Floating Random Walk Solution to the Dirichlet Problem

A floating random walk in a two-dimensional region starts at a point inside and takes steps of length equal to the minimum distance from the current location to the boundary of . This Demonstration illustrates floating random walks for regions of various shape.

Based on an undergraduate research project at the Illinois Geometry Lab by Yuheng Chang, Baihe Duan, Yirui Luo, Yitao Meng, Cameron Nachreiner and Yiyin Shen and mentored by A. J. Hildebrand.

The floating random walk algorithm is a probabilistic algorithm that can be applied to boundary value problems [1].

Reference

[1] A. Haji-Sheikh and E. M. Sparrow, "The Floating Random Walk and Its Application to Monte Carlo Solutions of Heat Equations," SIAM Journal on Applied Mathematics, 14(2), 1966 pp. 370–389. doi:10.1137/0114031.