The Hermite-Taylor correction function method for embedded boundary and Maxwell’s interface problems
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| Názov: | The Hermite-Taylor correction function method for embedded boundary and Maxwell’s interface problems |
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| Autori: | Yann-Meing Law, Daniel Appelö, Thomas Hagstrom |
| Zdroj: | Journal of Computational Physics. 537:114111 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Elsevier BV, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Advanced Numerical Methods in Computational Mathematics, 35Q61, 65M70, 78A45, Mechanics of Materials, Computational Mechanics, FOS: Mathematics, Numerical methods in engineering, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Electrical and Electronic Engineering, 0101 mathematics, 01 natural sciences, Electromagnetic Simulation and Numerical Methods |
| Popis: | 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. 30 pages, 33 figures |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2025.114111 |
| DOI: | 10.48550/arxiv.2301.01752 |
| Prístupová URL adresa: | http://arxiv.org/abs/2301.01752 https://publications.polymtl.ca/66061/ https://doi.org/10.1016/j.jcp.2025.114111 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....6a9e40aa1c5b473203b86fa0166d6b45 |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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.<br />30 pages, 33 figures |
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| ISSN: | 00219991 |
| DOI: | 10.1016/j.jcp.2025.114111 |