spectral.LegendreLobattoBasis

class spectral.LegendreLobattoBasis(domain: tuple[float, float] = (-1.0, 1.0))

Bases: SpectralBasis

Legendre-Gauss-Lobatto nodal polynomial basis.

Methods

__init__
diff_matrix	Return derivative matrix scaled to the physical domain.
mass_matrix	Return mass matrix associated with Legendre basis.
nodes	Return nodes mapped to the configured domain.

diff_matrix(nodes: ndarray) → ndarray

Return derivative matrix scaled to the physical domain.

Parameters:

nodesnp.ndarray

Physical domain nodes

Returns:

np.ndarray

Scaled differentiation matrix of shape (N, N)

mass_matrix(nodes: ndarray) → ndarray

Return mass matrix associated with Legendre basis.

Parameters:

nodesnp.ndarray

Physical domain nodes

Returns:

np.ndarray

Scaled mass matrix of shape (N, N)

nodes(num_points: int) → ndarray

Return nodes mapped to the configured domain.

Parameters:

num_pointsint

Number of Legendre-Gauss-Lobatto nodes

Returns:

np.ndarray

LGL nodes mapped to the physical domain