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Sparse approximate inverse preconditioning of deflated block-GMRES algorithm for the fast monostatic RCS calculation. (English) Zbl 1177.78055

Sparse approximate inverses together with the GMRES Krylov subspace algorithm is a popular combination to solve large asymmetric matrix equations. In this paper the authors apply it to the electric field integral equation implemented in a multi-level fast multipole code to solve radar cross section problems. This equation is known to have large condition numbers and therefore good preconditioners are necessary. In radar cross section calculations it is common to consider many right hand sides simultaneously and therefore block versions of the GMRES are considered. However, because of limited memory and computer capability and it is necessary to do restarts of the GMRES algorithm. The idea presented in this paper is to compute some approximate eigenvectors at restart form the old Krylov space and then add these to the restarted Krylov space. The idea is tested on several problems with a different number of approximate eigenvectors, different block size and number of iterations before restart.

MSC:

78M16 Multipole methods applied to problems in optics and electromagnetic theory
78A45 Diffraction, scattering
65F10 Iterative numerical methods for linear systems
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
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