Solution of Static Field Problems With Random Domains

Duy Hung Mac (1) , Stéphane Clenet (1) , Jean-Claude Mipo (2) , Olivier Moreau (3)

1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
2 Valéo systémes électriques
3 EDF R&D - EDF R&D

A method to solve stochastic partial differential equations on random domains consists in using a one-to-one random mapping function which transforms the random domain into a deterministic domain. With this method, the randomness is then borne by the constitutive relationship of the material. In this paper, this method is applied in electrokinetics in the case of scalar potential and vector potential formulations. An example is treated and the proposed method is compared to a nonintrusive method (NIM) based on the remeshing of the random domains.

Mots clés: Finite Element Method (FEM); Random Domains; Electromagnetism; Static Problem; Tranformation Method

Domaines: Probabilités [math.PR]; Analyse numérique [math.NA]; Electromagnétisme; Energie électrique

Duy Hung Mac, Stéphane Clenet, Jean-Claude Mipo, Olivier Moreau. Solution of Static Field Problems With Random Domains. IEEE Transactions on Magnetics, 2010, 46 (8), pp.3385-3388. ⟨10.1109/TMAG.2010.2045358⟩. ⟨hal-00857180⟩