def test_tri_mass_mat_trig():
"""Check the integral of some trig functions on a square using the mass matrix"""
from hedge.mesh.generator import make_square_mesh
from hedge.discretization.local import TriangleDiscretization
from math import sqrt, pi, cos, sin
mesh = make_square_mesh(a=-pi, b=pi, max_area=(2 * pi / 10) ** 2 / 2)
discr = discr_class(mesh, TriangleDiscretization(8), debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(lambda x, el: cos(x[0]) ** 2 * sin(x[1]) ** 2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = numpy.dot(ones, mass_op.apply(discr, f))
num_integral_2 = numpy.dot(f, mass_op.apply(discr, ones))
true_integral = pi ** 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
# print err_1, err_2
assert err_1 < 1e-10
assert err_2 < 1e-10
def test_tri_mass_mat_trig():
"""Check the integral of some trig functions on a square using the mass matrix"""
from hedge.mesh.generator import make_square_mesh
from hedge.discretization.local import TriangleDiscretization
from math import pi, cos, sin
mesh = make_square_mesh(a=-pi, b=pi, max_area=(2 * pi / 10)**2 / 2)
discr = discr_class(mesh,
TriangleDiscretization(8),
debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(
lambda x, el: cos(x[0])**2 * sin(x[1])**2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = numpy.dot(ones, mass_op.apply(discr, f))
num_integral_2 = numpy.dot(f, mass_op.apply(discr, ones))
true_integral = pi**2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
#print err_1, err_2
assert err_1 < 1e-10
assert err_2 < 1e-10
def test_quadrature_tri_mass_mat_monomial():
"""Check that quadrature integration on triangles is exact as designed."""
from hedge.mesh.generator import make_square_mesh
mesh = make_square_mesh(a=-1, b=1, max_area=4 * 1 / 8 + 0.001)
order = 4
discr = discr_class(
mesh, order=order, debug=discr_class.noninteractive_debug_flags(), quad_min_degrees={"quad": 3 * order}
)
m, n = 2, 1
f = Monomial((m, n))
f_vec = discr.interpolate_volume_function(lambda x, el: f(x))
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
vis.add_data(visf, [("f", f_vec * f_vec)])
visf.close()
from hedge.optemplate import MassOperator, Field, QuadratureGridUpsampler
f_fld = Field("f")
mass_op = discr.compile(MassOperator()(f_fld * f_fld))
from hedge.optemplate.primitives import make_common_subexpression as cse
f_upsamp = cse(QuadratureGridUpsampler("quad")(f_fld))
quad_mass_op = discr.compile(MassOperator()(f_upsamp * f_upsamp))
num_integral_1 = numpy.dot(ones, mass_op(f=f_vec))
num_integral_2 = numpy.dot(ones, quad_mass_op(f=f_vec))
true_integral = 4 / ((2 * m + 1) * (2 * n + 1))
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
print num_integral_1, num_integral_2, true_integral
print err_1, err_2
assert err_1 > 1e-8
assert err_2 < 1e-14
def test_quadrature_tri_mass_mat_monomial():
"""Check that quadrature integration on triangles is exact as designed."""
from hedge.mesh.generator import make_square_mesh
mesh = make_square_mesh(a=-1, b=1, max_area=4 * 1 / 8 + 0.001)
order = 4
discr = discr_class(mesh,
order=order,
debug=discr_class.noninteractive_debug_flags(),
quad_min_degrees={"quad": 3 * order})
m, n = 2, 1
f = Monomial((m, n))
f_vec = discr.interpolate_volume_function(lambda x, el: f(x))
from hedge.discretization import ones_on_volume
ones = ones_on_volume(discr)
if False:
from hedge.visualization import SiloVisualizer
vis = SiloVisualizer(discr)
visf = vis.make_file("test")
vis.add_data(visf, [("f", f_vec * f_vec)])
visf.close()
from hedge.optemplate import (MassOperator, Field, QuadratureGridUpsampler)
f_fld = Field("f")
mass_op = discr.compile(MassOperator()(f_fld * f_fld))
from hedge.optemplate.primitives import make_common_subexpression as cse
f_upsamp = cse(QuadratureGridUpsampler("quad")(f_fld))
quad_mass_op = discr.compile(MassOperator()(f_upsamp * f_upsamp))
num_integral_1 = numpy.dot(ones, mass_op(f=f_vec))
num_integral_2 = numpy.dot(ones, quad_mass_op(f=f_vec))
true_integral = 4 / ((2 * m + 1) * (2 * n + 1))
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
print num_integral_1, num_integral_2, true_integral
print err_1, err_2
assert err_1 > 1e-8
assert err_2 < 1e-14