Solving Maxwell's Equations with Mimetic Methods
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914412072271872 |
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| author | Corbino, Johnny |
| author_facet | Corbino, Johnny |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19056 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving Maxwell's Equations with Mimetic Methods Corbino, Johnny Numerical Analysis 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). |
| title | Solving Maxwell's Equations with Mimetic Methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.19056 |