A Sparse Factorization for Fast Computation of Localizing Modes

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.