An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

Authors:
X. Antoine;Y. Boubendir
Affiliations:
Dept. de Genie Indust., Inst. National Polytech. de Lorraine (INPL), Ecole Nationale Sup. des Mines de Nancy, Inst. Elie Cartan Nancy (IECN), Inst. Elie Cartan UMR 7502, Nancy-Univ., CNRS, INRIA, ...;School of Mathematics, University of Minnesota, S. E. Minneapolis, MN, USA
Venue:
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
Year:
2008

Citing 7
Cited 3

On single integral equations for the transmission problem of acoustics

SIAM Journal on Applied Mathematics
Consistency estimates for a double-layer potential and application to the numerical analysis of the boundary-element approximation of acoustic scattering by a penetrable object

Mathematics of Computation
Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods

Journal of Computational Physics
Fast and Efficient Algorithms in Computational Electromagnetics

Fast and Efficient Algorithms in Computational Electromagnetics
A Preconditioner for the Electric Field Integral Equation Based on Calderon Formulas

SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Preconditioning techniques for the solution of the Helmholtz equation by the finite element method

Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications

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
Preconditioning based on Calderon's formulae for periodic fast multipole methods for Helmholtz' equation

Journal of Computational Physics
Calderón preconditioning approaches for PMCHWT formulations for Maxwell's equations

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Quantified Score

Hi-index	0.00

Visualization

Abstract

The solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape is considered. The numerical approach is based on a two-field system of integral equations solved by a Krylov subspace method. To accelerate and to improve the convergence of this solver, an efficient and robust preconditioner, based on the Calderon formulae, is developed. Several numerical simulations, for a wide range of physical parameters, validating the choice of this preconditioner are presented.