Investigation of Numerical Techniques for the Fourier Matching Method Acoustic Scattering Model

摘要

The effects of extended precision computing and other numerical techniques are evaluated for the Fourier matching method (FMM) acoustic scattering model, initially developed by Assistant Professor D. Benjamin Reeder, CDR/USN (NPS), and Professor Timothy K. Stanton (MIT/WHOI). Theory on acoustic scattering, reverberation, scattering models, conformal mapping, scatterer boundary conditions, floating point arithmetic, computational error, and extended precision computing is presented as a foundation for research development. The paper presents an assessment of the effects of numerical techniques on model output with the initial expectation of obtaining a more accurate, converged solution at higher frequencies, higher modal combinations, and greater eccentricities of scatterer shape. Comparisons to results from Reeder and Stanton (2004) demonstrate effects of executed techniques. Analysis includes an evaluation of the relationship between variable precision settings and computational time, gains in the useful frequency regime of the FMM, and numerical analysis benefits. Demonstrated techniques confirm that increased precision has a positive effect on model performance. The utility of other numerical techniques is discussed, and limitations of current computer systems and other shortfalls are illustrated. A feasibility assessment for Navy use of the FMM and recommendations for further improvements to the FMM are included.