An efficient solver for problems of scattering by bodies of revolution

Details An efficient solver for problems of scattering by bodies of revolution An efficient solver for problems of scattering by bodies of revolution

2003-11-28

arxiv.org/abs/math/0311515v1

Mathematics

Numerical Analysis

33 pages, 4 figures

Scientific paper

This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the Lippmann-Schwinger integral equation in $O(N\log^2 N)$ operations, where $N$ is the number of the discretization points. The method achieves its efficiency through the use of the addition theorem and Fast Legendre Transforms (FLT). For globally smooth sound velocities/refractive indexes the method is spectrally accurate. More generally the order of convergence is tied to and in fact, limited by, the smoothness of the solution.

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