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_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_1d_mass_mat_trig():
"""Check the integral of some trig functions on an interval using the mass
matrix
"""
from hedge.mesh.generator import make_uniform_1d_mesh
from hedge.discretization.local import IntervalDiscretization
from math import pi, cos
from numpy import dot
mesh = make_uniform_1d_mesh(-4 * pi, 9 * pi, 17, periodic=True)
discr = discr_class(mesh,
IntervalDiscretization(8),
debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(lambda x, el: cos(x[0])**2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = dot(ones, mass_op.apply(discr, f))
num_integral_2 = dot(f, mass_op.apply(discr, ones))
num_integral_3 = discr.integral(f)
true_integral = 13 * pi / 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
err_3 = abs(num_integral_3 - true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
def test_1d_mass_mat_trig():
"""Check the integral of some trig functions on an interval using the mass matrix"""
from hedge.mesh.generator import make_uniform_1d_mesh
from hedge.discretization.local import IntervalDiscretization
from math import sqrt, pi, cos, sin
from numpy import dot
mesh = make_uniform_1d_mesh(-4 * pi, 9 * pi, 17, periodic=True)
discr = discr_class(mesh, IntervalDiscretization(8), debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(lambda x, el: cos(x[0]) ** 2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = dot(ones, mass_op.apply(discr, f))
num_integral_2 = dot(f, mass_op.apply(discr, ones))
num_integral_3 = discr.integral(f)
true_integral = 13 * pi / 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
err_3 = abs(num_integral_3 - true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
