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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectra1 Lanczos decomposition method
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Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectra1 Lanczos decomposition method

机译：使用Spectrum1 Lanczos分解方法的Maxwell方程的频域和时域有限元解

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摘要

An efficient solver is described for the solution of the electromagnetic fields in both time and frequency domains. The proposed method employs the node-based and the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution. First, a new explicit axisymmetric solver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced. The procedure is then extended to treat the three-dimensional problems in the low frequency regime. Finally, Maxwell's equations, in their general form, are solved in frequency and time domains. Depending on the application, our method requires the implementation of the Lanczos process only at the largest or smallest time or frequency of interest. Consequently, a multiple time and frequency domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time. The efficiency and effectiveness of this new technique are illustrated by using various practical numerical examples.
机译：描述了一种有效的求解器，用于时域和频域中的电磁场求解。所提出的方法采用基于节点和基于边缘的有限元方法（FEM）离散麦克斯韦方程组。所得的矩阵方程式通过基于解决方案的Krylov子空间（Lanczos）近似的光谱Lanczos分解方法（SLDM）求解。首先，介绍了一种新的显式轴对称求解器，用于非均匀介质中电磁场的扩散。然后扩展该程序以处理低频状态下的三维问题。最后，一般形式的麦克斯韦方程在频域和时域中求解。根据应用的不同，我们的方法仅要求在最大或最小的时间或频率上实施Lanczos流程。因此，可以以可忽略的额外计算时间实现电磁场的多时域和频域分析。通过使用各种实际的数值示例来说明此新技术的效率和有效性。

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