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.

中文翻译：

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使用高阶方案的显式时间积分的磁场模拟

使用一阶和二阶多项式的有限元方法对涉及非线性材料的瞬态磁准静态矢量势公式进行空间离散化。通过应用广义 Schur 补，将所得的微分代数方程系统重新表述为常微分方程 (ODE) 系统。ODE 系统使用显式欧拉方案进行时间积分，该方案在最大时间步长条件下是稳定的。为了克服这个限制，一个显式的多级 Runge-Kutta-Chebyshev 高阶时间积分方法被用来扩大最大稳定时间步长。比较两种时间积分方法的总体计算工作量。