Scott J. Levinson
Carol V. Sheppard
Stephen K. Mitchell
Appl. Res. Labs., Univ. of Texas at Austin, Austin, TX 78713
Recently, an efficient, numerically robust algorithm for calculating acoustic normal modes was shown to have more than an order of a magnitude improvement in speed while maintaining high accuracy over other algorithms (submitted to JASA by the authors, June '94). A limitation remains, however, in its dependence on presampled wave numbers in the search for the roots of the characteristic equation (eigenvalues). Since coarse wave-number presampling may result in some eigenvalues remaining undetected, the presampling part of this code is the most time consuming portion---particularly for multichannel environments. We introduce a new approach which overcomes this problem. Analytic derivatives (up to sixth order) are calculated to locally approximate the numerically robust characteristic equation with Pade' approximants when finding successive eigenvalues. The requirement of wave-number presampling is thereby avoided and eigenvalue root finding is achieved with a superlinear convergence property. Its speed and accuracy will be compared with previous methods for single and multichannel ocean acoustic environments. [Work supported by the Advanced Surveillance Acoustic Prediction System (ASAPS) Development for IUSS Program of the Space and Naval Warfare Systems Command (SPAWAR, PMW 181-1).]