def quadrature_rule(self):
dims = self.mesh_el_group.dim
if dims == 0:
return mp.ZeroDimensionalQuadrature()
elif dims == 1:
return mp.LegendreGaussQuadrature(self.order, force_dim_axis=True)
else:
return mp.XiaoGimbutasSimplexQuadrature(self.order, dims)
def _quadrature_rule(self):
dims = self.mesh_el_group.dim
if dims == 0:
return mp.Quadrature(np.empty((0, 1)), np.empty((0, 1)))
elif dims == 1:
return mp.LegendreGaussQuadrature(self.order)
else:
return mp.XiaoGimbutasSimplexQuadrature(self.order, dims)
def test_modal_coeffs_by_projection(dim):
shape = mp.Simplex(dim)
space = mp.space_for_shape(shape, order=5)
basis = mp.orthonormal_basis_for_space(space, shape)
quad = mp.XiaoGimbutasSimplexQuadrature(10, dim)
assert quad.exact_to >= 2 * space.order
modal_coeffs = np.random.randn(space.space_dim)
vdm = mp.vandermonde(basis.functions, quad.nodes)
evaluated = vdm @ modal_coeffs
modal_coeffs_2 = vdm.T @ (evaluated * quad.weights)
diff = modal_coeffs - modal_coeffs_2
assert la.norm(diff, 2) < 3e-13
def _(space: PN, shape: Simplex):
if not isinstance(shape, Simplex):
raise NotImplementedError((type(space).__name__, type(shape).__name))
if space.spatial_dim != shape.dim:
raise ValueError("spatial dimensions of shape and space must match")
import modepy as mp
if space.spatial_dim == 0:
quad = ZeroDimensionalQuadrature()
else:
try:
quad = mp.XiaoGimbutasSimplexQuadrature(space.order,
space.spatial_dim)
except QuadratureRuleUnavailable:
quad = mp.GrundmannMoellerSimplexQuadrature(
space.order // 2, space.spatial_dim)
assert quad.exact_to >= space.order
return quad