论文标题
Maxwell方程模拟有限差异化离散化的有限元框架
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
论文作者
论文摘要
麦克斯韦的方程是控制电磁诱导定律的部分微分方程的系统。我们研究了方程的模拟有限差异（MFD）离散化，该方程可保留重要的基本物理特性。我们表明，在质量倾斜和适当的缩放之后，MFD离散化等效于结构保存有限元（FE）方案。这允许使用FE框架对MFD方法进行透明分析，并为离散系统构建高效且稳健的线性求解器提供了途径。特别是，设计用于FE配方的预审器可以直接地应用于MFD系统。我们提出数值测试，以验证MFD方案的准确性并确认预处理的鲁棒性。
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.
