mass_matrices.py¶
Given a CoordinateTransformation
instance which stands for a
mapping , we compute the
mass matrices, ,
, and
, of spaces
, ,
and .
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- class mass_matrices.MassMatrices(bf, ct, quad_degree=None)[source]¶
The mass matrices.
- Parameters:
ct (CoordinateTransformation) – A CoordinateTransformation instance that represents the mapping .
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 isNone
, a suitable degree will be obtained frombf
.
- 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-2', 'Lobatto-2', 'Lobatto-2') >>> mm = MassMatrices(bf, ct) >>> mm.quad_degree [4, 4, 4] >>> MN = mm.NP >>> np.shape(MN) (27, 27) >>> ME = mm.EP >>> np.shape(ME) (54, 54) >>> MF = mm.FP >>> np.shape(MF) (36, 36) >>> MV = mm.VP >>> np.shape(MV) (8, 8) >>> MN[13, :].toarray() array([[0.00069202, 0.00092145, 0.00016439, 0.00092145, 0.01896296, 0.00381929, 0.00016439, 0.00381929, 0.00016439, ... >>> ME[25, :].toarray() array([[ 2.84993722e-04, 2.18286425e-02, 2.31867356e-02, 8.84765301e-03, 7.36065685e-04, -6.34982123e-03,... >>> MF[30,:].toarray() array([[ 9.57306626e-03, 1.40151619e-02, -3.83134271e-03, -1.56689038e-01, 5.83237762e-02, 7.05662159e-02,... >>> MV.toarray() array([[12.32813585, -0.99033139, -0.99033139, 0.29781084, -0.99033139, 0.29781084, 0.29781084, -0.04159915], [-0.99033139, 16.33440736, 0.29781084, -3.27422609, 0.29781084, -3.27422609, -0.04159915, 0.29781084],...
- property EP¶
The mass matrix .
- Returns:
Return a csc_matrix representing the mass matrix.
- property FP¶
The mass matrix .
- Returns:
Return a csc_matrix representing the mass matrix.
- property NP¶
The mass matrix .
- Returns:
Return a csc_matrix representing the mass matrix.
- property VP¶
The mass matrix .
- Returns:
Return a csc_matrix representing the mass matrix.
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