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######################################################## |
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# |
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# Copyright (c) 2009-2010 by University of Queensland |
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# Earth Systems Science Computational Center (ESSCC) |
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# http://www.uq.edu.au/esscc |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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######################################################## |
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__copyright__="""Copyright (c) 2009-2010 by University of Queensland |
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Earth Systems Science Computational Center (ESSCC) |
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http://www.uq.edu.au/esscc |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="https://launchpad.net/escript-finley" |
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############################################################FILE HEADER |
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# example08b.py |
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# Antony Hallam |
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# Seismic Wave Equation Simulation using acceleration solution. |
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# Extend the solution in example 08a to use absorbing boundary |
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# conditions. |
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|
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#######################################################EXTERNAL MODULES |
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from esys.escript import * |
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from esys.finley import Rectangle |
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import os |
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# smoothing operator |
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from esys.escript.pdetools import Projector, Locator |
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from esys.escript.unitsSI import * |
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import numpy as np |
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import pylab as pl |
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import matplotlib.cm as cm |
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from esys.escript.linearPDEs import LinearPDE |
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|
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########################################################MPI WORLD CHECK |
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if getMPISizeWorld() > 1: |
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import sys |
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print "This example will not run in an MPI world." |
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sys.exit(0) |
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|
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#################################################ESTABLISHING VARIABLES |
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# where to save output data |
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savepath = "data/example08b" |
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mkDir(savepath) |
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#Geometric and material property related variables. |
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mx = 1000. # model lenght |
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my = 1000. # model width |
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ndx = 500 # steps in x direction |
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ndy = 500 # steps in y direction |
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xstep=mx/ndx # calculate the size of delta x |
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ystep=abs(my/ndy) # calculate the size of delta y |
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lam=3.462e9 #lames constant |
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mu=3.462e9 #bulk modulus |
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rho=1154. #density |
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# Time related variables. |
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tend=0.5 # end time |
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h=0.0005 # time step |
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# data recording times |
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rtime=0.0 # first time to record |
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rtime_inc=tend/50.0 # time increment to record |
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#Check to make sure number of time steps is not too large. |
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print "Time step size= ",h, "Expected number of outputs= ",tend/h |
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|
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U0=0.1 # amplitude of point source |
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ls=500 # length of the source |
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source=np.zeros(ls,'float') # source array |
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decay1=np.zeros(ls,'float') # decay curve one |
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decay2=np.zeros(ls,'float') # decay curve two |
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time=np.zeros(ls,'float') # time values |
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g=np.log(0.01)/ls |
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|
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dfeq=50 #Dominant Frequency |
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a = 2.0 * (np.pi * dfeq)**2.0 |
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t0 = 5.0 / (2.0 * np.pi * dfeq) |
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srclength = 5. * t0 |
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ls = int(srclength/h) |
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print 'source length',ls |
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source=np.zeros(ls,'float') # source array |
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ampmax=0 |
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for it in range(0,ls): |
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t = it*h |
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tt = t-t0 |
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dum1 = np.exp(-a * tt * tt) |
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source[it] = -2. * a * tt * dum1 |
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# source[it] = exp(-a * tt * tt) !gaussian |
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if (abs(source[it]) > ampmax): |
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ampmax = abs(source[it]) |
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#source[t]=np.exp(g*t)*U0*np.sin(2.*np.pi*t/(0.75*ls))*(np.exp(-.1*g*t)-1) |
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#decay1[t]=np.exp(g*t) |
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#decay2[t]=(np.exp(-.1*g*t)-1) |
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time[t]=t*h |
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#tdecay=decay1*decay2*U0 |
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#decay1=decay1*U0; decay2=decay2*U0 |
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pl.clf(); |
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pl.plot(source) |
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#pl.plot(time,decay1);pl.plot(time,decay2); |
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#pl.plot(time,tdecay) |
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pl.savefig(os.path.join(savepath,'source.png')) |
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# will introduce a spherical source at middle left of bottom face |
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xc=[mx/2,0] |
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####################################################DOMAIN CONSTRUCTION |
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domain=Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy,order=2) # create the domain |
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x=domain.getX() # get the locations of the nodes in the domani |
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##########################################################ESTABLISH PDE |
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mypde=LinearPDE(domain) # create pde |
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mypde.setSymmetryOn() # turn symmetry on |
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# turn lumping on for more efficient solving |
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mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING) |
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kmat = kronecker(domain) # create the kronecker delta function of the domain |
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mypde.setValue(D=kmat*rho) #set the general form value D |
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|
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##########################################################ESTABLISH ABC |
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# Define where the boundary decay will be applied. |
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bn=50. |
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bleft=xstep*bn; bright=mx-(xstep*bn); bbot=my-(ystep*bn) |
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# btop=ystep*bn # don't apply to force boundary!!! |
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# locate these points in the domain |
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left=x[0]-bleft; right=x[0]-bright; bottom=x[1]-bbot |
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tgamma=0.85 # decay value for exponential function |
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def calc_gamma(G,npts): |
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func=np.sqrt(abs(-1.*np.log(G)/(npts**2.))) |
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return func |
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gleft = calc_gamma(tgamma,bleft) |
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gright = calc_gamma(tgamma,bleft) |
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gbottom= calc_gamma(tgamma,ystep*bn) |
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print 'gamma', gleft,gright,gbottom |
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# calculate decay functions |
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def abc_bfunc(gamma,loc,x,G): |
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func=exp(-1.*(gamma*abs(loc-x))**2.) |
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return func |
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fleft=abc_bfunc(gleft,bleft,x[0],tgamma) |
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fright=abc_bfunc(gright,bright,x[0],tgamma) |
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fbottom=abc_bfunc(gbottom,bbot,x[1],tgamma) |
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# apply these functions only where relevant |
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abcleft=fleft*whereNegative(left) |
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abcright=fright*wherePositive(right) |
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abcbottom=fbottom*wherePositive(bottom) |
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# make sure the inside of the abc is value 1 |
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abcleft=abcleft+whereZero(abcleft) |
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abcright=abcright+whereZero(abcright) |
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abcbottom=abcbottom+whereZero(abcbottom) |
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# multiply the conditions together to get a smooth result |
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abc=abcleft*abcright*abcbottom |
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#visualise the boundary function |
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#abcT=abc.toListOfTuples() |
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#abcT=np.reshape(abcT,(ndx+1,ndy+1)) |
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#pl.clf(); pl.imshow(abcT); pl.colorbar(); |
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#pl.savefig(os.path.join(savepath,"abc.png")) |
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############################################FIRST TIME STEPS AND SOURCE |
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# define small radius around point xc |
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src_length = 40; print "src_length = ",src_length |
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# set initial values for first two time steps with source terms |
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y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length) |
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src_dir=numpy.array([0.,-1.]) # defines direction of point source as down |
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y=y*src_dir |
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mypde.setValue(y=y) #set the source as a function on the boundary |
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# initial value of displacement at point source is constant (U0=0.01) |
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# for first two time steps |
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u=[0.0,0.0]*whereNegative(x) |
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u_m1=u |
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####################################################ITERATION VARIABLES |
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n=0 # iteration counter |
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t=0 # time counter |
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##############################################################ITERATION |
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while t<tend: |
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# get current stress |
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g=grad(u); stress=lam*trace(g)*kmat+mu*(g+transpose(g))*abc |
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mypde.setValue(X=-stress) # set PDE values |
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accel = mypde.getSolution() #get PDE solution for accelleration |
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u_p1=(2.*u-u_m1)+h*h*accel #calculate displacement |
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u_p1=u_p1*abc # apply boundary conditions |
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u_m1=u; u=u_p1 # shift values by 1 |
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# save current displacement, acceleration and pressure |
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if (t >= rtime): |
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saveVTK(os.path.join(savepath,"ex08b.%05d.vtu"%n),displacement=length(u),\ |
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acceleration=length(accel),tensor=stress) |
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rtime=rtime+rtime_inc #increment data save time |
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# increment loop values |
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t=t+h; n=n+1 |
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if (n < ls): |
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y=source[n]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(x-xc)-src_length) |
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y=y*src_dir; mypde.setValue(y=y) #set the source as a function on the boundary |
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print n,"-th time step t ",t |
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