Spectral stochastic finite element method for solving 3D stochastic eddy current problems

Issue title: Selected Papers from the 15th International Symposium on Applied Electromagnetics and Mechanics (ISEM 2011)

Article type: Research Article

Authors: Beddek, K.^{a; *} | Clénet, S.^b | Moreau, O.^c | Le Menach, Y.^a

Affiliations: [a] L2EP–University Lille1, Villeneuve d'Ascq, France | [b] L2EP–Arts et Métiers ParisTech, Lille, France | [c] Electricité de France, dept. THEMIS, Clamart, France

Correspondence: [*] Corresponding author: K. Beddek, L2EP–University Lille1, Villeneuve d'Ascq 59655, France. E-mail: [email protected]

Abstract: In this paper, a spectral stochastic finite element method (SSFEM) is described and applied to quantify uncertainties in an industrial eddy current non destructive testing (NDT) problem. A new iterative solver based on the fixed-point method is proposed to solve the large scale linear system. The efficiency of the suggested iterative solver to tackle the SSFEM computational complexity is demonstrated. The SSFEM results and the computation times obtained with 2 and 4 random variables are compared to those given by the anisotropic adaptive sparse grid non intrusive spectral projection (NISP). On this application, the SSFEM dedicated solver is competitive with the adaptive sparse grids strategy.

Keywords: Spectral stochastic finite element method, fixed-point method, eddy current problem, polynomial chaos expansion, intrusive solver

DOI: 10.3233/JAE-2012-1539

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 39, no. 1-4, pp. 753-760, 2012