# Numerical Electromagnetic Frequency Domain Analysis with Discrete Exterior Calculus

## TL;DR

This paper presents a novel frequency domain electromagnetic analysis method using discrete exterior calculus on arbitrary meshes, effectively handling complex boundary conditions and material properties.

## Contribution

It introduces a DEC-based formulation for electromagnetic problems on unstructured meshes, incorporating effective signed dual volumes and natural charge continuity.

## Key findings

- Accurate results for waveguides, fibers, and photonic crystals.
- Effective handling of various boundary conditions.
- Validation through multiple numerical examples.

## Abstract

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 3D and 2D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce effective signed dual volume to incorporate material information into Hodge star operators 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 demonstrate the implementation 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.