2011/09/28 by Oscar P. Bruno, Bruno, Oscar P., Vı́ctor Domínguez +3
Engineering · Physics and Astronomy · #65N35 #65N38 #65T40 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1109.6352
openalex publication_date 2011/09/28 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
In this paper we present a convergence analysis for the Nystrom method\nproposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of\nthe combined boundary integral equation formulations of sound-soft acoustic\nscattering problems in three-dimensional space. This fast and efficient scheme\ncombines FFT techniques and a polar change of variables that cancels out the\nkernel singularity. We establish the stability of the algorithms in the L2\nnorm and we derive convergence estimates in both the L2 and L^\∞\nnorms. In particular, our analysis establishes theoretically the previously\nobserved super-algebraic convergence of the method in cases in which the\nright-hand side is smooth.\n