DESIGN OF SPARSE-MATRIX REPRESENTATIONS FOR THE PROPAGATOR USED IN THE BPM AND DIRECTIONAL WAVE-FIELD DECOMPOSITION

Directional wave field decomposition can be accomplished with the aid of pseudo-differential operators. A fast numerical scheme requires spa rse matrix representations of these operators. This paper focuses on d esigning sparse matrices for the propagator while keeping the accuracy high at the cost of ignoring critical-angle phenomena. The matrix rep resentation follows from a rational approximation for the square root operator and the derivatives. The parameterization thus introduced len ds itself to an overall optimization procedure that minimizes the erro rs for a chosen discretization rate. As such, the approach leads to an accurate propagator up to the (local) critical angle on a coarse nume rical grid.