Bruno Carpentieri : January 7, 2004

Matrix-Free preconditionings of dense linear systems from electromagnetics.

Abstract

Electromagnetic applications are one major source of dense linear systems in numerical linear algebra. Typical examples include radar cross section calculation, design of antennae, medical equipment, absorbing materials and stealth technology. In recent years, due to the impressive development in computer technology the size of these linear systems is continually increasing in industry; the discretization matrix can have up to a few million unknowns. For solving these challenging problems, iterative Krylov solvers can be an efficient alternative to direct methods provided we have fast matrix-vector products and robust preconditioners.

In this talk, we focus on the latter component of Krylov solvers in that context. We present a matrix-free preconditioning approach that can be effectively combined with fast methods for the matrix-vector product, like the Fast Multipole Method or panel clustering.

Numerical experiments on a set of realistic industrial problems from radar cross section calculation provided by the EADS partner illustrate the potential of our method for solving large-scale applications in electromagnetism.

This is joint work with Iain S. Duff, Luc Giraud and Guillaume Sylvand (INRIA-CERMICS).