Making a Synthesis of FDTD and DGTD Schemes for Computational Electromagnetics
Making a Synthesis of FDTD and DGTD Schemes for Computational Electromagnetics
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DOI：
10.1109/jmmct.2020.3001910
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发表时间：
2020
影响因子：
2.3
通讯作者：
D. Balsara;J. Simpson
中科院分区：
文献类型：
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作者：
D. Balsara;J. Simpson
提出了一类新的间断Galerkin时域（DGTD）格式，该格式能够全局保持麦克斯韦方程组中固有的约束。该方法共享相同的Yee型网格结构的时域有限差分（FDTD）的计算电动力学计划。由于FDTD方案还保留全局约束，这项工作的新奇包括FDTD和DGTD方案的综合。虽然以前的DG方法是基于应用身份涉及高斯定律在弱形式的网格的体积元素，较新的方法是基于应用身份涉及斯托克斯定律在弱形式的网格的面元素。这种基本的范式转变是至关重要的，以获得全局约束保持DGTD方法在本文中。新的DGTD方法满足其设计精度。即使在最低分辨率下，更精确的方案也确实更精确。此外，随着网格的细化，方案更快地达到其设计精度。这些好处都归因于这里提出的DGTD方案的子小区分辨能力。高阶方法提供最短的求解时间，特别是当需要非常高的精度时。还展示了出色的可扩展性。
A novel class of discontinuous Galerkin time-domain (DGTD) schemes, invented by the first author, are presented that are capable of globally preserving the constraints that are inherent in Maxwell's equations. The methods share the same Yee-type mesh structure as finite-difference time-domain (FDTD) schemes for computational electrodynamics. Since FDTD schemes also preserve global constraints, the novelty of this work consists of making a synthesis of FDTD and DGTD schemes. While previous DG methods were based on applying identities involving Gauss’ law in weak form to the volumetric elements of a mesh, the newer methods are based on applying identities involving Stokes’ law in weak form to the facial elements of the mesh. This fundamental paradigm shift is crucial for obtaining the globally constraint-preserving DGTD methods in this paper. The new DGTD methods meet their design accuracies. The more accurate schemes are indeed more accurate even at the lowest resolutions. Moreover, as the mesh is refined, the schemes reach their design accuracies much faster. These benefits are all attributable to the subcell resolving ability of the DGTD schemes presented here. The higher order methods offer the lowest time to solution, especially when very high accuracies are demanded. Excellent scalability is also demonstrated.