Biomedical subjects

James A Given

Publications and source records attributed to James A Given.

2 recordsLinked to original sources

PubMed2003

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

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 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.

Journal Article↗

PubMed2002

First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface.

Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best first-passage diffusion algorithm) in solving the classical problem of computing the charge distribution on a conducting disk held at unit voltage. All three algorithms show detailed agreement with the known analytic solution to this problem.

Journal Article↗