Edge distribution method for solving elliptic boundary value problems with boundary singularities

James A. Given, Chi-Ok Hwang
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Elliptic boundary value problems are difficult to treat in the vicinity of singularities, i.e., edges and corners, of the boundary. The concentration of electrical charge on the edges and corners of a conductor is perhaps the simplest example of such problems. Here we provide a rapid method for accurate treatment of these problems. It utilizes a Green's-function-based implementation of last-passage Monte Carlo diffusion methods. This is combined with a diffusion algorithm for the scaling of
more » ... the scaling of solutions to the Laplace equation near a corner singularity to yield the solution of a benchmark problem: the charge distribution near the edge and corner of a conducting cube.
doi:10.1103/physreve.68.046128 pmid:14683023 fatcat:gtttnh25cfcuvjirwlbwanvua4