### ASA 126th Meeting Denver 1993 October 4-8

## 2aUW13. A spectral method for calculation of ocean acoustic normal modes
using Chebyshev polynomials.

**Matthew A. Dzieciuch
**

**
**
*Scripps Inst. of Oceanogr., IGPP-0225, UCSD, La Jolla, CA 92093
*

*
*
A new method employing Chebyshev polynomials to calculate the underwater
acoustic normal mode equation was developed. The method is a spectral approach
using Chebyshev polynomials as basis functions. This expansion has the
advantage of being a particularly efficient and accurate representation of the
normal modes (especially of the lower order) since they give an exceedingly
good representation of narrow boundary layers such as the sound-speed profile
that can undergo rapid changes near the surface. This representation reduces
the size of the eigenvalue problem to be solved. Since the CPU time scales with
N[sup 3], where N is the size of the matrix, any size reduction is an advantage
computationally. This approach has a significant speed advantage over finite
difference methods without sacrificing accuracy. A Chebyshev representation is
usually remarkably close to the minimax polynomial that minimizes the maximum
error implying high accuracy. Chebyshev polynomials are also useful for the
calculation of quantities involving the integral of the mode function, such as
modal group velocity, loss, and coupling coefficient matrices in non-adiabatic
propagation environments. These quantities can be calculated easily and
accurately given their spectral representations without introducing any further
numerical error.