Solving Maxwell's Equations with Mimetic Methods
This work addresses computational electromagnetics problems for researchers and engineers, but it appears incremental as it builds on existing mimetic methods and libraries.
The paper tackles solving Maxwell's equations by developing a mimetic finite-difference method that ensures physical consistency, and demonstrates its application in one- and two-dimensional electromagnetic simulations with specific examples like a sinusoidal wave and a Gaussian pulse.
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).