Transformation Methods for Static Field Problems With Random Domains

Duy Hung Mac (1) , Stéphane Clenet (1) , Jean-Claude Mipo (2)

1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
2 Valéo systémes électriques

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.

Mots clés: Finite Element Method (FEM); Random Domains; Static Problem; Transformation Methods; Electromagnetic analysis; random mapping; stochastic finite element method

Domaines: Probabilités [math.PR]; Electromagnétisme

Duy Hung Mac, Stéphane Clenet, Jean-Claude Mipo. Transformation Methods for Static Field Problems With Random Domains. IEEE Transactions on Magnetics, 2011, 47 (5), pp.1446-1449. ⟨10.1109/TMAG.2010.2096460⟩. ⟨hal-00857179⟩