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

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Revision 3892 - (show annotations)
Tue Apr 10 08:57:23 2012 UTC (7 years ago) by jfenwick
File MIME type: text/x-python
File size: 9571 byte(s)
Merged changes across from the attempt2 branch.
This version builds and passes python2 tests.
It also passes most python3 tests.



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

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