/[escript]/trunk/finley/test/python/seismic_wave.py
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Contents of /trunk/finley/test/python/seismic_wave.py

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Revision 865 - (show annotations)
Fri Oct 6 10:02:18 2006 UTC (13 years, 9 months ago) by gross
File MIME type: text/x-python
File size: 11006 byte(s)
some functions for minimizing a function added. there is still some work required but successfully applied in an aplication
1 """
2 seismic wave propagation
3
4 @var __author__: name of author
5 @var __licence__: licence agreement
6 @var __url__: url entry point on documentation
7 @var __version__: version
8 @var __date__: date of the version
9 """
10
11 __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
12 http://www.access.edu.au
13 Primary Business: Queensland, Australia"""
14 __license__="""Licensed under the Open Software License version 3.0
15 http://www.opensource.org/licenses/osl-3.0.php"""
16 __author__="Lutz Gross, l.gross@uq.edu.au"
17 __url__="http://www.iservo.edu.au/esys/escript"
18 __version__="$Revision$"
19 __date__="$Date$"
20
21 from esys.escript import *
22 from esys.escript.linearPDEs import LinearPDE
23 from esys.finley import Brick
24 import time
25
26 output=True
27 n_end=10000
28
29 resolution=1000. # number of elements per m in the finest region
30 o=1 # element order
31
32 l=100000. # width and length m (without obsorber)
33 h=30000. # height in m (without obsorber)
34 d_absorber=l*0.10 # thickness of absorbing layer
35
36 l_sand=5000. # thickness of sand region on surface
37 h_sand=2000. # thickness of sand layer under the water
38
39 l_x_water=10000. # length of water in x
40 l_y_water=10000. # length of water in y
41 h_water=2000. # depth of water region
42
43 x_sand=l/2-l_x_water/2-l_sand # x coordinate of location of sand region (without obsorber)
44 y_sand=l/2-l_y_water/2-l_sand # y coordinate of location of sand region (without obsorber)
45
46
47 # origin
48 origin={"x": -d_absorber, "y" : -d_absorber , "z" : -h-d_absorber }
49 # location and geometrical size of event reltive to origin:
50 xc=[l*0.2,l*0.3,-h*0.7]
51 src_radius = 2*resolution
52 # direction of event:
53 event=numarray.array([0.,0.,1.])*1.e6
54 # time and length of the event
55 tc=2.
56 tc_length=0.5
57
58 # material properties:
59 bedrock=0
60 absorber=1
61 water=2
62 sand=3
63
64 rho_tab={}
65 rho_tab[bedrock]=8e3
66 rho_tab[absorber]=rho_tab[bedrock]
67 rho_tab[water]=1e3
68 rho_tab[sand]=5e3
69
70 mu_tab={}
71 mu_tab[bedrock]=1.7e11
72 mu_tab[absorber]=mu_tab[bedrock]
73 mu_tab[water]=0.
74 mu_tab[sand]=1.5e10
75
76 lmbd_tab={}
77 lmbd_tab[bedrock]=1.7e11
78 lmbd_tab[absorber]=lmbd_tab[bedrock]
79 lmbd_tab[water]=1.e9
80 lmbd_tab[sand]=1.5e10
81
82 eta_tab={}
83 eta_tab[absorber]=-log(0.05)*sqrt(rho_tab[absorber]*(lmbd_tab[absorber]+2*mu_tab[absorber]))/d_absorber
84 eta_tab[sand]=eta_tab[absorber]/40.
85 eta_tab[water]=eta_tab[absorber]/40.
86 eta_tab[bedrock]=eta_tab[absorber]/40.
87
88 if output:
89 print "event location = ",xc
90 print "radius of event = ",src_radius
91 print "time of event = ",tc
92 print "length of event = ",tc_length
93 print "direction = ",event
94
95 t_end=30.
96 dt_write=0.1
97
98
99 def getDomain():
100 """
101 this defines a dom as a brick of length and width l and hight h
102
103
104 """
105 global netotal
106
107 v_p={}
108 for tag in rho_tab.keys():
109 v_p[tag]=sqrt((2*mu_tab[tag]+lmbd_tab[tag])/rho_tab[tag])
110 v_p_ref=min(v_p.values())
111
112 print "velocities: bedrock = %s, sand = %s, water =%s, absorber =%s, reference =%s"%(v_p[bedrock],v_p[sand],v_p[water],v_p[absorber],v_p_ref)
113
114 sections={}
115 sections["x"]=[d_absorber, x_sand, l_sand, l_x_water, l_sand, l-x_sand-2*l_sand-l_x_water, d_absorber]
116 sections["y"]=[d_absorber, y_sand, l_sand, l_y_water, l_sand, l-y_sand-2*l_sand-l_y_water, d_absorber]
117 sections["z"]=[d_absorber,h-h_water-h_sand,h_sand,h_water]
118 if output:
119 print "sections x = ",sections["x"]
120 print "sections y = ",sections["y"]
121 print "sections z = ",sections["z"]
122
123 mats= [
124 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
125 [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
126 [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
127 [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
128 [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
129 [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
130 [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
131
132 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
133 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
134 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
135 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
136 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
137 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
138 [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
139
140 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
141 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
142 [absorber, bedrock , sand , sand , sand , bedrock , absorber],
143 [absorber, bedrock , sand , sand , sand , bedrock , absorber],
144 [absorber, bedrock , sand , sand , sand , bedrock , absorber],
145 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
146 [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
147
148 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
149 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
150 [absorber, bedrock , sand , sand , sand , bedrock , absorber],
151 [absorber, bedrock , sand , water , sand , bedrock , absorber],
152 [absorber, bedrock , sand , sand , sand , bedrock , absorber],
153 [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
154 [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ] ]
155
156 num_elem={}
157 for d in sections:
158 num_elem[d]=[]
159 for i in range(len(sections[d])):
160 if d=="x":
161 v_p_min=v_p[mats[0][0][i]]
162 for q in range(len(sections["y"])):
163 for r in range(len(sections["z"])):
164 v_p_min=min(v_p[mats[r][q][i]],v_p_min)
165 elif d=="y":
166 v_p_min=v_p[mats[0][i][0]]
167 for q in range(len(sections["x"])):
168 for r in range(len(sections["z"])):
169 v_p_min=min(v_p[mats[r][i][q]],v_p_min)
170 elif d=="z":
171 v_p_min=v_p[mats[i][0][0]]
172 for q in range(len(sections["x"])):
173 for r in range(len(sections["y"])):
174 v_p_min=min(v_p[mats[i][r][q]],v_p_min)
175 num_elem[d].append(max(1,int(sections[d][i] * v_p_ref/v_p_min /resolution+0.5)))
176
177 ne_x=sum(num_elem["x"])
178 ne_y=sum(num_elem["y"])
179 ne_z=sum(num_elem["z"])
180 netotal=ne_x*ne_y*ne_z
181 if output: print "grid : %s x %s x %s (%s elements)"%(ne_x,ne_y,ne_z,netotal)
182 dom=Brick(ne_x,ne_y,ne_z,l0=o*ne_x,l1=o*ne_y,l2=o*ne_z,order=o)
183 x_old=dom.getX()
184 x_new=0
185
186 for d in sections:
187 if d=="x":
188 i=0
189 f=[1,0,0]
190 if d=="y":
191 i=1
192 f=[0,1,0]
193 if d=="z":
194 i=2
195 f=[0,0,1]
196 x=x_old[i]
197
198 p=origin[d]
199 ne=0
200 s=0.
201
202 for i in range(len(sections[d])-1):
203 msk=whereNonPositive(x-o*ne+0.5)
204 s=s*msk + (sections[d][i]/(o*num_elem[d][i])*(x-o*ne)+p)*(1.-msk)
205 ne+=num_elem[d][i]
206 p+=sections[d][i]
207 x_new=x_new + s * f
208 dom.setX(x_new)
209
210 fs=Function(dom)
211 x=Function(dom).getX()
212 x0=x[0]
213 x1=x[1]
214 x2=x[2]
215 p_z=origin["z"]
216 for i in range(len(mats)):
217 f_z=wherePositive(x2-p_z)*wherePositive(x2-p_z+sections["z"][i])
218 p_y=origin["y"]
219 for j in range(len(mats[i])):
220 f_y=wherePositive(x1-p_y)*wherePositive(x1-p_z+sections["y"][j])
221 p_x=origin["x"]
222 for k in range(len(mats[i][j])):
223 f_x=wherePositive(x0-p_x)*wherePositive(x0-p_x+sections["x"][k])
224 fs.setTags(mats[i][j][k],f_x*f_y*f_z)
225 p_x+=sections["x"][k]
226 p_y+=sections["y"][j]
227 p_z+=sections["z"][i]
228 return dom
229
230 def getMaterialProperties(dom):
231 rho =Scalar(rho_tab[bedrock],Function(dom))
232 eta =Scalar(eta_tab[bedrock],Function(dom))
233 mu =Scalar(mu_tab[bedrock],Function(dom))
234 lmbd=Scalar(lmbd_tab[bedrock],Function(dom))
235 tags=Scalar(bedrock,Function(dom))
236
237 for tag in rho_tab.keys():
238 rho.setTaggedValue(tag,rho_tab[tag])
239 eta.setTaggedValue(tag,eta_tab[tag])
240 mu.setTaggedValue(tag,mu_tab[tag])
241 lmbd.setTaggedValue(tag,lmbd_tab[tag])
242 tags.setTaggedValue(tag,tag)
243 return rho,mu,lmbd,eta
244
245
246 def wavePropagation(dom,rho,mu,lmbd,eta):
247 x=Function(dom).getX()
248 # ... open new PDE ...
249 mypde=LinearPDE(dom)
250 mypde.setSolverMethod(LinearPDE.LUMPING)
251 k=kronecker(Function(dom))
252 mypde.setValue(D=k*rho)
253
254 dt=(1./5.)*inf(dom.getSize()/sqrt((2*mu+lmbd)/rho))
255 if output: print "time step size = ",dt
256 # ... set initial values ....
257 n=0
258 t=0
259 t_write=0.
260 n_write=0
261 # initial value of displacement at point source is constant (U0=0.01)
262 # for first two time steps
263 u =Vector(0.,Solution(dom))
264 u_last=Vector(0.,Solution(dom))
265 v=Vector(0.,Solution(dom))
266
267 starttime = time.clock()
268 while t<t_end and n<n_end:
269 if output: print n+1,"-th time step t ",t+dt," max u and F: ",Lsup(u),
270 # ... get current stress ....
271 eps=symmetric(grad(u))
272 stress=lmbd*trace(eps)*k+2*mu*eps
273 # ... force due to event:
274 F=exp(-((t-tc)/tc_length)**2)*exp(-(length(x-xc)/src_radius)**2)*event
275 if output: print Lsup(F)
276 # ... get new acceleration ....
277 mypde.setValue(X=-stress,Y=F-eta*v)
278 a=mypde.getSolution()
279 # ... get new displacement ...
280 u_new=2*u-u_last+dt**2*a
281 # ... shift displacements ....
282 v=(u_new-u)/dt
283 u_last,u=u,u_new
284 # ... save current acceleration in units of gravity and displacements
285 if output:
286 if t>=t_write:
287 saveVTK("disp.%i.vtu"%n,displacement=u, amplitude=length(u))
288 t_write+=dt_write
289 n_write+=1
290 t+=dt
291 n+=1
292
293 endtime = time.clock()
294 totaltime = endtime-starttime
295 global netotal
296 print ">>number of elements: %s, total time: %s, per time step: %s <<"%(netotal,totaltime,totaltime/n)
297 if __name__ =="__main__":
298 dom=getDomain()
299 rho,mu,lmbd,eta=getMaterialProperties(dom)
300 wavePropagation(dom,rho,mu,lmbd,eta)

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