Non-reflecting boundary conditions
Journal of Computational Physics
Radiation boundary conditions for dispersive waves
SIAM Journal on Numerical Analysis
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
A formulation of asymptotic and exact boundary conditions using local operators
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
SIAM Journal on Numerical Analysis
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
On Optimal Finite-Difference Approximation of PML
SIAM Journal on Numerical Analysis
High-order non-reflecting boundary scheme for time-dependent waves
Journal of Computational Physics
Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems
Journal of Computational Physics
High-order Absorbing Boundary Conditions for anisotropic and convective wave equations
Journal of Computational Physics
Radiation boundary conditions for time-dependent waves based on complete plane wave expansions
Journal of Computational and Applied Mathematics
Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling
Journal of Computational Physics
Absorbing boundary conditions for scalar waves in anisotropic media. Part 1: Time harmonic modeling
Journal of Computational Physics
On the stability of the high-order Higdon Absorbing Boundary Conditions
Applied Numerical Mathematics
Journal of Computational Physics
Application of H-W boundary condition in dam-reservoir interaction problem
Finite Elements in Analysis and Design
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
Solution of the 3D-Helmholtz equation in exterior domains using spherical harmonic decomposition
Computers & Mathematics with Applications
On the Accuracy and Stability of the Perfectly Matched Layer in Transient Waveguides
Journal of Scientific Computing
Journal of Scientific Computing
A high-order based boundary condition for dynamic analysis of infinite reservoirs
Computers and Structures
A general approach for high order absorbing boundary conditions for the Helmholtz equation
Journal of Computational Physics
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Journal of Computational Physics
The Double Absorbing Boundary method
Journal of Computational Physics
Hi-index | 31.49 |
The solution of the time-dependent wave equation in an unbounded domain is considered. An artificial boundary B is introduced which encloses a finite computational domain. On B an absorbing boundary condition (ABC) is imposed. A formulation of local high-order ABCs recently proposed by Hagstrom and Warburton and based on a modification of the Higdon ABCs, is further developed and extended in a number of ways. First, the ABC is analyzed in new ways and important information is extracted from this analysis. Second, The ABCs are extended to the case of a dispersive medium, for which the Klein-Gordon wave equation governs. Third, the case of a stratified medium is considered and the way to apply the ABCs to this case is explained. Fourth, the ABCs are extended to take into account evanescent modes in the exact solution. The analysis is applied throughout this paper to two-dimensional wave guides. Two numerical algorithms incorporating these ABCs are considered: a standard semi-discrete finite element formulation in space followed by time-stepping, and a high-order finite difference discretization in space and time. Numerical examples are provided to demonstrate the performance of the extended ABCs using these two methods.