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 to simulate scattering for many different orientations of the obstacle or incident waves. The T-matrix is usually computed using the null field method. However, the null field method is often numerically unstable for acoustically large obstacles or for obstacles with large aspect ratios. We describe an efficient and stable method for computing the T-matrix for sound-soft, sound-hard, absorbing, and dielectric scattering, using numerical far field values obtained using any method. We demonstrate the algorithm by generalizing the recently proposed fundamental solution and non-polynomial finite element methods for the far field and T-matrix computations. References A. H. Barnett and T. Betcke. An exponentially convergent nonpolynomial finite element method for time-harmonic scattering from polygons. SIAM J. Sci. Comput., 2010, to appear. http://www.personal.reading.ac.uk/ sp900945/papers/BaBe09.pdf. D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 1998. A. Doicu, T. Wriedt, and Y. Eremin. Light Scattering by Systems of Particles. Null-Field Method with Discrete Sources---Theory and Programs. Springer Verlag, 2006. M. Ganesh and S. C. Hawkins. A far-field based T-matrix method for three dimensional acoustic scattering. ANZIAM J., 50:C121--C136, 2008. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1441 M. Ganesh and S. C. Hawkins. Three dimensional electromagnetic scattering T-matrix computations. J. Comput. Appl. Math., 2010. doi:10.1016/j.cam.2009.08.018. P. A. Martin. Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles. Cambridge University Press, 2006. M. I. Mishchenko, L. D. Travis, and A. A. Lacis. Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering. Cambridge University Press, 2006. P.C. Waterman. Matrix formulation of electromagnetic scattering. Proc. IEEE, 53:805--812, 1965.
@article{2581,
title = {A far-field based T-matrix method for two dimensional obstacle scattering},
journal = {ANZIAM Journal},
volume = {51},
year = {2010},
doi = {10.21914/anziamj.v51i0.2581},
language = {EN},
url = {http://dml.mathdoc.fr/item/2581}
}
Ganesh, Mahadevan; Hawkins, Stuart Collin. A far-field based T-matrix method for two dimensional obstacle scattering. ANZIAM Journal, Tome 51 (2010) . doi : 10.21914/anziamj.v51i0.2581. http://gdmltest.u-ga.fr/item/2581/