2020/07/25 by Gang Bao, Xue Jiang, Bao, Gang +5 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2007.13013
arxiv created 2020/07/25 · openalex publication_date 2020/07/25 · arxiv updated 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the Dirichlet-to-Neumann (DtN) operator, which is given as an infinite series, an exact transparent boundary condition is introduced and the scattering problem is formulated equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed to solve the discrete variational problem where the DtN operator is truncated into a finite number of terms. The a posteriori error estimate takes account of the finite element approximation error and the truncation error of the DtN operator which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.