A PADE APPROACH FOR EIGENVALUE IDENTIFICATION IN UNDERWATER ACOUSTIC NORMAL-MODE COMPUTATIONS

Recently, an efficient, numerically robust algorithm for calculating a coustic normal modes called MODELAB was implemented [J. Acoust. Sec. A m. 97, 1576-1585 (1995)]. In this paper, a new approach is introduced and shown to significantly reduce the most computationally intensive a spect of MODELAB: the requirement of fine wave number presampling duri ng the search for eigenvalues. Analytic derivatives (up to sixth order ) are efficiently calculated using a new recursion relation for the ch aracteristic equation. The derivatives are used to form Pade approxima nts, which in turn, are used to locally extrapolate the characteristic equation to find successive eigenvalues. Results indicate that an alg orithm using this technique can be more than a factor of five times fa ster than the MODELAB algorithm, and the new technique is shown to be particularly efficient at near-degenerate eigenvalues, which previousl y had been the most difficult to identify. (C) 1996 Acoustical Society of America.