Finite element formulation of exact non-reflecting boundary conditions for the time-dependent wave equation
✍ Scribed by Lonny L. Thompson; Runnong Huan
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 200 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0029-5981
No coin nor oath required. For personal study only.
✦ Synopsis
A modiÿed version of an exact Non-re ecting Boundary Condition (NRBC) ÿrst derived by Grote and Keller is implemented in a ÿnite element formulation for the scalar wave equation. The NRBC annihilate the ÿrst N wave harmonics on a spherical truncation boundary, and may be viewed as an extension of the secondorder local boundary condition derived by Bayliss and Turkel. Two alternative ÿnite element formulations are given. In the ÿrst, the boundary operator is implemented directly as a 'natural' boundary condition in the weak form of the initial-boundary value problem. In the second, the operator is implemented indirectly by introducing auxiliary variables on the truncation boundary. Several versions of implicit and explicit timeintegration schemes are presented for solution of the ÿnite element semidiscrete equations concurrently with the ÿrst-order di erential equations associated with the NRBC and an auxiliary variable. Numerical studies are performed to assess the accuracy and convergence properties of the NRBC when implemented in the ÿnite element method. The results demonstrate that the ÿnite element formulation of the (modiÿed) NRBC is remarkably robust, and highly accurate.