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A matrix-free two-grid preconditioner for solving boundary integral equations in electromagnetism. (English) Zbl 1095.78010
In this paper there are presented some multipole techniques for solving boundary integral equations in electromagnetism. The author uses a sparse approximate inverse as a smoother for an algebraic two-grid cycle where the inter-grids operators are based on spectral information from the preconditioned matrix. The sparse approximate inverse is computed from the near-field part of the dense coefficient matrix and the pattern is prescribed in advance by using physical information. The numerical results on small and medium size problems from radar cross section calculations illustrate this method.

78M25 Numerical methods in optics (MSC2010)
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
78A45 Diffraction, scattering
78A50 Antennas, waveguides in optics and electromagnetic theory
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