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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.15382 |
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| _version_ | 1866914862974631936 |
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| author | Han, Qiansheng Rasila, Antti Sottinen, Tommi |
| author_facet | Han, Qiansheng Rasila, Antti Sottinen, Tommi |
| contents | In this paper, we present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres algorithm. The method combines a traditional Walk-on-Spheres algorithm with use of reflections at the Neumann boundaries. We apply our algorithm to simulate numerical conformal mappings from certain quadrilaterals to the corresponding canonical domains, and to compute their conformal moduli. Finally, we give examples of the method on three dimensional polyhedral domains, and use it to simulate the heat flow on an L-shaped insulated polyhedron. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15382 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient simulation of mixed boundary value problems and conformal mappings Han, Qiansheng Rasila, Antti Sottinen, Tommi Numerical Analysis Complex Variables Probability 30-08, 30C20, 31-08, 31A15, 60J65, 65C05 G.1.8; G.3; I.3.5 In this paper, we present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres algorithm. The method combines a traditional Walk-on-Spheres algorithm with use of reflections at the Neumann boundaries. We apply our algorithm to simulate numerical conformal mappings from certain quadrilaterals to the corresponding canonical domains, and to compute their conformal moduli. Finally, we give examples of the method on three dimensional polyhedral domains, and use it to simulate the heat flow on an L-shaped insulated polyhedron. |
| title | Efficient simulation of mixed boundary value problems and conformal mappings |
| topic | Numerical Analysis Complex Variables Probability 30-08, 30C20, 31-08, 31A15, 60J65, 65C05 G.1.8; G.3; I.3.5 |
| url | https://arxiv.org/abs/2312.15382 |