Ll. Thompson et Rn. Huan, Implementation of exact non-reflecting boundary conditions in the finite element method for the time-dependent wave equation, COMPUT METH, 187(1-2), 2000, pp. 137-159
Citations number
17
Categorie Soggetti
Mechanical Engineering
Journal title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
When solving the wave equation in infinite regions using finite element met
hods, the domain must be truncated. We investigate the accuracy of time-dep
endent non-reflecting boundary conditions (NRBC) derived in Grote, Keller (
1995), when implemented in the finite element method. The NRBC annihilate t
he first N wave harmonics on a spherical truncation boundary. High-order te
mporal derivatives are formulated as a system of first-order ordinary diffe
rential equations. Several versions of implicit and explicit multi-step, ti
me-integration schemes are presented for solution of the finite element equ
ations concurrently with the first-order system appearing in the NRBC. An a
lternative scaling of the boundary variables is introduced which leads to a
well-conditioned coefficient matrix. Although the boundary conditions are
global over the boundary, when implemented in the finite element method, th
ey only require inner products of spherical harmonics within the force vect
or, and as a result, they are easy to implement and do not disturb the band
ed/sparse structure of the matrix equations. Several numerical examples are
presented which demonstrate the improvement in accuracy over standard fini
te element methods. (C) 2000 Elsevier Science S.A. All rights reserved.