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

Abstract

In this paper we present a convergence analysis for the Nyström method proposed in [J Comput Phys 169 (1):80–110, 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^∞ 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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