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from __future__ import division, print_function
##############################################################################
#
# Copyright (c) 2009-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
__copyright__="""Copyright (c) 2009-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
############################################################FILE HEADER
# example08b.py
# Antony Hallam
# Seismic Wave Equation Simulation using acceleration solution.
# Extend the solution in example 08a to use absorbing boundary
# conditions.
#######################################################EXTERNAL MODULES
import matplotlib
matplotlib.use('agg') #It's just here for automated testing
from esys.escript import *
from esys.weipa import saveVTK
import os
# smoothing operator
from esys.escript.pdetools import Projector, Locator
from esys.escript.unitsSI import *
import numpy as np
import pylab as pl
import matplotlib.cm as cm
from esys.escript.linearPDEs import LinearPDE, SolverOptions
try:
# This imports the rectangle domain function
from esys.finley import Rectangle
HAVE_FINLEY = True
except ImportError:
print("Finley module not available")
HAVE_FINLEY = False
########################################################MPI WORLD CHECK
if getMPISizeWorld() > 1:
import sys
print("This example will not run in an MPI world.")
sys.exit(0)
if HAVE_FINLEY:
#################################################ESTABLISHING VARIABLES
# where to save output data
savepath = "data/example08b"
mkDir(savepath)
#Geometric and material property related variables.
mx = 1000. # model lenght
my = 1000. # model width
ndx = 300 # steps in x direction
ndy = 300 # steps in y direction
xstep=mx/ndx # calculate the size of delta x
ystep=abs(my/ndy) # calculate the size of delta y
lam=3.462e9 #lames constant
mu=3.462e9 #bulk modulus
rho=1154. #density
# Time related variables.
testing=True
if testing:
print('The testing end time is currently selected. This severely limits the number of time iterations.')
print("Try changing testing to False for more iterations.")
tend=0.001
else:
tend=0.5 # end time
h=0.0001 # time step
# data recording times
rtime=0.0 # first time to record
rtime_inc=tend/50.0 # time increment to record
#Check to make sure number of time steps is not too large.
print("Time step size= ",h, "Expected number of outputs= ",tend/h)
U0=0.1 # amplitude of point source
dfeq=50 #Dominant Frequency
a = 2.0 * (np.pi * dfeq)**2.0
t0 = 5.0 / (2.0 * np.pi * dfeq)
srclength = 5. * t0
ls = int(srclength/h)
print('source length',ls)
source=np.zeros(ls,'float') # source array
decay1=np.zeros(ls,'float') # decay curve one
decay2=np.zeros(ls,'float') # decay curve two
time=np.zeros(ls,'float') # time values
g=np.log(0.01)/ls
ampmax=0
for it in range(0,ls):
t = it*h
tt = t-t0
dum1 = np.exp(-a * tt * tt)
source[it] = -2. * a * tt * dum1
# source[it] = exp(-a * tt * tt) !gaussian
if (abs(source[it]) > ampmax):
ampmax = abs(source[it])
#source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1)
#decay1[t]=np.exp(g*t)
#decay2[t]=(np.exp(-.1*g*t)-1)
time[it]=t*h
#tdecay=decay1*decay2*U0
#decay1=decay1*U0; decay2=decay2*U0
pl.clf();
pl.plot(source)
#pl.plot(time,decay1);pl.plot(time,decay2);
#pl.plot(time,tdecay)
pl.savefig(os.path.join(savepath,'source.png'))
# will introduce a spherical source at middle left of bottom face
xc=[mx/2,0]
####################################################DOMAIN CONSTRUCTION
domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain
x=domain.getX() # get the locations of the nodes in the domani
##########################################################ESTABLISH PDE
mypde=LinearPDE(domain) # create pde
mypde.setSymmetryOn() # turn symmetry on
# turn lumping on for more efficient solving
mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
kmat = kronecker(domain) # create the kronecker delta function of the domain
mypde.setValue(D=kmat*rho) #set the general form value D
##########################################################ESTABLISH ABC
# Define where the boundary decay will be applied.
bn=50.
bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn)
# btop=ystep*bn # don't apply to force boundary!!!
# locate these points in the domain
left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot
tgamma=0.85 # decay value for exponential function
def calc_gamma(G,npts):
func=np.sqrt(abs(-1.*np.log(G)/(npts**2.)))
return func
gleft = calc_gamma(tgamma,bleft)
gright = calc_gamma(tgamma,bleft)
gbottom= calc_gamma(tgamma,ystep*bn)
print('gamma', gleft,gright,gbottom)
# calculate decay functions
def abc_bfunc(gamma,loc,x,G):
func=exp(-1.*(gamma*abs(loc-x))**2.)
return func
fleft=abc_bfunc(gleft,bleft,x[0],tgamma)
fright=abc_bfunc(gright,bright,x[0],tgamma)
fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma)
# apply these functions only where relevant
abcleft=fleft*whereNegative(left)
abcright=fright*wherePositive(right)
abcbottom=fbottom*wherePositive(bottom)
# make sure the inside of the abc is value 1
abcleft=abcleft+whereZero(abcleft)
abcright=abcright+whereZero(abcright)
abcbottom=abcbottom+whereZero(abcbottom)
# multiply the conditions together to get a smooth result
abc=abcleft*abcright*abcbottom
#visualise the boundary function
#abcT=abc.toListOfTuples()
#abcT=np.reshape(abcT,(ndx+1,ndy+1))
#pl.clf(); pl.imshow(abcT); pl.colorbar();
#pl.savefig(os.path.join(savepath,"abc.png"))
############################################FIRST TIME STEPS AND SOURCE
# define small radius around point xc
src_length = 40; print("src_length = ",src_length)
# set initial values for first two time steps with source terms
y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
src_dir=np.array([0.,1.]) # defines direction of point source as down
y=y*src_dir
mypde.setValue(y=y) #set the source as a function on the boundary
# turn lumping on for more efficient solving
mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
# for first two time steps
u=[0.0,0.0]*wherePositive(x)
u_m1=u
####################################################ITERATION VARIABLES
n=0 # iteration counter
t=0 # time counter
##############################################################ITERATION
while t<tend:
# get current stress
g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))
mypde.setValue(X=-stress*abc) # set PDE values
accel = mypde.getSolution() #get PDE solution for accelleration
u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement
u_p1=u_p1*abc # apply boundary conditions
u_m1=u; u=u_p1 # shift values by 1
# save current displacement, acceleration and pressure
if (t >= rtime):
saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\
acceleration=length(accel),tensor=stress)
rtime=rtime+rtime_inc #increment data save time
# increment loop values
t=t+h; n=n+1
if (n < ls):
y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length)
y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary
print("time step %d, t=%s"%(n,t))
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