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| Հիմնական հեղինակներ: | , , |
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| Ձևաչափ: | Preprint |
| Հրապարակվել է: |
2024
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| Խորագրեր: | |
| Առցանց հասանելիություն: | https://arxiv.org/abs/2406.05367 |
| Ցուցիչներ: |
Ավելացրեք ցուցիչ
Չկան պիտակներ, Եղեք առաջինը, ով նշում է այս գրառումը!
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| _version_ | 1866909432573591552 |
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| author | Hsiao, George C. Sánchez-Vizuet, Tonatiuh Wendland, Wolfgang L. |
| author_facet | Hsiao, George C. Sánchez-Vizuet, Tonatiuh Wendland, Wolfgang L. |
| contents | We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method, we reformulate the problem in the Laplace domain using the electric field equation inside the scatterer and a system of boundary integral equations for the scattered electric field in free space. To analyze this nonlocal boundary problem, we replace it by an equivalent boundary value problem. Existence, uniqueness and stability of the weak solution to the equivalent BVP are established in appropriate function spaces in terms of the Laplace transformed variable. The stability bounds are translated into time-domain estimates which determine the regularity of the solution in terms of the regularity of the problem data. These estimates can be easily converted into error estimates for a numerical discretization on the convolution quadrature for time evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary-field formulation for transient electromagnetic scattering by dielectric scatterers and coated conductors Hsiao, George C. Sánchez-Vizuet, Tonatiuh Wendland, Wolfgang L. Analysis of PDEs Numerical Analysis Mathematical Physics 78A40, 78M10, 78M15, 45A05 We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method, we reformulate the problem in the Laplace domain using the electric field equation inside the scatterer and a system of boundary integral equations for the scattered electric field in free space. To analyze this nonlocal boundary problem, we replace it by an equivalent boundary value problem. Existence, uniqueness and stability of the weak solution to the equivalent BVP are established in appropriate function spaces in terms of the Laplace transformed variable. The stability bounds are translated into time-domain estimates which determine the regularity of the solution in terms of the regularity of the problem data. These estimates can be easily converted into error estimates for a numerical discretization on the convolution quadrature for time evolution. |
| title | Boundary-field formulation for transient electromagnetic scattering by dielectric scatterers and coated conductors |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics 78A40, 78M10, 78M15, 45A05 |
| url | https://arxiv.org/abs/2406.05367 |