Non-reflecting boundary conditions
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Journal of Computational Physics
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Absorbing PML boundary layers for wave-like equations
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Well-posed perfectly matched layers for advective acoustics
Journal of Computational Physics
A Stable, perfectly matched layer for linearized Euler equations in unslit physical variables
Journal of Computational Physics
On Optimal Finite-Difference Approximation of PML
SIAM Journal on Numerical Analysis
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Perfectly Matched Layers for the Convected Helmholtz Equation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Perfectly Matched Layers for Time-Harmonic Acoustics in the Presence of a Uniform Flow
SIAM Journal on Numerical Analysis
High-order local absorbing conditions for the wave equation: Extensions and improvements
Journal of Computational Physics
High-order Absorbing Boundary Conditions for anisotropic and convective wave equations
Journal of Computational Physics
Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods
SIAM Journal on Numerical Analysis
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 2: Time-dependent modeling
Journal of Computational Physics
Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case). The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL). PMDL is a simple variant of perfectly matched layers (PML) and is equivalent to rational approximation-based local ABCs. Specifically, we derive a sufficient condition for PMDL to accurately absorb wave modes with outgoing group velocities and this condition turns out to be a simple bound on the PMDL parameters. The reflection coefficient derived in this paper clearly reveals that the PMDL absorption is based on group velocities, and not phase velocities, and hence a PMDL can be designed to correctly identify and accurately absorb all outgoing wave modes (even those with opposing signs of phase and group velocities). The validity of the sufficient condition is demonstrated through a series of frequency domain simulations. In part 2 of this paper [S. Savadatti, M.N. Guddati, Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling, J. Comput. Phys. (2010), doi:10.1016/j.jcp.2010.05.017], the accuracy condition presented here is shown to govern both the well-posedness and accuracy aspects of PMDL designed for transient (time-dependent) modeling of scalar waves in anisotropic media.