Skip to contents

TMM

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

Overview

Benchmarked Partially validated Experimental
Theory Implementation

These pages follow the coefficient-map view of scattering and later numerical implementations for axisymmetric bodies (Waterman 1969, 2009; Ganesh and Hawkins 2022).

The transition matrix method (TMM) is the package’s current single-target bridge between exact modal-series solvers and broader angle-dependent scattering products.

Core idea

Represent the incident and scattered fields in complete modal bases and solve for the linear map between those coefficient vectors. In the supported package scope, that gives a reusable single-target retained state for monostatic target strength and, where externally constrained, for general-angle or orientation-averaged post-processing.

Best for

  • Single-target axisymmetric scattering problems that need more than one post-processed product from one solve
  • Sphere, oblate spheroid, and prolate spheroid problems with retained scattering products
  • Geometry-specific comparisons between exact modal families and a T-matrix viewpoint

Supports

  • Sphere, OblateSpheroid, ProlateSpheroid, and guarded Cylinder branches
  • Single homogeneous interiors under rigid, pressure-release, liquid-filled, and gas-filled boundaries
  • Stored retained state for scattering slices, grids, diagnostics, and orientation averages where validated

Main assumptions

  • Single-target scope only
  • Geometry-specific basis choice rather than one universal retained operator for every shape
  • Cylinder branch has narrower validated scope than sphere, oblate, and prolate branches

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: stored-state workflows, plots, benchmarks, and supported scope
  • Theory: T-matrix interpretation, boundary operators, and geometry-matched bases
Single-target TMM workflow, showing the spherical-coordinate branch used for spheres and oblates, the spheroidal branch used for prolates, and the cylindrical monostatic branch used for finite cylinders.
Single-target TMM workflow, showing the spherical-coordinate branch used for spheres and oblates, the spheroidal branch used for prolates, and the cylindrical monostatic branch used for finite cylinders.

References

Ganesh, M., and Stuart C. Hawkins. 2022. “A Numerically Stable T-Matrix Method for Acoustic Scattering by Nonspherical Particles with Large Aspect Ratios and Size Parameters.” The Journal of the Acoustical Society of America 151 (3): 1978–88. https://doi.org/10.1121/10.0009679.
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.
———. 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.