An Iterative T-Matrix
NAVAL RESEARCH LAB STENNIS SPACE CENTER MS
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The T-matrix method, a technique invented by Peter Waterman, 1965, 1969, 1977, 1980 has proven to be valuable for calculating classical scattering from bounded targets. The method is useful for acoustical, electromagnetic and elastic scattering and is based on coupled boundary integral equations and partial wave expansions of relevant physical quantities. Upon truncation of the partial wave expansion, which are in principle in finite, a system of equations is derived that can be expressed in terms of finite matrices. This system in turn leads to an expression that maps the incident field onto the scattered field. The outcome is a powerful algorithm that yields essentially exact results. The point at which the partial wave series is truncated is always an issue in using the method. If too few terms are included, the results will be very inaccurate. Conversely, if many terms beyond that required for convergence are included, at best the calculation will be needlessly time consuming and, at worst, can lead to numerical instability due to numerical round-off errors. What would be ideal is a technique that leads to optimum truncation, that is, the point just beyond which convergence is achieved. This type of technique can be obtained by a method based on starting with a small t-matrix and in which we build up the dimensions term by term via simple vector operations until convergence is achieved. The algorithm is described and results are illustrated for some examples.... Acoustic scattering, Shallow water, Waveguide propagation.
- Numerical Mathematics