Bradley Bonner (Bath. UK)

Practical aspects of diffraction coefficient computations

Abstract

The computation of diffraction coefficients for the scattering of high-frequency waves by conical scatterers can be reduced to the solution of a family of homogeneous boundary value problems for the Laplace-Beltrami-Helmholtz equation on a portion of the unit sphere bounded by a simple closed contour (in fact the intersection of the sphere with the conical scatterer). Distance on the contour is geodesic distance on the sphere. These can be solved by a nonstandard boundary integral equation method. The diffraction coefficient may be determined by then integrating the resulting solutions with respect to the wave number ([1]).

In this poster we present results on the practical aspects of these calculations, in particular;
(i) The stable and efficient evaluation of the kernel of the integral equation.
(ii) The choice of the quadrature rules for evaluating matrix entries.
(iii) Evaluation of the diffraction coefficients by integration with respect to the wave number.
(iv) Details of the computation in the electromagnetic case.

[1] V.M.Babich, V.P.Smyshlyaev, D.Dement'ev and B.A.Samokish, SIAM J Appl Math } 60(2000), 536-573.