Comparison of two approaches to compute magnetic field in problems with random domains

Abstract

Methods are now available to solve numerically electromagnetic problems with uncertain input data (behaviour law or geometry). The stochastic approach consists in modelling uncertain data using random variables. Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with uncertainties on the geometry. The basis functions (polynomial chaos) usually used to approximate the unknown fields in the random dimensions are no longer suited. One possibility proposed in the literature is to introduce additional functions (enrichment function) to tackle the problem of discontinuity. In this study, the authors focus on the method of random mappings and they show that in this case the discontinuity are naturally taken into account and that no enrichment function needs to be added.