def main():
parser = ArgumentParser(description=__doc__)
parser.add_argument('-m', '--max-order', metavar='order', type=int,
action='store', dest='max_order',
default=10, help=helps['max_order'])
parser.add_argument('output_dir', help=helps['output_dir'])
options = parser.parse_args()
indir = InDir(options.output_dir)
a, b = symbols("a, b")
r, s = symbols("r, s")
x, y = symbols("x, y")
order = options.max_order
dim = 2
n_el_nod = get_n_el_nod(order, dim) # number of DOFs per element
simplexP = []
exponentM = np.zeros((n_el_nod, 3), dtype=np.int32)
coefM = np.zeros((n_el_nod, n_el_nod))
exponentList = []
for m, idx in enumerate(iter_by_order(order, dim)):
# print(m, idx)
exponentM[m, :dim] = idx
pa = jacobi_P(idx[0], 0, 0, a)
pb = jacobi_P(idx[1], 2 * idx[0] + 1, 0, b) * (1 - b) ** idx[0]
# print("P_{} = {}".format(m, pa*pb))
polrs = cancel((pa * pb).subs(b, s).subs(
a, 2 * (1 + r) / (1 - s) - 1))
# print("P_{} = {}".format(m, polrs))
polxy = expand(polrs.subs(r, 2 * x - 1).subs(s, 2 * y - 1))
# polxy = expand(polrs.subs(r, x).subs(s, y))
simplexP.append(simplify(polxy))
exponentList.append(x ** idx[0] * y ** idx[1])
for j, exponent in enumerate(exponentList):
coefM[m, j] = simplexP[m].as_coefficients_dict()[exponent]
print("P_{}{} = {}".format(m, idx, simplexP[m]))
print()
np.savetxt(indir("legendre2D_simplex_expos.txt"), exponentM, fmt="%d")
# are coefs always integers?
np.savetxt(indir("legendre2D_simplex_coefs.txt"), coefM, fmt="%d")
def __init__(self, name, geometry, order, extended=False):
super().__init__(name, geometry, order, extended)
if self.dim == 1:
return
if order <= 5:
self.coefM = simplex_coefM5[:self.n_nod, :self.n_nod]
self.expoM = simplex_expoM5[:self.n_nod, :]
return
indir = InDir(__file__)
try:
self.coefM = nm.loadtxt(
indir("legendre2D_simplex_coefs.txt")
)[:self.n_nod, :self.n_nod]
self.expoM = nm.loadtxt(
indir("legendre2D_simplex_expos.txt")
)[:self.n_nod, :]
except IOError as e:
raise IOError(
("File {} not found, run gen_legendre_simplex_base.py"
+ " to generate it. This is needed approx order > 5.")
.format(e.args[0]))
:math:`Y_r`.
"""
import numpy as nm
from sfepy import data_dir
from sfepy.base.base import Struct
from sfepy.base.ioutils import InDir
from sfepy.fem import extend_cell_data
from sfepy.linalg import norm_l2_along_axis
from sfepy.homogenization.coefficients import Coefficients
from band_gaps_conf import BandGapsRigidConf, get_pars, normalize
normalize # Make pyflakes happy...
incwd = InDir(__file__)
dim = 2
if dim == 3:
filename = data_dir + '/meshes/3d/special/cube_sphere.mesh'
else:
filename = data_dir + '/meshes/2d/special/circle_in_square.mesh'
output_dir = incwd('output/band_gaps_rigid')
# Rigid inclusion diameter.
yr_diameter = 0.125
# aluminium, in 1e+10 Pa
def main():
parser = ArgumentParser(description=__doc__)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-m',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=10,
help=helps['max_order'])
parser.add_argument('--plot',
action='store_true',
dest='plot',
default=False,
help=helps['plot'])
options = parser.parse_args()
max_order = options.max_order
(legs, clegs, dlegs, cdlegs, lobs, clobs, dlobs, cdlobs, kerns, ckerns,
dkerns, cdkerns, denoms) = gen_lobatto(max_order)
if options.plot:
plot_polys(1, lobs)
plot_polys(11, dlobs)
plot_polys(2, kerns)
plot_polys(21, dkerns)
plot_polys(3, legs, var_name='y')
plot_polys(31, dlegs, var_name='y')
plt.show()
indir = InDir(os.path.join(top_dir, 'sfepy/discrete/fem/extmods/'))
fd = open(indir('lobatto1d_template.h'), 'r')
template = fd.read()
fd.close
fd = open(indir('lobatto1d.h'), 'w')
out = []
append_declarations(out, clobs, 'Lobatto', 'lobatto')
append_declarations(out, cdlobs, 'Derivatives of Lobatto', 'd_lobatto')
append_declarations(out, ckerns, 'Kernel', 'kernel', shift=2)
append_declarations(out,
cdkerns,
'Derivatives of kernel',
'd_kernel',
shift=2)
append_declarations(out, clegs, 'Legendre', 'legendre')
append_declarations(out, cdlegs, 'Derivatives of Legendre', 'd_legendre')
fd.write(template.replace('// REPLACE_TEXT', ''.join(out)))
fd.close()
fd = open(indir('lobatto1d_template.c'), 'r')
template = fd.read()
fd.close()
fd = open(indir('lobatto1d.c'), 'w')
out = []
names_lobatto = append_polys(out, clobs, 'Lobatto', 'lobatto')
names_d_lobatto = append_polys(out, cdlobs, 'Derivatives of Lobatto',
'd_lobatto')
names_kernel = append_polys(out, ckerns, 'Kernel', 'kernel', shift=2)
names_d_kernel = append_polys(out,
cdkerns,
'Derivatives of kernel',
'd_kernel',
shift=2)
names_legendre = append_polys(out,
clegs,
'Legendre',
'legendre',
var_name='y')
names_d_legendre = append_polys(out,
cdlegs,
'Derivatives of Legendre',
'd_legendre',
var_name='y')
out.append('\n// Lists of functions.\n')
out.append('\nconst int32 max_order = %d;\n' % max_order)
append_lists(out, names_lobatto, max_order + 1)
append_lists(out, names_d_lobatto, max_order + 1)
append_lists(out, names_kernel, max_order - 1)
append_lists(out, names_d_kernel, max_order - 1)
append_lists(out, names_legendre, max_order + 1)
append_lists(out, names_d_legendre, max_order + 1)
fd.write(template.replace('// REPLACE_TEXT', ''.join(out)))
fd.close()
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-m',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=10,
help=help['max_order'])
parser.add_option('',
'--plot',
action='store_true',
dest='plot',
default=False,
help=help['plot'])
options, args = parser.parse_args()
max_order = options.max_order
(legs, clegs, dlegs, cdlegs, lobs, clobs, dlobs, cdlobs, kerns, ckerns,
dkerns, cdkerns, denoms) = gen_lobatto(max_order)
if options.plot:
plot_polys(1, lobs)
plot_polys(11, dlobs)
plot_polys(2, kerns)
plot_polys(21, dkerns)
plot_polys(3, legs, var_name='y')
plot_polys(31, dlegs, var_name='y')
plt.show()
indir = InDir(os.path.join(top_dir, 'sfepy/fem/extmods/'))
fd = open(indir('lobatto_template.pyx'), 'r')
template = fd.read()
fd.close()
filename = indir('lobatto.pyx')
fd = open(filename, 'w')
out = []
names_lobatto = append_polys(out, clobs, 'Lobatto', 'lobatto')
names_d_lobatto = append_polys(out, cdlobs, 'Derivatives of Lobatto',
'd_lobatto')
names_kernel = append_polys(out, ckerns, 'Kernel', 'kernel', shift=2)
names_d_kernel = append_polys(out,
cdkerns,
'Derivatives of kernel',
'd_kernel',
shift=2)
names_legendre = append_polys(out,
clegs,
'Legendre',
'legendre',
var_name='y')
names_d_legendre = append_polys(out,
cdlegs,
'Derivatives of Legendre',
'd_legendre',
var_name='y')
out.append('\n# Lists of functions.\n')
out.append('\ncdef int32 max_order = %d\n' % max_order)
append_lists(out, names_lobatto, max_order + 1)
append_lists(out, names_d_lobatto, max_order + 1)
append_lists(out, names_kernel, max_order - 1)
append_lists(out, names_d_kernel, max_order - 1)
append_lists(out, names_legendre, max_order + 1)
append_lists(out, names_d_legendre, max_order + 1)
fd.write(template.replace('REPLACE_TEXT', ''.join(out)))
fd.close()
