/[escript]/trunk/doc/examples/cookbook/example08c.py
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Contents of /trunk/doc/examples/cookbook/example08c.py

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Revision 3195 - (show annotations)
Wed Sep 22 00:28:04 2010 UTC (8 years, 5 months ago) by ahallam
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Shortened runtime of cookbook examples to aid testing.
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 """
23 Author: Antony Hallam antony.hallam@uqconnect.edu.au
24 """
25
26 ############################################################FILE HEADER
27 # example08c.py
28 # Create either a 2D syncline or anticline model using pycad meshing
29 # tools. Wave equation solution.
30
31 #######################################################EXTERNAL MODULES
32 import matplotlib
33 matplotlib.use('agg') #It's just here for automated testing
34 from esys.pycad import * #domain constructor
35 from esys.pycad.gmsh import Design #Finite Element meshing package
36 from esys.finley import MakeDomain #Converter for escript
37 import os #file path tool
38 from math import * # math package
39 from esys.escript import *
40 from esys.escript.unitsSI import *
41 from esys.escript.linearPDEs import LinearPDE
42 from esys.escript.pdetools import Projector
43 from cblib import toRegGrid, subsample
44 import matplotlib
45 matplotlib.use('agg') #It's just here for automated testing
46
47 import pylab as pl #Plotting package
48 import numpy as np
49
50 ########################################################MPI WORLD CHECK
51 if getMPISizeWorld() > 1:
52 import sys
53 print "This example will not run in an MPI world."
54 sys.exit(0)
55
56 #################################################ESTABLISHING VARIABLES
57 #set modal to 1 for a syncline or -1 for an anticline structural
58 #configuration
59 modal=-1
60
61 # the folder to put our outputs in, leave blank "" for script path -
62 # note this folder path must exist to work
63 save_path= os.path.join("data","example08c")
64 mkDir(save_path)
65
66 ################################################ESTABLISHING PARAMETERS
67 #Model Parameters
68 width=1000.0*m #width of model
69 depth=1000.0*m #depth of model
70 dx=5
71 xstep=dx # calculate the size of delta x
72 ystep=dx # calculate the size of delta y
73
74 sspl=51 #number of discrete points in spline
75 dsp=width/(sspl-1) #dx of spline steps for width
76 dep_sp=500.0*m #avg depth of spline
77 h_sp=250.*m #heigh of spline
78 orit=-1.0 #orientation of spline 1.0=>up -1.0=>down
79
80 vel2=1800.; vel1=3000.
81 rho2=2300.; rho1=3100. #density
82 mu2=(vel2**2.)*rho2/8.; mu1=(vel1**2.)*rho1/8. #bulk modulus
83 lam2=mu2*6.; lam1=mu1*6. #lames constant
84
85
86 # Time related variables.
87 testing=True
88 if testing:
89 print 'The testing end time is curerntly sellected this severely limits the number of time iterations.'
90 print "Try changing testing to False for more iterations."
91 tend=0.001
92 else:
93 tend=0.5 # end time
94
95 h=0.0001 # time step
96 # data recording times
97 rtime=0.0 # first time to record
98 rtime_inc=tend/50.0 # time increment to record
99 # will introduce a spherical source at middle left of bottom face
100 xc=[width/2,0]
101 #Check to make sure number of time steps is not too large.
102 print "Time step size= ",h, "Expected number of outputs= ",tend/h
103
104 U0=0.1 # amplitude of point source
105 ls=500 # length of the source
106 source=np.zeros(ls,'float') # source array
107 decay1=np.zeros(ls,'float') # decay curve one
108 decay2=np.zeros(ls,'float') # decay curve two
109 time=np.zeros(ls,'float') # time values
110 g=np.log(0.01)/ls
111
112 dfeq=50 #Dominant Frequency
113 a = 2.0 * (np.pi * dfeq)**2.0
114 t0 = 5.0 / (2.0 * np.pi * dfeq)
115 srclength = 5. * t0
116 ls = int(srclength/h)
117 print 'source length',ls
118 source=np.zeros(ls,'float') # source array
119 ampmax=0
120 for it in range(0,ls):
121 t = it*h
122 tt = t-t0
123 dum1 = np.exp(-a * tt * tt)
124 source[it] = -2. * a * tt * dum1
125 if (abs(source[it]) > ampmax):
126 ampmax = abs(source[it])
127 time[t]=t*h
128
129 ####################################################DOMAIN CONSTRUCTION
130 # Domain Corners
131 p0=Point(0.0, 0.0, 0.0)
132 p1=Point(0.0, depth, 0.0)
133 p2=Point(width, depth, 0.0)
134 p3=Point(width, 0.0, 0.0)
135
136 # Generate Material Boundary
137 x=[ Point(i*dsp\
138 ,dep_sp+modal*orit*h_sp*cos(pi*i*dsp/dep_sp+pi))\
139 for i in range(0,sspl)\
140 ]
141 mysp = Spline(*tuple(x))
142 # Start and end of material boundary.
143 x1=mysp.getStartPoint()
144 x2=mysp.getEndPoint()
145
146 # Create TOP BLOCK
147 # lines
148 tbl1=Line(p0,x1)
149 tbl2=mysp
150 tbl3=Line(x2,p3)
151 l30=Line(p3, p0)
152 # curve
153 tblockloop = CurveLoop(tbl1,tbl2,tbl3,l30)
154 # surface
155 tblock = PlaneSurface(tblockloop)
156 # Create BOTTOM BLOCK
157 # lines
158 bbl1=Line(x1,p1)
159 bbl3=Line(p2,x2)
160 bbl4=-mysp
161 l12=Line(p1, p2)
162 # curve
163 bblockloop = CurveLoop(bbl1,l12,bbl3,bbl4)
164
165 # surface
166 bblock = PlaneSurface(bblockloop)
167
168 #clockwise check as splines must be set as polygons in the point order
169 #they were created. Otherwise get a line across plot.
170 bblockloop2=CurveLoop(mysp,Line(x2,p2),Line(p2,p1),Line(p1,x1))
171
172 ################################################CREATE MESH FOR ESCRIPT
173 # Create a Design which can make the mesh
174 d=Design(dim=2, element_size=dx, order=2)
175 # Add the subdomains and flux boundaries.
176 d.addItems(PropertySet("top",tblock),PropertySet("bottom",bblock),\
177 PropertySet("linetop",l30))
178 # Create the geometry, mesh and Escript domain
179 d.setScriptFileName(os.path.join(save_path,"example08c.geo"))
180 d.setMeshFileName(os.path.join(save_path,"example08c.msh"))
181 domain=MakeDomain(d, optimizeLabeling=True)
182 x=domain.getX()
183 print "Domain has been generated ..."
184
185 lam=Scalar(0,Function(domain))
186 lam.setTaggedValue("top",lam1)
187 lam.setTaggedValue("bottom",lam2)
188 mu=Scalar(0,Function(domain))
189 mu.setTaggedValue("top",mu1)
190 mu.setTaggedValue("bottom",mu2)
191 rho=Scalar(0,Function(domain))
192 rho.setTaggedValue("top",rho1)
193 rho.setTaggedValue("bottom",rho2)
194
195 ##########################################################ESTABLISH PDE
196 mypde=LinearPDE(domain) # create pde
197 mypde.setSymmetryOn() # turn symmetry on
198 # turn lumping on for more efficient solving
199 #mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
200 kmat = kronecker(domain) # create the kronecker delta function of the domain
201 mypde.setValue(D=rho*kmat) #set the general form value D
202
203 ##########################################################ESTABLISH ABC
204 # Define where the boundary decay will be applied.
205 bn=20.
206 bleft=xstep*bn; bright=width-(xstep*bn); bbot=depth-(ystep*bn)
207 # btop=ystep*bn # don't apply to force boundary!!!
208
209 # locate these points in the domain
210 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
211
212 tgamma=0.85 # decay value for exponential function
213 def calc_gamma(G,npts):
214 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
215 return func
216
217 gleft = calc_gamma(tgamma,bleft)
218 gright = calc_gamma(tgamma,bleft)
219 gbottom= calc_gamma(tgamma,ystep*bn)
220
221 print 'gamma', gleft,gright,gbottom
222
223 # calculate decay functions
224 def abc_bfunc(gamma,loc,x,G):
225 func=exp(-1.*(gamma*abs(loc-x))**2.)
226 return func
227
228 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
229 fright=abc_bfunc(gright,bright,x[0],tgamma)
230 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
231 # apply these functions only where relevant
232 abcleft=fleft*whereNegative(left)
233 abcright=fright*wherePositive(right)
234 abcbottom=fbottom*wherePositive(bottom)
235 # make sure the inside of the abc is value 1
236 abcleft=abcleft+whereZero(abcleft)
237 abcright=abcright+whereZero(abcright)
238 abcbottom=abcbottom+whereZero(abcbottom)
239 # multiply the conditions together to get a smooth result
240 abc=abcleft*abcright*abcbottom
241
242 ############################################FIRST TIME STEPS AND SOURCE
243 # define small radius around point xc
244 src_length = 40; print "src_length = ",src_length
245 # set initial values for first two time steps with source terms
246 xb=FunctionOnBoundary(domain).getX()
247 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(xb-src_length))
248 src_dir=numpy.array([0.,1.]) # defines direction of point source as down
249 y=y*src_dir
250 mypde.setValue(y=y) #set the source as a function on the boundary
251 # initial value of displacement at point source is constant (U0=0.01)
252 # for first two time steps
253 u=[0.0,0.0]*wherePositive(x)
254 u_m1=u
255
256 ####################################################ITERATION VARIABLES
257 n=0 # iteration counter
258 t=0 # time counter
259 ##############################################################ITERATION
260 while t<tend:
261 # get current stress
262 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
263 mypde.setValue(X=-stress*abc) # set PDE values
264 accel = mypde.getSolution() #get PDE solution for accelleration
265 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
266 u_p1=u_p1*abc # apply boundary conditions
267 u_m1=u; u=u_p1 # shift values by 1
268 # save current displacement, acceleration and pressure
269 if (t >= rtime):
270 saveVTK(os.path.join(save_path,"ex08c.%05d.vtu"%n),\
271 vector_displacement=u,displacement=length(u),\
272 vector_acceleration=accel,acceleration=length(accel),\
273 tensor=stress)
274 rtime=rtime+rtime_inc #increment data save time
275 # increment loop values
276 t=t+h; n=n+1
277 if (n < ls):
278 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
279 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
280 print n,"-th time step t ",t

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