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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
# example09.py
# Antony Hallam
# Seismic Wave Equation Simulation using acceleration solution.
# 3D model with multiple layers. Layercake example.
#######################################################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, ReadMesh
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/example09b"
meshpath = "data/example09m"
mkDir(savepath)
#Geometric and material property related variables.
step=4.0 # the element size
vel=1800. #starting velocity
rhoc=2000. #starting density
nlayers=9 #number of layers in layercake model.
####################################################TESTING SWITCH
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
#Model Parameters
mx=40.
my=40.
mz=20.
outputs=5
else:
tend=0.1 # end time
#Model Parameters
mx=100.0 #x width of model
my=100.0 #y width of model
mz=50.0 #depth of model
outputs=200
####################################################TIME RELATED VARIABLES
h=0.00001 # time step
# data recording times
rtime=0.0 # first time to record
rtime_inc=tend/outputs # 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)
####################################################CREATING THE SOURCE FUNCTION
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
if (abs(source[it]) > ampmax):
ampmax = abs(source[it])
time[it]=t*h
# will introduce a spherical source at middle left of bottom face
xc=[mx/2,my/2,0]
####################################################DOMAIN CONSTRUCTION
domain=ReadMesh(os.path.join(meshpath,'example09lc.fly')) # create the domain
x=domain.getX() # get the locations of the nodes in the domain
lam=Scalar(0,Function(domain))
mu=Scalar(0,Function(domain))
rho=Scalar(0,Function(domain))
#Setting parameters for each layer in the model.
for i in range(0,nlayers):
rho.setTaggedValue("volume_%d"%i,rhoc+i*100.)
lamc=(vel+i*100.)**2.*(rhoc+i*100.)/2.
muc=(vel+i*100.)**2.*(rhoc+i*100.)/4.
lam.setTaggedValue("volume_%d"%i,lamc)
mu.setTaggedValue("volume_%d"%i,muc)
##########################################################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=rho*kmat) #set the general form value D
############################################FIRST TIME STEPS AND SOURCE
# define small radius around point xc
src_rad = 20; print("src radius= ",src_rad)
# set initial values for first two time steps with source terms
xb=FunctionOnBoundary(domain).getX()
yx=(cos(length(xb-xc)*3.1415/src_rad)+1)*whereNegative(length(xb-xc)-src_rad)
stop=Scalar(0.0,FunctionOnBoundary(domain))
stop.setTaggedValue("intface_0",1.0)
src_dir=numpy.array([0.,0.,1.0]) # defines direction of point source as down
mypde.setValue(y=source[0]*yx*src_dir*stop) #set the source as a function on the boundary
# initial value of displacement at point source is constant (U0=0.01)
# for first two time steps
u=[0.0,0.0,0.0]*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))#*abc
mypde.setValue(X=-stress) # 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,"ex09b.%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):
mypde.setValue(y=source[n]*yx*src_dir*stop) #set the source as a function on the boundary
print("time step %d, t=%s"%(n,t))
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