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

摘要

In this paper we present a convergence analysis for the Nyström methodudproposed in [J Comput Phys 169 (1):80–110, 2001] for the solution of the combinedudboundary integral equation formulations of sound-soft acoustic scattering problemsudin three-dimensional space. This fast and efficient scheme combines FFT techniquesudand a polar change of variables that cancels out the kernel singularity. We establishudthe stability of the algorithms in the L^2 norm and we derive convergence estimatesudin both the L^2 and L^∞ norms. In particular, our analysis establishes theoretically theudpreviously observed super-algebraic convergence of the method in cases in which theudright-hand side is smooth.