Asymptotic and exact radiation boundary conditions
for time-dependent scattering
Lonny L. Thompson and Runnong Huan
Advanced Computational Mechanics Research Laboratory
Department of Mechanical Engineering and Engineering Mechanics
Clemson University
Clemson, South Carolina 29634-0921
NCA-Vol. 26, Proceedings of the ASME Noise Control and Acoustics Division - 1999, ASME 1999, pp. 511-521;
1999 International Mechanical Engineering Congress and Exposition,
Symposium on Computational Acoustics,
Nov. 14-19, 1999, Nashville, TN.
Abstract
Asymptotic and exact local radiation boundary conditions first
derived by Hagstrom and Hariharan are reformulated as
an auxiliary Cauchy problem for linear first-order systems of ordinary
equations on the boundary for each harmonic on a circle or sphere
in two- or three-dimensions, respectively.
With this reformulation, the resulting radiation boundary condition
involves first-order derivatives only and
can be computed efficiently and
concurrently with standard semi-discrete finite element methods for the near-field solution without changing the
banded/sparse structure of the finite element equations.
In 3D, with the number of equations in the Cauchy problem equal to the
mode number, this reformulation is exact.
If fewer equations are used, then the boundary conditions
form uniform asymptotic approximations to the exact condition.
Furthermore, using this approach, we formulate accurate radiation
boundary conditions for the two-dimensional
unbounded problem on a circle.
Numerical studies of time-dependent radiation and scattering
are performed to assess the accuracy and convergence
properties of the boundary conditions when
implemented in the finite element method.
The results demonstrate that the new formulation has
dramatically improved accuracy
and efficiency for time domain simulations compared to standard
boundary treatments.
Compressed Postscript file of Manuscript
Adobe PDF file of Manuscript