qttools.boundary_conditions.system_reduction

source module qttools.boundary_conditions.system_reduction

Classes

• SystemReducer — 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.

• IdentityReducer — 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.

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

• expand_solution — 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.

• expand_residuals — 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.

source method SystemReducer.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.

source method SystemReducer.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.

source method SystemReducer.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.

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

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

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

source method IdentityReducer.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.

source method IdentityReducer.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.

source method IdentityReducer.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.