TMATROM

Algorithm 975: TMATROM - A T-Matrix Reduced Order Model Software. 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 authors developed and mathematically analyzed a numerically stable formulation for computing the T-matrix (J. Comput. Appl. Math. 234 (2010), 1702--1709). The TMATROM software package provides an object-oriented implementation of the numerically stable formulation and can be used in conjunction with the user’s preferred forward solver for the two-dimensional Helmholtz model. We compare TMATROM with standard methods to compute the T-matrix for a range of two-dimensional test scatterers with large aspect ratios and acoustic sizes. Our numerical results demonstrate the robust numerical stability of the TMATROM implementation, even with scatterers for which the standard methods are numerically unstable. The efficiency and flexibility of the TMATROM software package to handle a wide range of two-dimensional scatterers with various shapes and material properties are also demonstrated.