Solving Maxwell's Equations with Mimetic Methods
Abstract
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic operators that satisfy a discrete analogue of the extended Gauss divergence theorem and show how they lead to a compact, physically consistent formulation for computational electromagnetics. Two numerical examples are presented: a one-dimensional sinusoidal wave interacting with a lossy dielectric slab, and a two-dimensional Gaussian pulse with Uniaxial Perfectly Matched Layer (UPML) absorbing boundary conditions. All implementations use the Mimetic Operators Library Enhanced (MOLE).
Cite
@article{arxiv.2603.19056,
title = {Solving Maxwell's Equations with Mimetic Methods},
author = {Johnny Corbino},
journal= {arXiv preprint arXiv:2603.19056},
year = {2026}
}
Comments
Clarified that the FDTD discretization corresponds to the 1D case; attributed both numerical examples to Sullivan