Algorithm 975

  title={Algorithm 975},
  author={Mahadevan Ganesh and Stuart C. Hawkins},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  pages={1 - 18}
  • M. GaneshS. Hawkins
  • Published 14 July 2017
  • Computer Science
  • ACM Transactions on Mathematical Software (TOMS)
The T-matrix (TMAT) of a scatterer fully describes the way the scatterer interacts with incident fields and scatters waves, and is therefore used extensively in several science and engineering applications. The T-matrix is independent of several input parameters in a wave propagation model and hence the offline computation of the T-matrix provides an efficient reduced order model (ROM) framework for performing online scattering simulations for various choices of the input parameters. The… 

Backscattering problems by a non-convex kite-shape objects in acoustic frequency domain

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Algorithm 1009

  • S. Hawkins
  • Geology
    ACM Transactions on Mathematical Software
  • 2020
MieSolver provides an efficient solver for the problem of wave propagation through a heterogeneous configuration of nonidentical circular cylinders that is numerically stable and highly accurate.

A proof that multiple waves propagate in ensemble-averaged particulate materials

It is shown that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field, and a simple formula is provided for the reflection coefficient which can be explicitly evaluated for monopole scatterers.


For over 70 years it has been assumed that scalar wave propagation in (ensembleaveraged) random particulate materials can be characterized by a single effective wavenumber. Here, however, we show



A far field based T-matrix method for three dimensional acoustic scattering

The acoustic scattering properties of an obstacle are completely described by its infinite acoustic T-matrix. The T-matrix is particularly useful when one is interested in analysing changes in sound

A far-field based T-matrix method for two dimensional obstacle scattering

The infinite T-matrix completely describes the acoustic scattering properties of an obstacle. The T-matrix is extremely important for many applications because it is computationally cheap to use the

T-matrix methods in acoustic scattering.

  • P. Waterman
  • Physics
    The Journal of the Acoustical Society of America
  • 2009
From the structure of the matrices involved, one can infer the Rayleigh limit explicitly for objects having no density contrast, and one finds T(Ray)=iR-R(2), where the R-matrix involves integrals of the regular spherical wave functions over the object's surface.

Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method

This work numerically demonstrate the convergence analysis and the a priori parameter estimates for both point-source and plane-wave incident waves for time-harmonic acoustic scattering in two and three dimensions.

A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications

The present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds and exhibits super-algebraic convergence; it can be applied to smooth and nonsmooth scatterers, and it does not suffer from accuracy breakdowns of any kind.

Surface fields and the T matrix

The T-matrix equations are revisited with an eye to computing surface fields. Electromagnetic scattering by cylinders is considered for both surface- and volume-type scatterers. Elliptical and other

Case study about the accuracy behavior of three different T-matrix methods.

It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields, which proves their usefulness by analyzing the far-field scattering behavior of Chebyshev particles of higher orders.