capytaine.bem.engines module

Definition of the methods to build influence matrices, using possibly some sparse structures.

class capytaine.bem.engines.BasicMatrixEngine(*, green_function=None, linear_solver='lu_decomposition')[source]

Bases: MatrixEngine

Default matrix engine.

Features:

  • Caching of the last computed matrices.

  • Supports plane symmetries and nested plane symmetries.

  • Linear solver can be customized. Default is lu_decomposition with caching of the LU decomposition.

Parameters:

  • green_function (AbstractGreenFunction) – the low level implementation used to compute the coefficients of the matrices.

  • linear_solver (str or function, optional) – Setting of the numerical solver for linear problems Ax = b. It can be set with the name of a preexisting solver (available: “lu_decomposition”, “lu_decompositon_with_overwrite” and “gmres”, the former is the default choice) or by passing directly a solver function.

build_S_matrix(mesh1, mesh2, free_surface, water_depth, wavenumber) → ndarray[source]

Similar to build_matrices, but returning only \(S\)

build_fullK_matrix(mesh1, mesh2, free_surface, water_depth, wavenumber) → ndarray[source]

Similar to build_matrices, but returning only full \(K\) (that is the three components of the gradient, not just the normal one)

build_matrices(mesh1, mesh2, free_surface, water_depth, wavenumber, adjoint_double_layer=True)[source]

Build the influence matrices between mesh1 and mesh2.

Parameters:

  • mesh1 (MeshLike or list of points) – mesh of the receiving body (where the potential is measured)

  • mesh2 (MeshLike) – mesh of the source body (over which the source distribution is integrated)

  • free_surface (float) – position of the free surface (default: \(z = 0\))

  • water_depth (float) – position of the sea bottom (default: \(z = -\infty\))

  • wavenumber (float) – wavenumber (default: 1.0)

  • adjoint_double_layer (bool, optional) – compute double layer for direct method (F) or adjoint double layer for indirect method (T) matrices (default: True)

Returns:

the matrices \(S\) and \(K\)

Return type:

tuple of matrix-like (Numpy arrays or BlockCirculantMatrix)

compute_ram_estimation(problem)[source]
green_function: AbstractGreenFunction
last_computed_matrices: Tuple[ndarray | BlockDiagonalMatrix | BlockCirculantMatrix, ndarray | BlockDiagonalMatrix | BlockCirculantMatrix | LUDecomposedMatrix | LUDecomposedBlockDiagonalMatrix | LUDecomposedBlockCirculantMatrix] | None
linear_solver(A: ndarray | BlockDiagonalMatrix | BlockCirculantMatrix | LUDecomposedMatrix | LUDecomposedBlockDiagonalMatrix | LUDecomposedBlockCirculantMatrix, b: ndarray) → ndarray[source]

Solve a linear system with left-hand side A and right-hand-side b

Parameters:

  • A (matrix-like) – Expected to be the second output of build_matrices

  • b (np.ndarray) – Vector of the correct length

Returns:

x – Vector such that A@x = b

Return type:

np.ndarray

class capytaine.bem.engines.Counter[source]

Bases: object

class capytaine.bem.engines.MatrixEngine[source]

Bases: ABC

Abstract method to build a matrix.

abstractmethod build_S_matrix(mesh1, mesh2, free_surface, water_depth, wavenumber)[source]
abstractmethod build_fullK_matrix(mesh1, mesh2, free_surface, water_depth, wavenumber)[source]
abstractmethod build_matrices(mesh1, mesh2, free_surface, water_depth, wavenumber, adjoint_double_layer)[source]
capytaine.bem.engines.solve_gmres(A, b)[source]