[1] A procedure is outlined for determining compressed representations of the plane wave response matrix (P matrix) for transverse magnetic scattering with respect to the z axis from convex cylinders. The method is based on the determination of band-limited spectral modes that excite spatially localized solutions to the wave equation and satisfy global boundary conditions. Numerical examples indicate that the proposed method provides a representation of the P matrix with reduced computational complexity.Citation: Adams, R. J., G. Wang, F. X. Canning, and B. A. Davis (2006), Sparse representation of plane wave response matrices for convex targets using local solution modes with band-limited excitations, Radio Sci., 41, RS6008,

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Localizing modes provide an effective basis for developing efficient, error-controlled factorizations of the dense matrices encountered in integral equation formulations of wave phenomena at low to moderate frequencies. An essential component of these factorization algorithms is the numerical determination of the underlying localizing modes. This communication describes the details of an efficient procedure for computing the so-called non-overlapping, localizing modes. The principle component of the procedure is a QR-like factorization of the sparse multilevel data structure used to compress discrete integral operators. Numerical examples demonstrate the performance of the algorithm.

IntroductionA single-bounce, bandlimited beam transform method (BTM) is outlined for determining compressed representations of the plane wave response matrix (P-matrix) for TM, electromagnetic scattering from convex cylinders. The method is based on the determination of bandlimited spectral modes which excite spatially localized solutions to the wave equation and satisfy global boundary conditions. Numerical examples are presented which indicate that the computational complexity of the BTM representation of the P-matrix scales approximately as N'5. BackgroundNumerical solutions of surface integral equation formulations of time-harmonic electromagnetic radiation and scattering from perfectly conducting targets involve solving linear systems ofthe form

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