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Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization. [ABSTRACT FROM AUTHOR]

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]