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##############################################################################
#
# 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)
#
##############################################################################
from __future__ import division, print_function
__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"
"""
Author: Antony Hallam antony.hallam@uqconnect.edu.au
"""
############################################################FILE HEADER
# example10d.py
# Model of gravitational Potential for a gravity POLE.
#######################################################EXTERNAL MODULES
# To solve the problem it is necessary to import the modules we require.
import matplotlib
matplotlib.use('agg') #Its just here for automated testing
from esys.escript import * # This imports everything from the escript library
from esys.escript.unitsSI import *
from esys.escript.linearPDEs import LinearPDE # This defines LinearPDE as LinearPDE
from esys.weipa import saveVTK # This imports the VTK file saver from weipa
import os, sys #This package is necessary to handle saving our data.
from math import pi, sqrt, sin, cos
from esys.escript.pdetools import Projector, Locator
from esys.finley import ReadGmsh
import pylab as pl #Plotting package
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
try:
from scipy.optimize import leastsq
HAVE_SCIPY=True
except:
HAVE_SCIPY=False
try:
# This imports the rectangle domain function
from esys.finley import MakeDomain
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 and HAVE_SCIPY:
#################################################ESTABLISHING VARIABLES
#Domain related.
mx = 10000*m #meters - model length
my = 10000*m #meters - model width
#PDE related
rho=10.0
rholoc=[mx/2.,my/2.]
G=6.67300*10E-11
R=10
z=50.
################################################ESTABLISHING PARAMETERS
#the folder to put our outputs in, leave blank "" for script path
save_path= os.path.join("data","example10")
#ensure the dir exists
mkDir(save_path)
#####################################################ANALYTIC SOLUTION
def analytic_gz(x,z,R,drho):
G=6.67300*10E-11
return G*2*np.pi*R*R*drho*(z/(x*x+z*z))
sol_angz=[]
sol_anx=[]
for x in range(int(-mx/20),int(mx/20),10):
sol_angz.append(analytic_gz(x,z,R,rho))
sol_anx.append(x+mx/2)
##############INVERSION
def gzpot(p, y, x, *args):
#rho, rhox, rhoy, R = p
rhox=args[0]/2.; rhoy=args[1]/2.
rho, R, z =p
#Domain related.
mx = args[0]; my = args[1];
#PDE related
G=6.67300*10E-11
#DOMAIN CONSTRUCTION
domain=ReadGmsh('data/example10m/example10m.msh',2)
domx=Solution(domain).getX()
mask=wherePositive(R-length(domx-rholoc))
rhoe=rho*mask
kro=kronecker(domain)
q=whereZero(domx[1]-my)+whereZero(domx[1])+whereZero(domx[0])+whereZero(domx[0]-mx)
#ESCRIPT PDE CONSTRUCTION
mypde=LinearPDE(domain)
mypde.setValue(A=kro,Y=4.*np.pi*G*rhoe,q=q,r=0.0)
mypde.setSymmetryOn()
sol=mypde.getSolution()
g_field=grad(sol) #The graviational accelleration g.
g_fieldz=g_field*[0,1] #The vertical component of the g field.
gz=length(g_fieldz) #The magnitude of the vertical component.
#MODEL SIZE SAMPLING
sol_escgz=[]
sol_escx=[]
for i in range(0,len(x)):
sol_escgz.append([x[i],rhoy+z])
sample=[] # array to hold values
rec=Locator(gz.getFunctionSpace(),sol_escgz) #location to record
psol=rec.getValue(gz)
err = np.sum((np.array(y) - np.array(psol))**2.)
print("Lsup= ",Lsup(np.array(psol)-np.array(sol_angz))/Lsup(np.array(psol)))
return err
#Initial Guess
#guess=[400,mx/4,my/4,50]
guess=[15.,20.]
#plsq = leastsq(gzpot, guess, args=(sol_angz, sol_anx, mx, my, ndx, ndy),maxfev=20)
#print plsq
objf=[]
x=np.arange(1,20)
y=np.arange(1,20)
z=np.arange(40,60)
fig=pl.figure(figsize=(5,5))
for p in x:
objf.append(gzpot([p,10.,50.],sol_angz,sol_anx, mx, my))
sp=fig.add_subplot(311)
sp.plot(x,objf)
sp.set_title("Variable RHO")
objf=[]
for R in y:
objf.append(gzpot([10.,R,50.],sol_angz,sol_anx, mx, my))
sp=fig.add_subplot(312)
sp.plot(y,objf)
sp.set_title("Variable Radius")
objf=[]
for D in z:
objf.append(gzpot([10.,10.,D],sol_angz,sol_anx, mx, my))
sp=fig.add_subplot(313)
sp.plot(z,objf)
sp.set_title("Variable Depth")
fig.savefig("ex10e_objf.pdf",dpi=150)
#ob=np.array(objf)
#X,Y=pl.meshgrid(x,y)
#fig=pl.figure()
#ax=Axes3D(fig)
#ax.plot_surface(X,Y,ob)
#pl.show()
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