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""" |
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seismic wave propagation |
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@var __author__: name of author |
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@var __licence__: licence agreement |
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@var __url__: url entry point on documentation |
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@var __version__: version |
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@var __date__: date of the version |
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""" |
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__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
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http://www.access.edu.au |
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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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__author__="Lutz Gross, l.gross@uq.edu.au" |
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__url__="http://www.iservo.edu.au/esys/escript" |
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__version__="$Revision$" |
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__date__="$Date$" |
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from esys.escript import * |
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from esys.escript.linearPDEs import LinearPDE |
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from esys.finley import Brick |
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import time |
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output=True |
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n_end=10000 |
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resolution=10000. # number of elements per m |
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l=80000. # width and length m |
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h=30000. # height in m |
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o=1 # element order |
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rho_bedrock=8e3 |
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mu_bedrock=1.7e11 |
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lambda_bedrock=1.7e11 |
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l_x_water=10000 # length of water in x |
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l_y_water=10000 # length of water in y |
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h_water=max(2000,resolution) # depth of water region |
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water_tag=2 |
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rho_water=1e3 |
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mu_water=0. |
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lambda_water=1.e9 |
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d0_sand=10000 # thickness of sand region on surface |
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d_sand=max(2000,resolution) # thickness of sand layer under the water |
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sand_tag=3 |
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rho_sand=5e3 |
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mu_sand=1.5e10 |
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lambda_sand=1.5e10 |
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# location and geometrical size of event: |
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xc=[30000.,40000.,10000.] |
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src_radius = 0.1*h |
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# direction of event: |
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event=numarray.array([1.,0.,0.])*1.e6 |
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# time and length of the event |
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tc_length=2. |
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tc=sqrt(5.*tc_length) |
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if output: |
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print "event location = ",xc |
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print "radius of event = ",src_radius |
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print "time of event = ",tc |
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print "length of event = ",tc_length |
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print "direction = ",event |
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t_end=20. |
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def getDomain(): |
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""" |
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this defines a dom as a brick of length and width l and hight h |
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""" |
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global netotal |
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v_p_bedrock=sqrt((2*mu_bedrock+lambda_bedrock)/rho_bedrock) |
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v_p_sand=sqrt((2*mu_sand+lambda_sand)/rho_sand) |
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v_p_water=sqrt((2*mu_water+lambda_water)/rho_water) |
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print v_p_bedrock,v_p_sand,v_p_water |
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ne_l_x_bed=int((l-d0_sand-l_x_water)/resolution+0.5) |
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ne_l_y_bed=int((l-d0_sand-l_y_water)/resolution+0.5) |
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ne_h_bed=int((h-d_sand-h_water)/resolution+0.5) |
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ne_l_sand=int(d0_sand*v_p_bedrock/v_p_sand/resolution+0.5) |
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ne_h_sand=int(d_sand*v_p_bedrock/v_p_sand/resolution+0.5) |
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ne_l_x_water=int(l_x_water*v_p_bedrock/v_p_water/resolution+0.5) |
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ne_l_y_water=int(l_y_water*v_p_bedrock/v_p_water/resolution+0.5) |
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ne_h_water=int(h_water*v_p_bedrock/v_p_water/resolution+0.5) |
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ne_l_x=ne_l_x_bed+ne_l_sand+ne_l_x_water |
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ne_l_y=ne_l_y_bed+ne_l_sand+ne_l_y_water |
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ne_h=ne_h_bed+ne_h_sand+ne_h_water |
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print ne_l_x,ne_l_x_bed,ne_l_sand,ne_l_x_water |
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print ne_l_y,ne_l_y_bed,ne_l_sand,ne_l_y_water |
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print ne_h,ne_h_bed,ne_h_sand,ne_h_water |
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netotal=ne_l_x*ne_l_y*ne_h |
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if output: print "grid : %s x %s x %s (%s elements)"%(ne_l_x,ne_l_y,ne_h,netotal) |
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dom=Brick(ne_l_x,ne_l_y,ne_h,l0=o*ne_l_x,l1=o*ne_l_y,l2=o*ne_h,order=o) |
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x=dom.getX() |
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x0=x[0] |
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x0_new = (l-d0_sand-l_x_water)/(o*ne_l_x_bed)*x0 |
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msk=whereNonPositive(x0-o*ne_l_x_bed) |
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x0_new = x0_new * msk + (d0_sand/(o*ne_l_sand)*(x0-o*ne_l_x_bed)+l-d0_sand-l_x_water)*(1.-msk) |
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msk=whereNonPositive(x0-o*(ne_l_x_bed+ne_l_sand)) |
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x0_new = x0_new * msk + (l_x_water/(o*ne_l_x_water)*(x0-o*(ne_l_x_bed+ne_l_sand))+l-l_x_water)*(1.-msk) |
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x1=x[1] |
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x1_new = (l-d0_sand-l_y_water)/(o*ne_l_y_bed)*x1 |
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msk=whereNonPositive(x1-(o*ne_l_y_bed)) |
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x1_new = x1_new * msk + (d0_sand/(o*ne_l_sand)*(x1-o*ne_l_y_bed)+l-d0_sand-l_y_water)*(1.-msk) |
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msk=whereNonPositive(x1-o*(ne_l_y_bed+ne_l_sand)) |
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x1_new = x1_new * msk + (l_y_water/(o*ne_l_y_water)*(x1-o*(ne_l_y_bed+ne_l_sand))+l-l_y_water)*(1.-msk) |
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x2=x[2] |
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x2_new = (h-d_sand-h_water)/(o*ne_h_bed)*x2 |
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msk=whereNonPositive(x2-(o*ne_h_bed+1)) |
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x2_new = x2_new * msk + (d_sand/(o*ne_h_sand)*(x2-(o*ne_h_bed+1))+h-d_sand-h_water)*(1.-msk) |
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msk=whereNonPositive(x2-(o*(ne_h_bed+ne_h_sand)+1)) |
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x2_new = x2_new * msk + (h_water/(o*ne_h_water)*(x2-(o*(ne_h_bed+ne_h_sand)+1))+h-h_water)*(1.-msk) |
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dom.setX(x0_new*[1,0,0]+x1_new*[0,1,0]+x2_new*[0,0,1]) |
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fs=Function(dom) |
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x=Function(dom).getX() |
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fs.setTags(sand_tag,wherePositive(x[0]-(l-l_x_water-d0_sand)) \ |
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*wherePositive(x[1]-(l-l_y_water-d0_sand)) \ |
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*wherePositive(x[2]-(h-h_water-d_sand))) |
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fs.setTags(water_tag,wherePositive(x[0]-(l-l_x_water)) \ |
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*wherePositive(x[1]-(l-l_y_water)) \ |
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*wherePositive(x[2]-(h-h_water))) |
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return dom |
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def getMaterialProperties(dom): |
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rho =Scalar(rho_bedrock,Function(dom)) |
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rho.setTaggedValue(sand_tag,rho_sand) |
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rho.setTaggedValue(water_tag,rho_water) |
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lame_mu =Scalar(mu_bedrock,Function(dom)) |
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lame_mu.setTaggedValue(sand_tag,mu_sand) |
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lame_mu.setTaggedValue(water_tag,mu_water) |
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lame_lambda=Scalar(lambda_bedrock,Function(dom)) |
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lame_lambda.setTaggedValue(sand_tag,lambda_sand) |
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lame_lambda.setTaggedValue(water_tag,lambda_water) |
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return rho,lame_mu,lame_lambda |
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def wavePropagation(dom,rho,lame_mu,lame_lambda): |
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x=Function(dom).getX() |
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# ... open new PDE ... |
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mypde=LinearPDE(dom) |
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mypde.setSolverMethod(LinearPDE.LUMPING) |
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k=kronecker(Function(dom)) |
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mypde.setValue(D=k*rho) |
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v_p=sqrt((2*lame_mu+lame_lambda)/rho) |
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if output: print "v_p=",v_p |
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v_s=sqrt(lame_mu/rho) |
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if output: print "v_s=",v_s |
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dt=(1./5.)*inf(dom.getSize()/v_p) |
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if output: print "time step size = ",dt |
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# ... set initial values .... |
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n=0 |
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t=0 |
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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 =Vector(0.,Solution(dom)) |
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u_last=Vector(0.,Solution(dom)) |
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starttime = time.clock() |
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while t<t_end and n<n_end: |
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if output: print n+1,"-th time step t ",t+dt," max u and F: ",Lsup(u), |
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# ... get current stress .... |
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eps=symmetric(grad(u)) |
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stress=lame_lambda*trace(eps)*k+2*lame_mu*eps |
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# ... force due to event: |
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F=exp(-((t-tc)/tc_length)**2)*exp(-(length(x-xc)/src_radius)**2)*event |
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if output: print Lsup(F) |
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# ... get new acceleration .... |
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mypde.setValue(X=-stress,Y=F) |
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a=mypde.getSolution() |
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# ... get new displacement ... |
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u_new=2*u-u_last+dt**2*a |
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# ... shift displacements .... |
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u_last,u=u,u_new |
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# ... save current acceleration in units of gravity and displacements |
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if output: |
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if n%10==0: saveVTK("disp.%i.vtu"%(n/10),displacement=u, amplitude=length(u)) |
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t+=dt |
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n+=1 |
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endtime = time.clock() |
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totaltime = endtime-starttime |
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global netotal |
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print ">>number of elements: %s, total time: %s, per time step: %s <<"%(netotal,totaltime,totaltime/n) |
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if __name__ =="__main__": |
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dom=getDomain() |
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rho,lame_mu,lame_lambda=getMaterialProperties(dom) |
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wavePropagation(dom,rho,lame_mu,lame_lambda) |
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