A Matrix-free Two-grid Preconditioner for Solving Boundary Integral Equations in Electromagnetism

Authors:
B. Carpentieri
Affiliations:
Institute for Mathematics and Scientific Computing, Karl-Franzens University, Heinrichstraße 36, 8010, Graz, Austria
Venue:
Computing
Year:
2006

Citing 0
Cited 3

A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

Journal of Computational Physics
Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation

Journal of Computational Physics

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Abstract

In this paper, we describe a matrix-free iterative algorithm based on the GMRES method for solving electromagnetic scattering problems expressed in an integral formulation. Integral methods are an interesting alternative to differential equation solvers for this problem class since they do not require absorbing boundary conditions and they mesh only the surface of the radiating object giving rise to dense and smaller linear systems of equations. However, in realistic applications the discretized systems can be very large and for some integral formulations, like the popular Electric Field Integral Equation, they become ill-conditioned when the frequency increases. This means that iterative Krylov solvers have to be combined with fast methods for the matrix-vector products and robust preconditioning to be affordable in terms of CPU time. In this work we describe a matrix-free two-grid preconditioner for the GMRES solver combined with the Fast Multipole Method. The preconditioner is an algebraic two-grid cycle built on top of a sparse approximate inverse that is used as smoother, while the grid transfer operators are defined using spectral information of the preconditioned matrix. Experiments on a set of linear systems arising from real radar cross section calculation in industry illustrate the potential of the proposed approach for solving large-scale problems in electromagnetism.