A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential equations. However, solving large systems of linear algebraic equations with indefinite ill-conditioned matrices is a challenge. The high order of the matrices limits the capabilities of the Gaussian method to solve such systems, since this requires large RAM and much calculation. To reduce these requirements, an iterative preconditioned algorithm based on integral Laguerre transform in time is used. This approach allows using multigrid algorithms and, as a result, needs less RAM compared to the direct methods of solving systems of linear algebraic equations.

翻译：本文研究了一种用于模拟谐波电磁场的麦克斯韦方程组数值求解方法。矢量有限元法能够实现微分方程的物理保真离散化，然而求解具有不定病态矩阵的大规模线性代数方程组仍具挑战。此类矩阵的高阶性限制了高斯法求解此类系统的能力，因其需要大量内存与计算资源。为降低这些要求，本文采用了一种基于时间域积分拉盖尔变换的迭代预处理算法。该算法能够利用多重网格技术，相较于直接求解线性代数方程组的方法，可显著减少内存需求。