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Contents of /trunk/doc/examples/cookbook/example08c.py

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Revision 3089 - (show annotations)
Mon Aug 9 07:20:58 2010 UTC (8 years, 6 months ago) by ahallam
File MIME type: text/x-python
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Updates to example scripts - should now be working except for example09b.py which needs more memory.
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 pylab as pl #Plotting package
45 import numpy as np
46
47 ########################################################MPI WORLD CHECK
48 if getMPISizeWorld() > 1:
49 import sys
50 print "This example will not run in an MPI world."
51 sys.exit(0)
52
53 #################################################ESTABLISHING VARIABLES
54 #set modal to 1 for a syncline or -1 for an anticline structural
55 #configuration
56 modal=-1
57
58 # the folder to put our outputs in, leave blank "" for script path -
59 # note this folder path must exist to work
60 save_path= os.path.join("data","example08c")
61 mkDir(save_path)
62
63 ################################################ESTABLISHING PARAMETERS
64 #Model Parameters
65 width=1000.0*m #width of model
66 depth=1000.0*m #depth of model
67 dx=5
68 xstep=dx # calculate the size of delta x
69 ystep=dx # calculate the size of delta y
70
71 sspl=51 #number of discrete points in spline
72 dsp=width/(sspl-1) #dx of spline steps for width
73 dep_sp=500.0*m #avg depth of spline
74 h_sp=250.*m #heigh of spline
75 orit=-1.0 #orientation of spline 1.0=>up -1.0=>down
76
77 vel2=1800.; vel1=3000.
78 rho2=2300.; rho1=3100. #density
79 mu2=(vel2**2.)*rho2/8.; mu1=(vel1**2.)*rho1/8. #bulk modulus
80 lam2=mu2*6.; lam1=mu1*6. #lames constant
81
82
83 # Time related variables.
84 tend=0.5 # end time
85 h=0.0001 # time step
86 # data recording times
87 rtime=0.0 # first time to record
88 rtime_inc=tend/50.0 # time increment to record
89 # will introduce a spherical source at middle left of bottom face
90 xc=[width/2,0]
91 #Check to make sure number of time steps is not too large.
92 print "Time step size= ",h, "Expected number of outputs= ",tend/h
93
94 U0=0.1 # amplitude of point source
95 ls=500 # length of the source
96 source=np.zeros(ls,'float') # source array
97 decay1=np.zeros(ls,'float') # decay curve one
98 decay2=np.zeros(ls,'float') # decay curve two
99 time=np.zeros(ls,'float') # time values
100 g=np.log(0.01)/ls
101
102 dfeq=50 #Dominant Frequency
103 a = 2.0 * (np.pi * dfeq)**2.0
104 t0 = 5.0 / (2.0 * np.pi * dfeq)
105 srclength = 5. * t0
106 ls = int(srclength/h)
107 print 'source length',ls
108 source=np.zeros(ls,'float') # source array
109 ampmax=0
110 for it in range(0,ls):
111 t = it*h
112 tt = t-t0
113 dum1 = np.exp(-a * tt * tt)
114 source[it] = -2. * a * tt * dum1
115 if (abs(source[it]) > ampmax):
116 ampmax = abs(source[it])
117 time[t]=t*h
118
119 ####################################################DOMAIN CONSTRUCTION
120 # Domain Corners
121 p0=Point(0.0, 0.0, 0.0)
122 p1=Point(0.0, depth, 0.0)
123 p2=Point(width, depth, 0.0)
124 p3=Point(width, 0.0, 0.0)
125
126 # Generate Material Boundary
127 x=[ Point(i*dsp\
128 ,dep_sp+modal*orit*h_sp*cos(pi*i*dsp/dep_sp+pi))\
129 for i in range(0,sspl)\
130 ]
131 mysp = Spline(*tuple(x))
132 # Start and end of material boundary.
133 x1=mysp.getStartPoint()
134 x2=mysp.getEndPoint()
135
136 # Create TOP BLOCK
137 # lines
138 tbl1=Line(p0,x1)
139 tbl2=mysp
140 tbl3=Line(x2,p3)
141 l30=Line(p3, p0)
142 # curve
143 tblockloop = CurveLoop(tbl1,tbl2,tbl3,l30)
144 # surface
145 tblock = PlaneSurface(tblockloop)
146 # Create BOTTOM BLOCK
147 # lines
148 bbl1=Line(x1,p1)
149 bbl3=Line(p2,x2)
150 bbl4=-mysp
151 l12=Line(p1, p2)
152 # curve
153 bblockloop = CurveLoop(bbl1,l12,bbl3,bbl4)
154
155 # surface
156 bblock = PlaneSurface(bblockloop)
157
158 #clockwise check as splines must be set as polygons in the point order
159 #they were created. Otherwise get a line across plot.
160 bblockloop2=CurveLoop(mysp,Line(x2,p2),Line(p2,p1),Line(p1,x1))
161
162 ################################################CREATE MESH FOR ESCRIPT
163 # Create a Design which can make the mesh
164 d=Design(dim=2, element_size=dx, order=2)
165 # Add the subdomains and flux boundaries.
166 d.addItems(PropertySet("top",tblock),PropertySet("bottom",bblock),\
167 PropertySet("linetop",l30))
168 # Create the geometry, mesh and Escript domain
169 d.setScriptFileName(os.path.join(save_path,"example08c.geo"))
170 d.setMeshFileName(os.path.join(save_path,"example08c.msh"))
171 domain=MakeDomain(d, optimizeLabeling=True)
172 x=domain.getX()
173 print "Domain has been generated ..."
174
175 lam=Scalar(0,Function(domain))
176 lam.setTaggedValue("top",lam1)
177 lam.setTaggedValue("bottom",lam2)
178 mu=Scalar(0,Function(domain))
179 mu.setTaggedValue("top",mu1)
180 mu.setTaggedValue("bottom",mu2)
181 rho=Scalar(0,Function(domain))
182 rho.setTaggedValue("top",rho1)
183 rho.setTaggedValue("bottom",rho2)
184
185 ##########################################################ESTABLISH PDE
186 mypde=LinearPDE(domain) # create pde
187 mypde.setSymmetryOn() # turn symmetry on
188 # turn lumping on for more efficient solving
189 #mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING)
190 kmat = kronecker(domain) # create the kronecker delta function of the domain
191 mypde.setValue(D=rho*kmat) #set the general form value D
192
193 ##########################################################ESTABLISH ABC
194 # Define where the boundary decay will be applied.
195 bn=20.
196 bleft=xstep*bn; bright=width-(xstep*bn); bbot=depth-(ystep*bn)
197 # btop=ystep*bn # don't apply to force boundary!!!
198
199 # locate these points in the domain
200 left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
201
202 tgamma=0.85 # decay value for exponential function
203 def calc_gamma(G,npts):
204 func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
205 return func
206
207 gleft = calc_gamma(tgamma,bleft)
208 gright = calc_gamma(tgamma,bleft)
209 gbottom= calc_gamma(tgamma,ystep*bn)
210
211 print 'gamma', gleft,gright,gbottom
212
213 # calculate decay functions
214 def abc_bfunc(gamma,loc,x,G):
215 func=exp(-1.*(gamma*abs(loc-x))**2.)
216 return func
217
218 fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
219 fright=abc_bfunc(gright,bright,x[0],tgamma)
220 fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
221 # apply these functions only where relevant
222 abcleft=fleft*whereNegative(left)
223 abcright=fright*wherePositive(right)
224 abcbottom=fbottom*wherePositive(bottom)
225 # make sure the inside of the abc is value 1
226 abcleft=abcleft+whereZero(abcleft)
227 abcright=abcright+whereZero(abcright)
228 abcbottom=abcbottom+whereZero(abcbottom)
229 # multiply the conditions together to get a smooth result
230 abc=abcleft*abcright*abcbottom
231
232 ############################################FIRST TIME STEPS AND SOURCE
233 # define small radius around point xc
234 src_length = 40; print "src_length = ",src_length
235 # set initial values for first two time steps with source terms
236 xb=FunctionOnBoundary(domain).getX()
237 y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(xb-src_length))
238 src_dir=numpy.array([0.,1.]) # defines direction of point source as down
239 y=y*src_dir
240 mypde.setValue(y=y) #set the source as a function on the boundary
241 # initial value of displacement at point source is constant (U0=0.01)
242 # for first two time steps
243 u=[0.0,0.0]*wherePositive(x)
244 u_m1=u
245
246 ####################################################ITERATION VARIABLES
247 n=0 # iteration counter
248 t=0 # time counter
249 ##############################################################ITERATION
250 while t<tend:
251 # get current stress
252 g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
253 mypde.setValue(X=-stress*abc) # set PDE values
254 accel = mypde.getSolution() #get PDE solution for accelleration
255 u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
256 u_p1=u_p1*abc # apply boundary conditions
257 u_m1=u; u=u_p1 # shift values by 1
258 # save current displacement, acceleration and pressure
259 if (t >= rtime):
260 saveVTK(os.path.join(save_path,"ex08c.%05d.vtu"%n),\
261 vector_displacement=u,displacement=length(u),\
262 vector_acceleration=accel,acceleration=length(accel),\
263 tensor=stress)
264 rtime=rtime+rtime_inc #increment data save time
265 # increment loop values
266 t=t+h; n=n+1
267 if (n < ls):
268 y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
269 y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
270 print n,"-th time step t ",t

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