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

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.