SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page A2638-A2659, January 2021.
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical properties. We show that, after mass-lumping and appropriate scaling, the MFD discretization is equivalent to a structure-preserving finite-element (FE) scheme. This allows for a transparent analysis of the MFD method using the FE framework and provides an avenue for the construction of efficient and robust linear solvers for the discretized system. In particular, block preconditioners designed for FE formulations can be applied to the MFD system in a straightforward fashion. We present numerical tests which verify the accuracy of the MFD scheme and confirm the robustness of the preconditioners.

中文翻译：

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麦克斯韦方程组模拟有限差分离散化的有限元框架

SIAM 科学计算杂志，第 43 卷，第 4 期，第 A2638-A2659 页，2021 年 1 月。
麦克斯韦方程组是控制电磁感应定律的偏微分方程组。我们研究了方程的模拟有限差分 (MFD) 离散化，它保留了重要的潜在物理特性。我们表明，经过质量集总和适当的缩放后，MFD 离散化等效于结构保持有限元 (FE) 方案。这允许使用有限元框架对 MFD 方法进行透明分析，并为为离散化系统构建高效且稳健的线性求解器提供了途径。特别是，专为 FE 公式设计的块预处理器可以直接应用于 MFD 系统。我们提出了验证 MFD 方案的准确性并确认预处理器的鲁棒性的数值测试。