pygeon.numerics.linear_system module

Module for the LinearSystem class.

class pygeon.numerics.linear_system.LinearSystem(A, b=None)

Bases: object

Class for storing a linear system consisting of the matrix and its right-hand side. The class keeps track of essential boundary conditions and reduces the system appropriately before solving.

__init__(A, b=None)

Initialize a LinearSystem object.

Parameters:

• A (sps.csc_array) – The coefficient matrix of the linear system.

• b (np.ndarray, optional) – The right-hand side vector of the linear system. Defaults to None.

Returns:

None

reset_bc()

Reset the boundary conditions.

This method sets the degrees of freedom (is_dof) to True for all elements in the b vector, and sets the essential values (ess_vals) to zero for all elements in the b vector.

flag_ess_bc(is_ess_dof, ess_vals)

Flags the essential boundary conditions for the degrees of freedom specified by is_ess_dof.

Parameters:

• is_ess_dof (np.ndarray) – Boolean array indicating the degrees of freedom to flag as essential.

• ess_vals (np.ndarray) – Array of essential values corresponding to the flagged degrees of freedom.

Returns:

None

reduce_system()

Reduces the linear system by applying a restriction operator and returning the reduced system.

Returns:

A tuple containing the reduced matrix A, the reduced vector b, and the restriction operator R.

solve(solver=<function spsolve>)

Solve the linear system of equations.

Parameters:

solver (Callable) – The solver function to use. Defaults to sps.linalg.spsolve.

Returns:

The solution to the linear system of equations.

Return type:

np.ndarray

repeat_ess_vals()

Repeat the essential values of the linear system.

If the input vector b has dimension 1, the method returns the essential values as is. Otherwise, it repeats the essential values for each column of b.

Returns:

The repeated essential values.

Return type:

numpy.ndarray or scipy.sparse.csc_array

pygeon.numerics.linear_system.create_restriction(keep_dof)

Helper function to create the restriction mapping

Parameters:

keep_dof (np.ndarray) – Boolean array indicating which degrees of freedom (dofs) to keep. True for the dofs of the system, False for the overwritten values.

Returns:

The restriction mapping matrix.

Return type:

sps.csc_array