mass_matrices_trace.py

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class mass_matrices_trace.MassMatricesTrace(bf, ct, quad_degree=None)[source]

The mass matrices of trace spaces \text{TN}_{N}(\partial\Omega), \text{TE}_{N-1}(\partial\Omega) and \text{TF}_{N-1}(\partial\Omega).

Parameters:

  • bf (MimeticBasisPolynomials) – A MimeticBasisPolynomials (not MimeticBasisPolynomials2D) instance.

  • ct (CoordinateTransformation) – A CoordinateTransformation instance that represents the mapping \Phi:\Omega_{\mathrm{ref}}\to\Omega.

  • quad_degree (list, tuple) – (default: None) The degree used for the numerical integral. It should be a list or tuple of three positive integers. If it is None, a suitable degree will be obtained from bf.

Example:

>>> from coordinate_transformation import CoordinateTransformation
>>> from coordinate_transformation import Phi, d_Phi
>>> from mimetic_basis_polynomials import MimeticBasisPolynomials
>>> ct = CoordinateTransformation(Phi, d_Phi)
>>> bf = MimeticBasisPolynomials('Lobatto-4', 'Lobatto-3', 'Lobatto-2')
>>> MMT = MassMatricesTrace(bf, ct)
>>> MMT.TF 
<52x52 sparse matrix of type '<class 'numpy.float64'>'...
property TE

The mass matrix \mathbb{M}_{\text{E}}.

Returns:

Return a csc_matrix representing the mass matrix.

property TF

The mass matrix \mathbb{M}_{\text{F}}.

Returns:

Return a csc_matrix representing the mass matrix.

property TN

The mass matrix \mathbb{M}_{\text{N}}.

Returns:

Return a csc_matrix representing the mass matrix.

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