GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
Solution of dense systems of linear equations in the discrete-dipole approximation
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
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
On a class of preconditioners for solving the Helmholtz equation
Applied Numerical Mathematics
Higher-Order Fourier Approximation in Scattering by Two-Dimensional, Inhomogeneous Media
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The efficient solution of electromagnetic scattering for inhomogeneous media
Journal of Computational and Applied Mathematics
The efficient solution of direct medium problems by using translation techniques
Mathematics and Computers in Simulation
| Hi-index | 7.29 |
We consider a time-harmonic electromagnetic scattering problem for an inhomogeneous medium. Some symmetry hypotheses on the refractive index of the medium and on the electromagnetic fields allow to reduce this problem to a two-dimensional scattering problem. This boundary value problem is defined on an unbounded domain, so its numerical solution cannot be obtained by a straightforward application of usual methods, such as for example finite difference methods, and finite element methods. A possible way to overcome this difficulty is given by an equivalent integral formulation of this problem, where the scattered field can be computed from the solution of a Fredholm integral equation of second kind. The numerical approximation of this problem usually produces large dense linear systems. We consider usual iterative methods for the solution of such linear systems, and we study some preconditioning techniques to improve the efficiency of these methods. We show some numerical results obtained with two well known Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.