Numerical electromagnetic frequency domain analysis with discrete exterior calculus

Journal Article · Fri Dec 01 04:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.08.068· OSTI ID:22701641

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. - Highlights: • The formulation of 2D and 3D electromagnetic equations with DEC are presented. • Characteristic Hodge stars are constructed without well-centered triangulation or Delaunay triangulation. • Systematical treatment of various boundary conditions, including PMC, PEC, periodic, and absorbing boundary conditions. • Switching between E to H field can change PEC from essential boundary condition to natural boundary condition. • Quality factor of an open dielectric sphere is considered.

• OSTI ID: 22701641
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 350; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIELECTRIC MATERIALS
DIRICHLET PROBLEM
DUALITY
ELECTRIC CONDUCTORS
NUMERICAL ANALYSIS
QUALITY FACTOR
THREE-DIMENSIONAL CALCULATIONS