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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Python GetFEM interface
#
# Copyright (C) 2004-2020 Yves Renard, Julien Pommier.
#
# 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.
$Id$
"""
import numpy as np
# Import basic modules
import getfem as gf
plot_result = False;
if plot_result:
import meshio
import matplotlib.pyplot as plt
from matplotlib import ticker
## Parameters
NX = 100 # Mesh parameter.
Dirichlet_with_multipliers = True # Dirichlet condition with multipliers
# or penalization
dirichlet_coefficient = 1e10 # Penalization coefficient
# 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 P2 fem to all elements of the both MeshFem
mfu.set_fem(gf.Fem('FEM_PK(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(np.logical_not(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)
# 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')
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
sl4 = gf.Slice(("none",), mfu, 1)
sl4.export_to_vtu('laplacian.vtu', "ascii", mfu, Ue, 'Exact_solution', mfu, U,'Computed_solution')
print('You can view the solution with (for example):')
print('paraview laplacian.vtu')
if plot_result:
reader = meshio.read('laplacian.vtu')
points = reader.points
cells = reader.cells[0].data
point_data = reader.point_data["Computed_solution"]
fig = plt.figure(figsize=(7, 7))
axes2 = fig.add_subplot(aspect="auto",projection='3d')
axes2.triplot(points[:, 0], points[:, 1], cells, color="gray")
contour = axes2.plot_trisurf(points[:, 0], points[:, 1],
point_data, cmap="jet")
fig.colorbar(contour)
axes2.view_init(30, 100)
fig.tight_layout()
formatter = ticker.ScalarFormatter(useMathText=True)
formatter.set_scientific(True)
axes2.yaxis.set_major_formatter(formatter)
axes2.set_title("uref")
fig.savefig("uref.pdf")
plt.show()
if (H1error > 1e-3):
print('Error too large !')
exit(1)
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