2020/01/16 by Gang Bao, Bao, Gang, Mingming Zhang +5 · 1 citation
Computer Science · Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2001.05914
arxiv created 2020/01/16 · openalex publication_date 2020/01/16 · arxiv updated 2020/01/17 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28
This paper is concerned with a numerical solution of the acoustic scattering by a bounded impenetrable obstacle in three dimensions. The obstacle scattering problem is formulated as a boundary value problem in a bounded domain by using a Dirichlet-to-Neumann (DtN) operator. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator, where the latter is shown to decay exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element method is developed for the obstacle scattering problem. The truncation parameter is determined by the truncation error of the DtN operator and the mesh elements for local refinement are marked through the finite element approximation error. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.