Skip to content

system_reduction#

Includes abstract classes for reducing the boundary system to a smaller system.

Classes:

  • SystemReducer –

    Interface for reducing the boundary system to a smaller system.

  • IdentityReducer –

    A system reducer that does not perform any reduction. It simply returns the input as output.

SystemReducer #

Bases: ABC

Interface for reducing the boundary system to a smaller system. The boundary system can exhibit sparsity or symmetries, which can be exploited to reduce the size of the system.

Methods:

  • contract_system –

    Contract the boundary system to a reduced system.

  • expand_solution –

    Expand the solution from the reduced system to the full system.

  • expand_residuals –

    Expand the residuals from the reduced system to the full system.

contract_system abstractmethod #

contract_system(boundary_system: tuple[NDArray, ...]) -> tuple[NDArray, ...]

Contract the boundary system to a reduced system. This method should identify and remove redundancies in the boundary system, resulting in a smaller system that is easier to solve.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

Returns:

  • reduced_system ( tuple[NDArray, ...] ) –

    The reduced boundary system.

expand_solution abstractmethod #

expand_solution(boundary_system: tuple[NDArray, ...], reduced_system: tuple[NDArray, ...], reduced_solution: NDArray | tuple[NDArray, ...]) -> NDArray | tuple[NDArray, ...]

Expand the solution from the reduced system to the full system. The method should be called after contract_system and solving the system. It should take the solution of the reduced system and map it back to the full system, filling in any missing values as necessary.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

  • reduced_system (tuple[NDArray, ...]) –

    The reduced boundary system.

  • reduced_solution (NDArray | tuple[NDArray, ...]) –

    The solution of the reduced system.

Returns:

  • full_solution ( NDArray | tuple[NDArray, ...] ) –

    The solution of the full system.

expand_residuals abstractmethod #

expand_residuals(boundary_system: tuple[NDArray, ...], reduced_system: tuple[NDArray, ...], rel_residuals: NDArray, abs_residuals: NDArray) -> tuple[NDArray, NDArray]

Expand the residuals from the reduced system to the full system. The method should be called after contract_system and solving the system. It should take the residuals of the reduced system and map them back to the full system, filling in any missing values as necessary.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

  • reduced_system (tuple[NDArray, ...]) –

    The reduced boundary system.

  • rel_residuals (NDArray) –

    The relative residuals of the reduced system.

  • abs_residuals (NDArray) –

    The absolute residuals of the reduced system.

Returns:

  • full_rel_residuals ( NDArray ) –

    The relative residuals of the full system.

  • full_abs_residuals ( NDArray ) –

    The absolute residuals of the full system.

IdentityReducer #

Bases: SystemReducer

A system reducer that does not perform any reduction. It simply returns the input as output. This can be used as a default reducer when no reduction is desired.

Methods:

contract_system #

contract_system(boundary_system: tuple[NDArray, ...]) -> tuple[NDArray, ...]

Do not contract the boundary system, return it as is. The retured system alias the input system.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

Returns:

  • reduced_system ( tuple[NDArray, ...] ) –

    The reduced boundary system.

expand_solution #

expand_solution(boundary_system: tuple[NDArray, ...], reduced_system: tuple[NDArray, ...], reduced_solution: NDArray | tuple[NDArray, ...]) -> NDArray | tuple[NDArray, ...]

Do not expand the solution, return it as is. The returned solution alias the input solution.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

  • reduced_system (tuple[NDArray, ...]) –

    The reduced boundary system.

  • reduced_solution (NDArray | tuple[NDArray, ...]) –

    The solution of the reduced system.

Returns:

  • full_solution ( NDArray | tuple[NDArray, ...] ) –

    The solution of the full system.

expand_residuals #

expand_residuals(boundary_system: tuple[NDArray, ...], reduced_system: tuple[NDArray, ...], rel_residuals: NDArray, abs_residuals: NDArray) -> tuple[NDArray, NDArray]

Do not expand the residuals, return them as is. The returned residuals alias the input residuals.

Parameters:

  • boundary_system (tuple[NDArray, ...]) –

    The full boundary system.

  • reduced_system (tuple[NDArray, ...]) –

    The reduced boundary system.

  • rel_residuals (NDArray) –

    The relative residuals of the reduced system.

  • abs_residuals (NDArray) –

    The absolute residuals of the reduced system.

Returns:

  • full_rel_residuals ( NDArray ) –

    The relative residuals of the full system.

  • full_abs_residuals ( NDArray ) –

    The absolute residuals of the full system.