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arXiv · 1109.6352

Convergence analysis of a high-order Nystrom integral-equation method for surface scattering problems

Oscar P. Bruno·Victor Dominguez·Francisco-Javier Sayas
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Abstract

In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering problems in three-dimensional space. This fast and efficient scheme combines FFT techniques and a polar change of variables that cancels out the kernel singularity. We establish the stability of the algorithms in the $L^2$ norm and we derive convergence estimates in both the $L^2$ and $L^\infty$ norms. In particular, our analysis establishes theoretically the previously observed super-algebraic convergence of the method in cases in which the right-hand side is smooth.

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Oscar P. Bruno, Victor Dominguez, Francisco-Javier Sayas. 2011-09-28. Convergence analysis of a high-order Nystrom integral-equation method for surface scattering problems. https://arxiv.org/abs/1109.6352

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