Computers & Mathematics with Applications
A stable well-conditioned integral equation for electromagnetism scattering
Journal of Computational and Applied Mathematics
Preconditioning techniques for the iterative solution of scattering problems
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations
Journal of Computational Physics
A Sherman-Morrison approach to the solution of linear systems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
The BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Mixed discretization schemes for electromagnetic surface integral equations
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Calderón preconditioning approaches for PMCHWT formulations for Maxwell's equations
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
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We describe a preconditioning technique for the Galerkin approximation of the electric field integral equation (EFIE), which arises in the scattering theory for harmonic electromagnetic waves. It is based on a discretization of the Calderon formulas and the Helmholtz decomposition. We prove several properties of the method, in particular that it produces a variational solution on a subspace of the Galerkin space for which we have an LBB inf-sup condition. When the Krylov spaces associated with the continuous operators are nondegenerate we prove that the discrete Krylov spaces converge as the mesh refinement goes to zero; when, moreover, the EFIE is nondegenerate on the continuous Krylov spaces, the discrete Krylov iterates converge towards the continuous ones. We also argue that one might expect the continuous Krylov iterates to exhibit superlinear convergence of the form $n \mapsto C^n(n!)^{-\alpha}$ for some C 0 and $\alpha0$. Finally, we illustrate the theory with numerical experiments.