Radiation boundary conditions for elastic wave propagation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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
High-order non-reflecting boundary scheme for time-dependent waves
Journal of Computational Physics
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
A new absorbing layer for elastic waves
Journal of Computational Physics
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
Journal of Computational Physics
High-order Absorbing Boundary Conditions for anisotropic and convective wave equations
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods
SIAM Journal on Numerical Analysis
Reflectionless truncation of target area for axially symmetric anisotropic elasticity
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
Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy
Journal of Computational Physics
Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy
Journal of Computational Physics
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With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general elastic media, we investigate the accuracy aspects of local ABCs designed for untilted non-elliptic anisotropy in the frequency domain (time-harmonic analysis). While simple space-time transformations are available to treat the wavemodes with opposing phase and group velocities present in elliptic anisotropic media, no such transformations are known to exist for the case of non-elliptic anisotropy. In this paper, we use the concept of layer groupings along with an unconventional stretching of the finite element mesh to guarantee the accuracy of local ABCs designed to treat all propagating wavemodes, even those with opposing phase and group velocities. The local ABC used here is the perfectly matched discrete layer (PMDL) which is a simple variant of perfectly matched layers (PMLs) that is also equivalent to rational approximation-based local ABCs (rational ABCs); it inherits the straightforward approximation properties of rational ABCs along with the versatility of PML. The approximation properties of PMDL quantified through its reflection matrix allow us to (a) show that it is impossible to design an accurate PMDL with wavenumber-independent parameters, (b) theoretically demonstrate the ability of wavenumber-dependent parameters to ensure accuracy, and finally (c) design a practical though unconventional stretching of the finite element PMDL mesh that facilitates the implementation of wavenumber-dependent parameters. The validity of this work is demonstrated through a series of numerical experiments.