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#!/usr/bin/env python
# Python GetFEM++ interface
#
# Copyright (C) 2015-2015 Yves Renard
#
# This file is a part of GetFEM++
#
# GetFEM++ is free software; you can redistribute it and/or modify it
# under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation; either version 2.1 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
# License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
#
############################################################################
""" 2D Poisson problem test.
This program is used to check that python-getfem is working. This is
also a good example of use of GetFEM++.
Poisson problem solved with a Discontinuous Galerkin method (or
interior penalty method). See for instance
"Unified analysis of discontinuous Galerkin methods for elliptic
problems", D.N. Arnold, F. Brezzi, B. Cockburn, L.D. Marini, SIAM J.
Numer. Anal. vol. 39:5, pp 1749-1779, 2002.
$Id: demo_laplacian_DG.py 4429 2013-10-01 13:15:15Z renard $
"""
# Import basic modules
import getfem as gf
import numpy as np
## Parameters
NX = 20 # Mesh parameter.
Dirichlet_with_multipliers = True # Dirichlet condition with multipliers
# or penalization
dirichlet_coefficient = 1e10 # Penalization coefficient
interior_penalty_factor = 1e2*NX # Parameter of the interior penalty term
verify_neighbour_computation = True;
# Create a simple cartesian mesh
m = gf.Mesh('regular_simplices', np.arange(0,1+1./NX,1./NX), np.arange(0,1+1./NX,1./NX))
# Create a MeshFem for u and rhs fields of dimension 1 (i.e. a scalar field)
mfu = gf.MeshFem(m, 1)
mfrhs = gf.MeshFem(m, 1)
# Assign the discontinuous P2 fem to all convexes of the both MeshFem
mfu.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(2,2)'))
mfrhs.set_fem(gf.Fem('FEM_PK(2,2)'))
# Integration method used
mim = gf.MeshIm(m, gf.Integ('IM_TRIANGLE(4)'))
# Boundary selection
flst = m.outer_faces()
fnor = m.normal_of_faces(flst)
tleft = abs(fnor[1,:]+1) < 1e-14
ttop = abs(fnor[0,:]-1) < 1e-14
fleft = np.compress(tleft, flst, axis=1)
ftop = np.compress(ttop, flst, axis=1)
fneum = np.compress(True - ttop - tleft, flst, axis=1)
# Mark it as boundary
DIRICHLET_BOUNDARY_NUM1 = 1
DIRICHLET_BOUNDARY_NUM2 = 2
NEUMANN_BOUNDARY_NUM = 3
m.set_region(DIRICHLET_BOUNDARY_NUM1, fleft)
m.set_region(DIRICHLET_BOUNDARY_NUM2, ftop)
m.set_region(NEUMANN_BOUNDARY_NUM, fneum)
# Inner edges for the interior penalty terms
in_faces = m.inner_faces()
INNER_FACES=4
m.set_region(INNER_FACES, in_faces)
if (verify_neighbour_computation):
TEST_FACES=5
adjf = m.adjacent_face(42, 0);
if (len(adjf) != 2):
print ('No adjacent edge found, change the element number')
exit(1)
m.set_region(TEST_FACES, np.array([[42,adjf[0][0]], [0,adjf[1][0]]]));
# Interpolate the exact solution (Assuming mfu is a Lagrange fem)
Ue = mfu.eval('y*(y-1)*x*(x-1)+x*x*x*x*x')
# Interpolate the source term
F1 = mfrhs.eval('-(2*(x*x+y*y)-2*x-2*y+20*x*x*x)')
F2 = mfrhs.eval('[y*(y-1)*(2*x-1) + 5*x*x*x*x, x*(x-1)*(2*y-1)]')
# Model
md = gf.Model('real')
# Main unknown
md.add_fem_variable('u', mfu)
# Laplacian term on u
md.add_Laplacian_brick(mim, 'u')
# Volumic source term
md.add_initialized_fem_data('VolumicData', mfrhs, F1)
md.add_source_term_brick(mim, 'u', 'VolumicData')
# Neumann condition.
md.add_initialized_fem_data('NeumannData', mfrhs, F2)
md.add_normal_source_term_brick(mim, 'u', 'NeumannData',
NEUMANN_BOUNDARY_NUM)
# Dirichlet condition on the left.
md.add_initialized_fem_data("DirichletData", mfu, Ue)
if (Dirichlet_with_multipliers):
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mfu,
DIRICHLET_BOUNDARY_NUM1,
'DirichletData')
else:
md.add_Dirichlet_condition_with_penalization(mim, 'u', dirichlet_coefficient,
DIRICHLET_BOUNDARY_NUM1,
'DirichletData')
# Dirichlet condition on the top.
# Two Dirichlet brick in order to test the multiplier
# selection in the intersection.
if (Dirichlet_with_multipliers):
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mfu,
DIRICHLET_BOUNDARY_NUM2,
'DirichletData')
else:
md.add_Dirichlet_condition_with_penalization(mim, 'u', dirichlet_coefficient,
DIRICHLET_BOUNDARY_NUM2,
'DirichletData')
# Interior penalty terms
md.add_initialized_data('alpha', [interior_penalty_factor])
jump = "((u-Interpolate(u,neighbour_elt))*Normal)"
test_jump = "((Test_u-Interpolate(Test_u,neighbour_elt))*Normal)"
grad_mean = "((Grad_u+Interpolate(Grad_u,neighbour_elt))*0.5)"
grad_test_mean = "((Grad_Test_u+Interpolate(Grad_Test_u,neighbour_elt))*0.5)"
md.add_linear_generic_assembly_brick(mim, "-(({F}).({G}))-(({H}).({I}))+alpha*(({J}).({K}))".format(F=grad_mean, G=test_jump, H=jump, I=grad_test_mean, J=jump, K=test_jump), INNER_FACES);
gf.memstats()
# md.listvar()
# md.listbricks()
# Assembly of the linear system and solve.
md.solve()
# Main unknown
U = md.variable('u')
L2error = gf.compute(mfu, U-Ue, 'L2 norm', mim)
H1error = gf.compute(mfu, U-Ue, 'H1 norm', mim)
print 'Error in L2 norm : ', L2error
print 'Error in H1 norm : ', H1error
# Export data
mfu.export_to_pos('laplacian.pos', Ue,'Exact solution',
U,'Computed solution')
print 'You can view the solution with (for example):'
print 'gmsh laplacian.pos'
if (verify_neighbour_computation):
A=gf.asm('generic', mim, 1, 'u*Test_u*(Normal.Normal)', TEST_FACES, md)
B=gf.asm('generic', mim, 1, '-Interpolate(u,neighbour_elt)*Interpolate(Test_u,neighbour_elt)*(Interpolate(Normal,neighbour_elt).Normal)', TEST_FACES, md)
err_v = np.linalg.norm(A-B)
A=gf.asm('generic', mim, 1, '(Grad_u.Normal)*(Grad_Test_u.Normal)', TEST_FACES, md)
B=gf.asm('generic', mim, 1, '(Interpolate(Grad_u,neighbour_elt).Normal)*(Interpolate(Grad_Test_u,neighbour_elt).Normal)', TEST_FACES, md)
err_v = err_v + np.linalg.norm(A-B)
if (err_v > 1E-13):
print 'Test on neighbour element computation: error to big: ', err_v
exit(1)
if (H1error > 1e-3):
print 'Error too large !'
exit(1)
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