Work

The Hermite-Taylor correction function method for embedded boundary and Maxwell’s interface problems

Year: 2025

Type: article

Abstract: We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$ in each Cartesian coordinate. This makes the development of a systematic approach to enforce boundary and interface conditions difficult. Here we use the correction function method to update the numerical solution where the Hermite-Taylor method cannot be applied directly. Time derivatives of boundary and interface conditions, converted into spatial derivatives, are enforced to obtain a stable method and relax the time-step size restriction of the Hermite-Taylor correction function method. The proposed high-order method offers a flexible systematic approach to handle embedded boundary and interface problems, including problems with discontinuous solutions at the interface. This method is also easily adaptable to other first order hyperbolic systems.

Source: Journal of Computational Physics

DOI: 10.1016/j.jcp.2025.114111

Authors: Yann-Meing Law, Daniel Appelö, Thomas Hagstrom

Language: English

Topic: Electromagnetic Simulation and Numerical Methods

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,980

Funder: National Science Foundation

Awards: Numerical Methods for Wave Equations in Time and Frequency Domain, High Order Wave Equation Algorithms for the Frequency Domain, Numerical Methods for Waves: Nonlocal, Nonlinear, and Multiscale Systems