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TMATDG: applying TDG methods to multiple scattering via T-matrix approximation

Armando Maria Monforte

Abstract

We present a MATLAB package for the solution of multiple scattering problems, coupling Trefftz Discontinuos Galerkin methods for Helmholtz scattering with the T-matrix method. We rely on the TMATROM package to numerically approximate the T-matrices and deal with multiple scattering problem, providing a framework to handle scattering by polygonal obstacles.

TMATDG: applying TDG methods to multiple scattering via T-matrix approximation

Abstract

We present a MATLAB package for the solution of multiple scattering problems, coupling Trefftz Discontinuos Galerkin methods for Helmholtz scattering with the T-matrix method. We rely on the TMATROM package to numerically approximate the T-matrices and deal with multiple scattering problem, providing a framework to handle scattering by polygonal obstacles.
Paper Structure (13 sections, 23 equations, 5 figures)

This paper contains 13 sections, 23 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Multiple scattering problem and T-matrix
  3. The T-matrix method
  4. The TMATROM package
  5. DtN-TDG approximation of the single scattering problem
  6. DtN-TDG approximation on the circle
  7. TMATDG: combining TDG with TMATROM
  8. Approximating the T-matrix of a single obstacle
  9. Dealing with multiple scattering problems
  10. Examples
  11. Single scatterer, rotation and translation
  12. Multiple scattering problem and configuration changes
  13. A parameter-depending problem

Figures (5)

  • Figure 1: Domain geometry for Dirichlet (left) and transmission (right) problem.
  • Figure 2: Real part of total field for the square penetrable scatterer of Section \ref{['ex:single']} in 3 different cases: Left: plane incident wave; Center: rotated and translated scatterer with the same incident wave; Right: circular incident wave.
  • Figure 3: Real part of total field for the ensemble of scatterers of Section \ref{['ex:multiple']} with two different arrangements. On the left we plot near the obstacles; on the right this is not possible since the obstacles are too close to each other and the TDG solutions are computed on disks of radius $R_D+2h$.
  • Figure 4:
  • Figure 5: Real part of total field for the scatterer arrangement of Section \ref{['ex:parameter']}, with $\rho = 0.8$ and $\rho = 1.05$ respectively.