论文标题
基于离散的外观演算的电磁学中的A-Phi公式求解器
An A-Phi Formulation Solver in Electromagnetics Based on Discrete Exterior Calculus
论文作者
论文摘要
本文提出了基于离散的外观（DEC）的电磁学中A-PHI公式的有效数值求解器。 A-Phi公式不受低频崩溃的影响，是宽带和多尺度分析的理想选择。本文中使用了广义的洛伦兹仪表，该量规将A a方程和PHI方程解耦。 A-Phi公式通过使用DEC离散化，这是差异几何形状中外部演算的离散版本。通常，DEC可以被视为有限差异方法的广义版本，其中Stokes的定理和高斯定理自然保留。此外，与有限的差异方法相比，在应用矩形网格的情况下，可以使用非结构化的网格方案（例如四面体网格）实现DEC。因此，拟议的DEC A-PHI求解器本质上是稳定的，没有虚假解决方案，并且可以有效地捕获高度复杂的结构。在本文中，引入了有关A-PHI公式和DEC的背景知识，以及实施具有不同边界条件的DEC A-PHI求解器时的技术细节。还提供了用于验证的目的的数值示例。
An efficient numerical solver for the A-Phi formulation in electromagnetics based on the discrete exterior calculus (DEC) is proposed in this paper. The A-Phi formulation is immune to low-frequency breakdown and ideal for broadband and multi-scale analysis. The generalized Lorenz gauge is used in this paper, which decouples the A equation and the Phi equation. The A-Phi formulation is discretized by using the DEC, which is the discretized version of the exterior calculus in differential geometry. In general, DEC can be viewed as a generalized version of the finite difference method, where Stokes' theorem and Gauss's theorem are naturally preserved. Furthermore, compared with finite difference method, where rectangular grids are applied, DEC can be implemented with unstructured mesh schemes, such as tetrahedral meshes. Thus, the proposed DEC A-Phi solver is inherently stable, free of spurious solutions and can capture highly complex structures efficiently. In this paper, the background knowledge about the A-Phi formulation and DEC is introduced, as well as technical details in implementing the DEC A-Phi solver with different boundary conditions. Numerical examples are provided for validation purposes as well.
