The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908315431206912 |
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| author | Law, Yann-Meing Appelö, Daniel Hagstrom, Thomas |
| author_facet | Law, Yann-Meing Appelö, Daniel Hagstrom, Thomas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_01752 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems Law, Yann-Meing Appelö, Daniel Hagstrom, Thomas Numerical Analysis 35Q61, 65M70, 78A45 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. |
| title | The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems |
| topic | Numerical Analysis 35Q61, 65M70, 78A45 |
| url | https://arxiv.org/abs/2301.01752 |