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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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|
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""" |
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Author: Antony Hallam antony.hallam@uqconnect.edu.au |
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""" |
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############################################################FILE HEADER |
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# example08c.py |
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# Create either a 2D syncline or anticline model using pycad meshing |
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# tools. Wave equation solution. |
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|
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#######################################################EXTERNAL MODULES |
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import matplotlib |
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matplotlib.use('agg') #It's just here for automated testing |
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from esys.pycad import * #domain constructor |
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from esys.pycad.gmsh import Design #Finite Element meshing package |
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from esys.finley import MakeDomain #Converter for escript |
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import os #file path tool |
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from math import * # math package |
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from esys.escript import * |
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from esys.escript.unitsSI import * |
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from esys.escript.linearPDEs import LinearPDE |
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from esys.escript.pdetools import Projector |
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from cblib import toRegGrid, subsample |
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import pylab as pl #Plotting package |
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import numpy as np |
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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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#set modal to 1 for a syncline or -1 for an anticline structural |
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#configuration |
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modal=-1 |
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|
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# the folder to put our outputs in, leave blank "" for script path - |
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# note this folder path must exist to work |
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save_path= os.path.join("data","example08c") |
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mkDir(save_path) |
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|
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################################################ESTABLISHING PARAMETERS |
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#Model Parameters |
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width=1000.0*m #width of model |
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depth=1000.0*m #depth of model |
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dx=5 |
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xstep=dx # calculate the size of delta x |
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ystep=dx # calculate the size of delta y |
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|
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sspl=51 #number of discrete points in spline |
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dsp=width/(sspl-1) #dx of spline steps for width |
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dep_sp=500.0*m #avg depth of spline |
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h_sp=250.*m #heigh of spline |
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orit=-1.0 #orientation of spline 1.0=>up -1.0=>down |
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|
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vel2=1800.; vel1=3000. |
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rho2=2300.; rho1=3100. #density |
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mu2=(vel2**2.)*rho2/8.; mu1=(vel1**2.)*rho1/8. #bulk modulus |
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lam2=mu2*6.; lam1=mu1*6. #lames constant |
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|
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|
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# Time related variables. |
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tend=0.5 # end time |
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h=0.0001 # 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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# will introduce a spherical source at middle left of bottom face |
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xc=[width/2,0] |
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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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if (abs(source[it]) > ampmax): |
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ampmax = abs(source[it]) |
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time[t]=t*h |
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|
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####################################################DOMAIN CONSTRUCTION |
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# Domain Corners |
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p0=Point(0.0, 0.0, 0.0) |
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p1=Point(0.0, depth, 0.0) |
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p2=Point(width, depth, 0.0) |
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p3=Point(width, 0.0, 0.0) |
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|
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# Generate Material Boundary |
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x=[ Point(i*dsp\ |
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,dep_sp+modal*orit*h_sp*cos(pi*i*dsp/dep_sp+pi))\ |
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for i in range(0,sspl)\ |
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] |
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mysp = Spline(*tuple(x)) |
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# Start and end of material boundary. |
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x1=mysp.getStartPoint() |
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x2=mysp.getEndPoint() |
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|
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# Create TOP BLOCK |
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# lines |
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tbl1=Line(p0,x1) |
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tbl2=mysp |
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tbl3=Line(x2,p3) |
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l30=Line(p3, p0) |
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# curve |
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tblockloop = CurveLoop(tbl1,tbl2,tbl3,l30) |
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# surface |
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tblock = PlaneSurface(tblockloop) |
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# Create BOTTOM BLOCK |
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# lines |
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bbl1=Line(x1,p1) |
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bbl3=Line(p2,x2) |
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bbl4=-mysp |
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l12=Line(p1, p2) |
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# curve |
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bblockloop = CurveLoop(bbl1,l12,bbl3,bbl4) |
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|
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# surface |
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bblock = PlaneSurface(bblockloop) |
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|
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#clockwise check as splines must be set as polygons in the point order |
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#they were created. Otherwise get a line across plot. |
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bblockloop2=CurveLoop(mysp,Line(x2,p2),Line(p2,p1),Line(p1,x1)) |
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|
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################################################CREATE MESH FOR ESCRIPT |
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# Create a Design which can make the mesh |
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d=Design(dim=2, element_size=dx, order=2) |
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# Add the subdomains and flux boundaries. |
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d.addItems(PropertySet("top",tblock),PropertySet("bottom",bblock),\ |
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PropertySet("linetop",l30)) |
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# Create the geometry, mesh and Escript domain |
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d.setScriptFileName(os.path.join(save_path,"example08c.geo")) |
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d.setMeshFileName(os.path.join(save_path,"example08c.msh")) |
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domain=MakeDomain(d, optimizeLabeling=True) |
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x=domain.getX() |
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print "Domain has been generated ..." |
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|
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lam=Scalar(0,Function(domain)) |
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lam.setTaggedValue("top",lam1) |
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lam.setTaggedValue("bottom",lam2) |
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mu=Scalar(0,Function(domain)) |
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mu.setTaggedValue("top",mu1) |
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mu.setTaggedValue("bottom",mu2) |
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rho=Scalar(0,Function(domain)) |
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rho.setTaggedValue("top",rho1) |
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rho.setTaggedValue("bottom",rho2) |
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|
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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=rho*kmat) #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=20. |
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bleft=xstep*bn; bright=width-(xstep*bn); bbot=depth-(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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|
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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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|
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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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|
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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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xb=FunctionOnBoundary(domain).getX() |
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y=source[0]*(cos(length(x-xc)*3.1415/src_length)+1)*whereNegative(length(xb-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]*wherePositive(x) |
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u_m1=u |
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|
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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)) |
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mypde.setValue(X=-stress*abc) # 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(save_path,"ex08c.%05d.vtu"%n),\ |
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vector_displacement=u,displacement=length(u),\ |
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vector_acceleration=accel,acceleration=length(accel),\ |
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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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