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TMM

Source: vignettes/tmm/index.Rmd
index.Rmd

Overview

Benchmarked Partially validated Experimental
Theory Implementation

The transition-matrix method (TMM) represents a target by the linear map from incident modal coefficients to scattered modal coefficients. Its retained state can support more than a monostatic target-strength curve.

Core idea

Choose a basis matched to the supported geometry, solve the boundary problem for the coefficient map, and optionally retain its frequency-wise blocks for angular scattering, orientation averages, and diagnostics (Waterman 1969, 2009).

Best for

  • Supported single-target canonical geometries requiring retained angular products
  • Bistatic slices, scattering grids, and orientation post-processing from one solved state
  • Cross-checking geometry-specific modal families within a transition-matrix representation

Supports

  • Sphere, oblate-spheroid, prolate-spheroid, and guarded finite-cylinder branches
  • Supported fixed-rigid, pressure-release, penetrable, and spherical-shell boundaries
  • Optional retained T-matrix blocks for branch-specific post-processing

Main assumptions

  • A single target represented by one of the documented geometry-specific bases
  • Homogeneous-region or supported concentric spherical-shell material structure
  • Post-processing uses the documented body-fixed angular convention
  • Validation and retained-state support differ by geometry and boundary branch

Validation status

  • Benchmarked against SPHMS, PSMS, and FCMS on the currently supported canonical shape branches.
  • Validated against external BEMPP far-field checks for sphere, oblate, and prolate pressure-release cases.
  • Retained prolate angular products are also checked against the exact general-angle spheroidal solution.
  • TMM is partially validated because the sphere, oblate, and prolate branches have external checks, but retained general-angle cylinder products remain outside the validated public scope.
  • TMM is currently marked experimental because the retained-state workflow and branch matrix are still guarded while shape-specific support continues to be tightened.

Family pages

  • Implementation: branch matrix, retained-state workflows, output, and validation
  • Theory: coefficient maps, boundary operators, and geometry-matched bases

References

Waterman, P. C. 1969. “New Formulation of Acoustic Scattering.” The Journal of the Acoustical Society of America 45 (6): 1417–29. https://doi.org/10.1121/1.1911619.
Waterman, P. C. 2009. “T -Matrix Methods in Acoustic Scattering.” The Journal of the Acoustical Society of America 125 (1): 42–51. https://doi.org/10.1121/1.3035839.