Numerical electromagnetic frequency domain analysis with discrete exterior calculus

JOURNAL OF COMPUTATIONAL PHYSICS

卷:350

Article

Chen, Shu C.¹  Chew, Weng Cho² 

[1] Univ Illinois, Dept Phys, Champaign, IL USA

[2] Univ Illinois, Dept Elect & Comp Engn, Champaign, IL 61820 USA

关键词: Maxwell's equations;    Differential forms;    Discrete exterior calculus;    Arbitrary simplicial mesh;    Circumcenter/Voronoi dual;    Hodge star;   

DOI  :  10.1016/j.jcp.2017.08.068

来源: Elsevier

【 摘 要 】

In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3-D and 2-D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce a general construction for signed dual volume to incorporate material information and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we examine the boundary terms induced by the dual mesh and provide a systematical treatment of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free