freegsnke.implicit_euler module

Implements implicit time integration.

Copyright 2025 UKAEA, UKRI-STFC, and The Authors, as per the COPYRIGHT and README files.

This file is part of FreeGSNKE.

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class freegsnke.implicit_euler.implicit_euler_solver(Mmatrix, Rmatrix, full_timestep, max_internal_timestep)[source]

Bases: object

An implicit Euler time stepper for the linearized circuit equations. Solves an equation of type

\[M\dot{I} + RI = F\]
,

with generic M, R and F. The internal_stepper and full_stepper solve for I(t+dt) using

\[I(t+dt) = (M + Rdt)^{-1} (Fdt + MI(t))\]
.

The implementation actually allows for

\[I(t+dt) = (M + Rdt)^{-1} (Fdt + LI(t))\]

with M != L

__init__(Mmatrix, Rmatrix, full_timestep, max_internal_timestep)[source]

Sets up the implicit euler solver

Parameters:

  • Mmatrix (np.ndarray) – (NxN) Mutual inductance matrix

  • Rmatrix (np.ndarray) – (NxN) Diagonal resistance matrix

  • full_timestep (float) – Full timestep (dt) for the stepper

  • max_internal_timestep (float) – Maximum size of the intermediate timesteps taken during the stepper. If max_internal_timestep < full_timestep, multiple steps are taken up to dt=full_timestep

calc_inverse_operator()[source]

Calculates the inverse operator (M + Rdt)^-1 Note this needs done when M or R are updated

full_stepper(It, forcing)[source]

Calculates the next full timestep I(t + self.full_timestep) by repeatedly solving for the internal timestep I(t + self.internal_timestep) for self.n_steps steps

Parameters:

  • It (np.ndarray) – Length N vector of the currents, I, at time t

  • forcing (np.ndarray) – Lenght N vector of the forcing, F, at time t

internal_stepper(It, dtforcing)[source]

Calculates the next internal timestep I(t + internal_timestep)

Parameters:

  • It (np.ndarray) – Length N vector of the currents, I, at time t

  • dtforcing (np.ndarray) – Lenght N vector of the forcing F dt, at time t multiplied by self.internal_timestep

set_Lmatrix(Lmatrix)[source]

Set a separate mutual inductance matrix L != M.

Parameters:

Lmatrix (np.ndarray) – (NxN) Mutual inductance matrix

set_Mmatrix(Mmatrix)[source]

Updates the mutual inductance matrix.

Parameters:

Mmatrix (np.ndarray) – (NxN) Mutual inductance matrix

set_Rmatrix(Rmatrix)[source]

Updates the resistance matrix.

Parameters:

Rmatrix (np.ndarray) – (NxN) Diagonal resistance matrix

set_timesteps(full_timestep, max_internal_timestep)[source]

Sets the timesteps for the stepper and (re)calculate the inverse operator

Parameters:

  • full_timestep (float) – Full timestep (dt) for the stepper

  • max_internal_timestep (float) – Maximum size of the intermediate timesteps taken during the stepper. If max_internal_timestep < full_timestep, multiple steps are taken up to dt=full_timestep