Transformation Methods for Static Field Problems With Random Domains

Abstract

The numerical solution of partial differential equations onto random domains can be done by using a mapping transforming this random domain into a deterministic domain. The issue is then to determine this one to one random mapping. In this paper, we present two methods-one based on the resolution of the Laplace equations, one based on a geometric transformation-to determine the random mapping. A stochastic magnetostatic example is treated to compare these methods.