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PSMS

Source: vignettes/psms/index.Rmd
index.Rmd

Overview

Benchmarked Validated
Theory Implementation

These pages are rooted in exact spheroidal-coordinate separations and later fisheries-acoustics use of prolate-spheroid models (Spence and Granger 1951; Furusawa 1988).

The prolate spheroidal modal series solution (PSMS) is the exact single-target modal family for homogeneous prolate spheroids. It is the spheroidal analogue of spherical partial-wave theory and the natural exact reference for elongated canonical bodies whose surface follows a prolate spheroid.

Core idea

Separate the Helmholtz equation in prolate spheroidal coordinates, expand the incident, scattered, and interior fields in spheroidal wave functions, and solve the retained boundary systems order by order.

Best for

  • Rigid, pressure-release, liquid-filled, and gas-filled prolate spheroids
  • Canonical elongated-body benchmarks
  • Validating prolate branches of more general methods such as TMM

Supports

  • ProlateSpheroid shapes on FLS or GAS objects
  • Exact monostatic target strength for homogeneous single-region spheroids
  • Spheroidal modal solutions in which medium 1 is seawater and medium 2 is the spheroid interior

Main assumptions

  • Perfect prolate spheroidal geometry
  • Homogeneous interior region
  • Linear, time-harmonic acoustics
  • No shell or internal secondary component

Validation status

  • Benchmarked against the canonical prolate-spheroid spectra stored in benchmark_ts.
  • Validated against the external Prol_Spheroid implementation on shared prolate cases.

Family pages

  • Implementation: workflows, comparisons, and timing tables
  • Theory: full spheroidal-coordinate derivation and retained modal systems

References

Furusawa, Masahiko. 1988. “Prolate Spheroidal Models for Predicting General Trends of Fish Target Strength.” Journal of the Acoustical Society of Japan (E) 9 (1): 13–24. https://doi.org/10.1250/ast.9.13.
Spence, R. D., and Sara Granger. 1951. “The Scattering of Sound from a Prolate Spheroid.” The Journal of the Acoustical Society of America 23 (6): 701–6. https://doi.org/10.1121/1.1906827.