Efficient simulation of mixed boundary value problems and conformal mappings

Autor:	Han, Qiansheng, Rasila, Antti, Sottinen, Tommi
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Mathematics - Complex Variables Mathematics - Probability 30-08 30C20 31-08 31A15 60J65 65C05 G.1.8 G.3 I.3.5
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 13 figures. Source code and data avalable available at https://github.com/arasila/wos_conformal/
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.15382 Zobrazit plný text záznamu View this record from Arxiv