A Plane Wave Discontinuous Galerkin Method with a Dirichlet-to-Neumann\n Boundary Condition for the Scattering Problem in Acoustics

2016/11/22 by Shelvean Kapita, Kapita, Shelvean, Peter Monk +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1611.07337

openalex publication_date 2016/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the numerical solution of an acoustic scattering problem by the\nPlane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded\ndomain in \ℝ². In order to apply the PWDG method, we introduce an\nartificial boundary to truncate the domain, and we impose a non-local\nDirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To\ndefine the method, we introduce new consistent numerical fluxes that\nincorporate the truncated series of the DtN map. Error estimates with respect\nto the truncation order of the DtN map, and with respect to mesh width are\nderived. Numerical results suggest that the accuracy of the PWDG method for the\nacoustic scattering problem can be significantly improved by using DtN boundary\nconditions.\n

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