Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Perfectly matched layers for Maxwell's equations in second order formulation
Journal of Computational Physics
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
High order finite difference methods for wave propagation in discontinuous media
Journal of Computational Physics
High-order local absorbing conditions for the wave equation: Extensions and improvements
Journal of Computational Physics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
Journal of Computational Physics
Stable Boundary Treatment for the Wave Equation on Second-Order Form
Journal of Scientific Computing
Radiation boundary conditions for time-dependent waves based on complete plane wave expansions
Journal of Computational and Applied Mathematics
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Journal of Computational Physics
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Energy transmitted along a waveguide decays less rapidly than in an unbounded medium. In this paper we study the efficiency of a PML in a time-dependent waveguide governed by the scalar wave equation. A straight forward application of a Neumann boundary condition can degrade accuracy in computations. To ensure accuracy, we propose extensions of the boundary condition to an auxiliary variable in the PML. We also present analysis proving stability of the constant coefficient PML, and energy estimates for the variable coefficients case. In the discrete setting, the modified boundary conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates. Numerical stability and convergence of our numerical method follows. Finally we give a number of numerical examples, illustrating the stability of the layer and the high order accuracy of our proposed boundary conditions.