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##############################################################################
#
# Copyright (c) 2003-2018 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 print_function, division
__copyright__="""Copyright (c) 2003-2018 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"
from esys.escript import *
from esys.escript.linearPDEs import Poisson
from esys import finley
ne_list=[10,15,22,33,50,75]
height_list=[0.25,0.5,1.]
def getDomain(dim,ne,height):
if dim==2:
ne1=int(ne*height+0.5)
mydomain=finley.Rectangle(n0=ne,n1=ne1,l1=height,order=1)
totne=ne1*ne
else:
ne2=int(ne*height+0.5)
mydomain=finley.Brick(n0=ne,n1=ne,n2=ne2,l2=height,order=2)
totne=ne2*ne*ne
print("%d -dimensional domain generated."%dim)
print("height of the domain is ",height)
print("total number of elements is ",totne)
return mydomain
def Solve1(mydomain,height):
print("Fully constraint solution")
l=[1.,1.,1.]
l[mydomain.getDim()-1]=height
cf=ContinuousFunction(mydomain)
x=cf.getX()
#construct exact solution:
u_ex=Scalar(1.,cf)
for i in range(mydomain.getDim()):
u_ex*=x[i]*(x[i]-l[i])
#construct mask:
msk=Scalar(0.,cf)
for i in range(mydomain.getDim()):
msk+=whereZero(x[i])+whereZero(x[i]-l[i])
#construct right hand side
f=Scalar(0,cf)
for i in range(mydomain.getDim()):
f_p=Scalar(1,cf)
for j in range(mydomain.getDim()):
if i==j:
f_p*=-2.
else:
f_p*=x[j]*(x[j]-l[j])
f+=f_p
mypde=Poisson(mydomain)
mypde.setTolerance(1.e-10)
mypde.setValue(f=f,q=msk)
u=mypde.getSolution()
error=Lsup(u-u_ex)/Lsup(u_ex)
print("error = ",error)
return error
def Solve2(mydomain,height):
print("Partially constraint solution")
l=[1.,1.,1.]
l[mydomain.getDim()-1]=height
print(l)
cf=ContinuousFunction(mydomain)
x=cf.getX()
#construct exact solution:
u_ex=Scalar(1.,cf)
for i in range(mydomain.getDim()):
u_ex*=x[i]*(2*l[i]-x[i])
#construct mask:
msk=Scalar(0.,cf)
for i in range(mydomain.getDim()):
msk+=whereZero(x[i])
#construct right hand side
f=Scalar(0,cf)
for i in range(mydomain.getDim()):
f_p=Scalar(1,cf)
for j in range(mydomain.getDim()):
if i==j:
f_p*=2.
else:
f_p*=x[j]*(2*l[j]-x[j])
f+=f_p
mypde=Poisson(mydomain)
mypde.setTolerance(1.e-10)
mypde.setValue(f=f,q=msk)
u=mypde.getSolution()
error=Lsup(u-u_ex)/Lsup(u_ex)
print("error = ",error)
return error
def main() :
error=0
for ne in ne_list:
for dim in [2,3]:
# for dim in [2]:
for height in height_list:
print("***************************************************************")
mydomain= getDomain(dim,ne,height)
print("---------------------------------------------------------------")
error=max(error,Solve1(mydomain,height))
print("---------------------------------------------------------------")
error=max(error,Solve2(mydomain,height))
print("***************************************************************")
print("***************************************************************")
print("maximum error: ",error)
print("***************************************************************")
import profile as Pr, pstats as Ps
if __name__ == "__main__":
pr = Pr.Profile()
pr.calibrate(10000)
Pr.run('main()','eos_stats')
stats = Ps.Stats('eos_stats')
stats.strip_dirs()
stats.sort_stats('time')
stats.print_stats()
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