Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes

Bernhard Kähne; Markus Clemens; Sebastian Schöps

Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes

Computational Engineering, Finance, and Science 2020-11-09 v1

Authors: Bernhard Kähne , Markus Clemens , Sebastian Schöps

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.

Keywords

physics simulation finite element method

Cite

@article{arxiv.2011.03075,
  title  = {Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes},
  author = {Bernhard Kähne and Markus Clemens and Sebastian Schöps},
  journal= {arXiv preprint arXiv:2011.03075},
  year   = {2020}
}