Cedric Doucet : November 18, 2009

Solution of sparse linear systems of equations for electrical engineering: the case study of FLUX software

Cédric Doucet, Université de Grenoble

Wednesday, November 18, 10:00 a.m. in the CERFACS conference room

Abstract:

This presentation deals with sparse linear systems of equations in FLUX.  This modelling software computes static and quasi-static electromagnetic fields by the finite element method.  We notice that solving only one linear system may last several hours whereas the simulation of a device may require to solve hundreds of linear systems. The main problem comes from the fact that solutions are computed by classical Krylov subspace methods (CG,BiCG,BiCGSTAB,GMRES) which may suffer from slow convergence.  Incomplete LU factorizations (IC,ILU,ILUT) used to accelerate the speed of convergence of these solvers are not always efficient.
We investigate three strategies to overcome this problem.
Firstly, we replace iterative methods by a direct solver (SuperLU) in order to obtain a constant computational time against conditioning.
Secondly, we improve the preconditioning step by applying a diagonal scaling algorithm to linear systems of equations.
Finally, we propose a constructive theoretical approach to modify discrete variational formulations of continous problems by considering new hierarchies of mixed finite elements.
Our strategies and numerical results are discussed using concrete examples of industrial modellings.