An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures

07/25/2020
by   Gang Bao, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 26

page 28

page 29

02/18/2022

An Adaptive Finite Element DtN Method for Maxwell's Equations

This paper is concerned with a numerical solution to the scattering of a...
01/14/2021

An adaptive finite element DtN method for the elastic wave scattering problem in three dimensions

Consider the elastic scattering of an incident wave by a rigid obstacle ...
02/16/2021

A homogenized damping model for the propagation of elastic wave in a porous solid

This paper develops an averaging technique based on the combination of t...
04/22/2020

An adaptive finite element DtN method for the open cavity scattering problems

Consider the scattering of a time-harmonic electromagnetic plane wave by...
08/05/2021

The Nyström method for elastic wave scattering by unbounded rough surfaces

We consider the numerical algorithm for the two-dimensional time-harmoni...
02/16/2020

A half-plane time-domain BEM for SH-wave scattering by a subsurface inclusion

A direct time-domain numerical approach named the half-plane boundary el...
03/04/2020

Deriving peridynamic influence functions for one-dimensional elastic materials with periodic microstructure

The influence function in peridynamic material models has a large effect...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.