# Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shapes

@article{Meade1995ComparisonOL, title={Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shapes}, author={Douglas B. Meade and Walter Joseph Slade and Andrew F. Peterson and Kevin J. Webb}, journal={IEEE Transactions on Antennas and Propagation}, year={1995}, volume={43}, pages={6-10} }

The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss-Turkel (1980) condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an infinite domain using traditional finite element and finite difference techniques. Unlike the standard Bayliss-Turkel condition, the generalizations considered here are applicable to noncircular solution domains. The accuracy of these conditions are…

## 24 Citations

Local absorbing boundary conditions for elliptical shaped boundaries

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2008

This work compares several local absorbing boundary conditions for solving the Helmholtz equation by a finite difference or finite element method, exterior to a general scatterer, and introduces a new boundary condition for an ellipse based on a modal expansion.

A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems

- Mathematics
- 1998

We compare the accuracy of a variety of approximate boundary conditions (ABCs) and two versions of an infinite element method (IEM) for approximating solutions of exterior Helmholtz problems. The…

Comparison of Two-Dimensional Conformal Local Adiation Boundary Conditions

- Mathematics
- 1996

ABSTRACT Numerical solutions for openndash;region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation…

Local absorbing boundaries of elliptical shape for scalar waves

- Mathematics
- 2004

We discuss the performance of a family of local and weakly-non-local in space and time absorbing boundary conditions, prescribed on truncation boundaries of elliptical shape for the solution of the…

A DISCRETE NON-LOCAL OUTGOING BOUNDARY CONDITION FOR WATER WAVES RADIATION AND SCATTERING

- 1998

Abstract.A discrete non-local (DNL) boundary condition is used to solve water waves radiation and scattering problems. This boundary condition absorbs waves of any wave-length and any frequency…

Local absorbing boundaries of elliptical shape for scalar wave propagation in a half-plane

- Mathematics
- 2004

We have recently discussed the performance of local second-order two-dimensional absorbing boundary conditions of elliptical shape for scattering and radiation problems involving sound-hard obstacles…

Transient fluid-structure interaction of elongated bodies by finite-element method using elliptical and spheroidal absorbing boundaries.

- Physics, MedicineThe Journal of the Acoustical Society of America
- 2003

It is demonstrated that significant computational economy can be achieved for elongated bodies with the use of BGT dampers in both elliptical and spheroidal coordinate systems developed for transient problems involving acoustic radiation as well as fluid-structure interaction and implemented in the context of finite-element method based upon unsymmetric pressure-displacement formulation.

Important Considerations in the Evaluation of Absorbing Boundary Conditions

- Mathematics
- 1996

Abstract In this paper, we study the interaction of an absorbing boundary condition (ABC) with the discretization error. In many cases the major source of error is due to the discretization error and…

Numerical Implementation of a Conformable Two-Dimensional Radiation Boundary Condition

- 1995

In open region di erential equation problems it is common to limit the computational domain by introducing an arti cial boundary. The arti cal boundary condition must be chosen to produce as little…

RADIATION BOUNDARY CONDITIONS FOR THE HELMHOLTZ EQUATION FOR ELLIPSOIDAL, PROLATE SPHEROIDAL, OBLATE SPHEROIDAL AND SPHERICAL DOMAIN BOUNDARIES

- Physics
- 2012

One of the most popular radiation boundary conditions for the Helmholtz equation in exterior 3-D regions has been the sequence of operators developed by Bayliss et al.1 for computational domains with…

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