A non-conforming domain decomposition approximation for the Helmholtz\n screen problem with hypersingular operator

2015/06/01 by Norbert Heuer, Heuer, Norbert, Gredy Salmerón +1 · 1 citation
Computer Science · Engineering · #65N38 #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1506.00688

openalex publication_date 2015/06/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We present and analyze a non-conforming domain decomposition approximation\nfor a hypersingular operator governed by the Helmholtz equation in three\ndimensions. This operator appears when considering the corresponding Neumann\nproblem in unbounded domains exterior to open surfaces. We consider small wave\nnumbers and low-order approximations with Nitsche coupling across interfaces.\nUnder appropriate assumptions on mapping properties of the weakly singular and\nhypersingular operators with Helmholtz kernel, we prove that this method\nconverges almost quasi-optimally. Numerical experiments confirm our error\nestimate.\n

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