6 research outputs found
Convergence analysis of a high-order Nyström integral-equation method for surface scattering problems
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