Solving Maxwell's Equations with Mimetic Methods

Johnny Corbino

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arXiv · 2603.19056

Solving Maxwell's Equations with Mimetic Methods

Johnny Corbino

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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).

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Johnny Corbino. 2026-03-19. Solving Maxwell's Equations with Mimetic Methods. https://arxiv.org/abs/2603.19056

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