Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes

TL;DR

This paper explores explicit time integration methods for magnetic field simulations, comparing a basic Euler scheme with a higher-order Runge-Kutta-Chebyshev method to improve stability and efficiency.

Contribution

It introduces the application of higher-order explicit Runge-Kutta-Chebyshev methods to magneto-quasistatic simulations, extending stable time step sizes beyond traditional explicit Euler limits.

Findings

Higher-order methods increase maximum stable time step size.

Explicit multistage schemes reduce overall computational effort.

Comparison shows improved efficiency with advanced schemes.

Abstract

A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential equations (ODE). The ODE system is integrated in time using the explicit Euler scheme, which is conditionally stable by a maximum time step size. To overcome this limit, an explicit multistage Runge-Kutta-Chebyshev time integration method of higher order is employed to enlarge the maximum stable time step size. Both time integration methods are compared regarding the overall computational effort.