Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation
Mathematics of Computation
Inhomogeneous conditions at open boundaries for wave propagation problems
Applied Numerical Mathematics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
A mathematical analysis of the PML method
Journal of Computational Physics
Nonreflecting boundary conditions for Maxwell's equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Nodal high-order methods on unstructured grids
Journal of Computational Physics
High-order non-reflecting boundary scheme for time-dependent waves
Journal of Computational Physics
Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
Following the scheme developed by Engquist and Majda [Math Comp. 31 (1977) 629] for first-order systems, we derive a theoretical perfectly absorbing nonlocal boundary condition for Maxwell's equations at a flat outer boundary. This condition can be approximated to any desired order by a differential equation on the boundary, and a sequence of such equations is developed here in terms of tangential derivatives of the electromagnetic fields at the boundary. The resulting set of equations, comprising Maxwell's equations in the interior together with any of the local boundary conditions, is shown to admit no exponentially growing solutions, and questions of their well-posedness are addressed.