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