATION
201     while t<tend:
202     # get current stress
203 ahallam 3069 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))#*abc
204 ahallam 3055 mypde.setValue(X=-stress) # set PDE values
205     accel = mypde.getSolution() #get PDE solution for accelleration
206     u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
207 ahallam 3069 u_p1=u_p1#*abc # apply boundary conditions
208 ahallam 3055 u_m1=u; u=u_p1 # shift values by 1
209     # save current displacement, acceleration and pressure
210     if (t >= rtime):
211 ahallam 3069 saveVTK(os.path.join(savepath,"ex09.%05d.vtu"%n),displacement=length(u),\
212 ahallam 3055 acceleration=length(accel),tensor=stress)
213     rtime=rtime+rtime_inc #increment data save time
214     # increment loop values
215     t=t+h; n=n+1
216     if (n < ls):
217     y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
218     y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
219     print n,"-th time step t ",t

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