A numerical method for scattering problems with unbounded interfaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909394342510592 |
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| author | Goodwill, Tristan Epstein, Charles L. |
| author_facet | Goodwill, Tristan Epstein, Charles L. |
| contents | We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of subdomains in which the scatterer has a "simple" structure. A subdomain is simple if the domain Green's function for this subdomain is either available analytically or can be computed numerically with arbitrary accuracy by a tractable method. These domain Green's functions are then used to reformulate the scattering problem as a system of boundary integral equations on the union of the subdomain boundaries. This reformulation gives a practical numerical method, as the resulting integral equations can then be solved, to any desired degree of accuracy, by using coordinate complexification over a finite interval, and standard discretization techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A numerical method for scattering problems with unbounded interfaces Goodwill, Tristan Epstein, Charles L. Numerical Analysis 35C15, 35Q60, 65M80, 65R20, 65E05 We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of subdomains in which the scatterer has a "simple" structure. A subdomain is simple if the domain Green's function for this subdomain is either available analytically or can be computed numerically with arbitrary accuracy by a tractable method. These domain Green's functions are then used to reformulate the scattering problem as a system of boundary integral equations on the union of the subdomain boundaries. This reformulation gives a practical numerical method, as the resulting integral equations can then be solved, to any desired degree of accuracy, by using coordinate complexification over a finite interval, and standard discretization techniques. |
| title | A numerical method for scattering problems with unbounded interfaces |
| topic | Numerical Analysis 35C15, 35Q60, 65M80, 65R20, 65E05 |
| url | https://arxiv.org/abs/2411.11204 |