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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. [ABSTRACT FROM AUTHOR]

An algorithm is presented for the sparse pseudo inversion of discrete forms of the plane wave transform. The starting point for the sparse pseudo inverse is a new sparse representation of the discrete plane wave transform (DPWT). While other sparse representations of the DPWT exist, the sparse representation developed here is shown to be amenable to sparse factorization. This feature is used to develop an efficient, error-controlled pseudo-inverse of the DPWT. Representative numerical examples are provided to illustrate the general properties of the proposed algorithms. Areas for additional work are identified, and potential applications of the results are discussed. [ABSTRACT FROM AUTHOR]

The details of a Galerkin discretization scheme for a modified form of the electric field integral equation are outlined for smooth, three-dimensional, perfectly conducting scatterers. Limitations of the divergence conforming finite-element bases in pit- serving the self-stabilizing properties of the electric field integral equation operator are indicated. A numerically efficient alternative is outlined which relies on an operator-based Helmholtz decomposition. The condition number of the resulting matrix equation is demonstrated to be frequency independent for scattering from a perfectly conducting sphere at various frequencies. [ABSTRACT FROM AUTHOR]

The properties of different forms of the combined field integral equation (CFIE) formulation of electromagnetic scattering from convex, perfect electrically conducting geometries are considered. Several difficulties encountered in the numerical implementation of the traditional CFIEs of electromagnetic scattering theory are discussed. An alternate form of the CFIE is introduced which is free of many of the deficiencies of traditional formulations for smooth, convex geometries. The improved numerical properties of the new formulation are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]