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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)
#
##############################################################################
"""
a simple comparison for row-sum and HRZ lumping in case of the advection equation
"""
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 LinearSinglePDE, SolverOptions
from esys.escript.pdetools import Locator
from esys import finley
from math import pi
v=numpy.array([-1,0])
n=5.
def ref_u(x,t):
return whereNonPositive(x[0]-t)
#return exp(-5*(x[0]-t)**2)
def runTaylorGalerkinIncremental(order):
domain=finley.Rectangle(100,10,order)
x=domain.getX()
# test Velet scheme
dt=inf(domain.getSize()/length(v))*(1./6.)
q=whereZero(x[0])+whereZero(x[0]-1.)
mypde_f=LinearSinglePDE(domain)
mypde_f.setSymmetryOn()
mypde_f.setValue(D=1,q=q)
u_f=ref_u(x,0)
mypde_HRZ=LinearSinglePDE(domain)
mypde_HRZ.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
mypde_HRZ.setValue(D=1,q=q)
u_HRZ=ref_u(x,0)
mypde_RS=LinearSinglePDE(domain)
mypde_RS.getSolverOptions().setSolverMethod(SolverOptions.ROWSUM_LUMPING)
mypde_RS.setValue(D=1,q=q)
u_RS=ref_u(x,0)
l=Locator(domain,[0.5,0.5])
t=0
u=ref_u(x,t)
t_list=[t]
u_list=[l(u)]
f_list=[l(u_f)]
HRZ_list=[l(u_HRZ)]
RS_list=[l(u_RS)]
print(t_list[-1], u_list[-1], f_list[-1], HRZ_list[-1] , RS_list[-1])
while t< 1./Lsup(v):
t+=dt
u=ref_u(x,t)
mypde_f.setValue(X=-dt/2.*u_f*v, r=ref_u(x,t-dt/2)-u_f)
mypde_HRZ.setValue(X=-dt/2.*u_HRZ*v, r=ref_u(x,t-dt/2)-u_f)
mypde_RS.setValue(X=-dt/2.*u_RS*v, r=ref_u(x,t-dt/2)-u_f)
u_f_h=u_f+mypde_f.getSolution()
u_HRZ_h=u_HRZ+mypde_HRZ.getSolution()
u_RS_h=u_RS+mypde_RS.getSolution()
mypde_f.setValue(X=-dt*u_f_h*v, r=u-u_f)
mypde_HRZ.setValue(X=-dt*u_HRZ_h*v, r=u-u_HRZ)
mypde_RS.setValue(X=-dt*u_RS_h*v, r=u-u_RS)
u_f=u_f+mypde_f.getSolution()
u_HRZ=u_HRZ+mypde_HRZ.getSolution()
u_RS=u_RS+mypde_RS.getSolution()
t_list.append(t)
u_list.append(l(u))
f_list.append(l(u_f))
HRZ_list.append(l(u_HRZ))
RS_list.append(l(u_RS))
print(t_list[-1], u_list[-1], f_list[-1], HRZ_list[-1] , RS_list[-1], " : ",sup(u))
import matplotlib.pyplot as plt
if getMPIRankWorld() == 0:
plt.clf()
plt.plot(t_list, u_list, '-', label="exact", linewidth=1)
plt.plot(t_list, f_list, '-', label="full", linewidth=1)
plt.plot(t_list, HRZ_list, '-', label="HRZ lumping", linewidth=1)
plt.plot(t_list, RS_list, '-', label="row sum lumping", linewidth=1)
plt.axis([0.,max(t_list),-.3,2.])
plt.xlabel('time')
plt.ylabel('displacement')
plt.legend()
plt.savefig('lumping_SUPG_du_%d.png'%order, format='png')
def runTaylorGalerkinDirect(order):
domain=finley.Rectangle(500,10,order)
x=domain.getX()
# test Velet scheme
dt=inf(domain.getSize()/length(v))*(1./6.)
q=whereZero(x[0])+whereZero(x[0]-1.)
mypde_f=LinearSinglePDE(domain)
mypde_f.setSymmetryOn()
mypde_f.setValue(D=1,q=q)
u_f=ref_u(x,0)
mypde_HRZ=LinearSinglePDE(domain)
mypde_HRZ.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
mypde_HRZ.setValue(D=1,q=q)
u_HRZ=ref_u(x,0)
mypde_RS=LinearSinglePDE(domain)
mypde_RS.getSolverOptions().setSolverMethod(SolverOptions.ROWSUM_LUMPING)
mypde_RS.setValue(D=1,q=q)
u_RS=ref_u(x,0)
l=Locator(domain,[0.5,0.5])
t=0
u=ref_u(x,t)
t_list=[t]
u_list=[l(u)]
f_list=[l(u_f)]
HRZ_list=[l(u_HRZ)]
RS_list=[l(u_RS)]
print(t_list[-1], u_list[-1], f_list[-1], HRZ_list[-1] , RS_list[-1])
while t< 1./Lsup(v):
t+=dt
u=ref_u(x,t)
mypde_f.setValue(X=-dt/2.*u_f*v, r=ref_u(x,t-dt/2), Y=u_f )
mypde_HRZ.setValue(X=-dt/2.*u_HRZ*v, r=ref_u(x,t-dt/2), Y=u_HRZ)
mypde_RS.setValue(X=-dt/2.*u_RS*v, r=ref_u(x,t-dt/2), Y= u_RS)
u_f_h=mypde_f.getSolution()
u_HRZ_h=mypde_HRZ.getSolution()
u_RS_h=mypde_RS.getSolution()
mypde_f.setValue(X=-dt*u_f_h*v, r=u, Y=u_f )
mypde_HRZ.setValue(X=-dt*u_HRZ_h*v, r=u, Y=u_HRZ)
mypde_RS.setValue(X=-dt*u_RS_h*v, r=u, Y= u_RS)
u_f=mypde_f.getSolution()
u_HRZ=mypde_HRZ.getSolution()
u_RS=mypde_RS.getSolution()
t_list.append(t)
u_list.append(l(u))
f_list.append(l(u_f))
HRZ_list.append(l(u_HRZ))
RS_list.append(l(u_RS))
print(t_list[-1], u_list[-1], f_list[-1], HRZ_list[-1] , RS_list[-1], " : ",sup(u))
import matplotlib.pyplot as plt
if getMPIRankWorld() == 0:
plt.clf()
plt.plot(t_list, u_list, '-', label="exact", linewidth=1)
plt.plot(t_list, f_list, '-', label="full", linewidth=1)
plt.plot(t_list, HRZ_list, '-', label="HRZ lumping", linewidth=1)
plt.plot(t_list, RS_list, '-', label="row sum lumping", linewidth=1)
plt.axis([0.,max(t_list),-.3,2.])
plt.xlabel('time')
plt.ylabel('displacement')
plt.legend()
plt.savefig('lumping_SUPG_u_%d.png'%order, format='png')
# runTaylorGalerkinIncremental(1)
# runTaylorGalerkinIncremental(2)
runTaylorGalerkinDirect(1)
# runTaylorGalerkinDirect(2)
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