Exact non-reflecting boundary conditions
Journal of Computational Physics
Non-reflecting boundary conditions
Journal of Computational Physics
Numerical simulation of gravity waves
Journal of Computational Physics
Approximation of analytic functions: a method of enhanced convergence
Mathematics of Computation
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Exact nonreflecting boundary conditions for the time dependent wave equation
SIAM Journal on Applied Mathematics
On nonreflecting boundary conditions
Journal of Computational Physics
Nonreflecting boundary conditions for time-dependent scattering
Journal of Computational Physics
Nonreflecting boundary conditions for Maxwell's equations
Journal of Computational Physics
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
High-order boundary perturbation methods
Mathematical modeling in optical science
Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics
Journal of Scientific Computing
Error analysis and preconditioning for an enhanced DtN-FE algorithm for exterior scattering problems
Journal of Computational and Applied Mathematics
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering
Journal of Computational Physics
Exact Non-Reflecting Boundary Conditions on Perturbed Domains and hp-Finite Elements
Journal of Scientific Computing
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The authors present a new method for the realization of exact non-reflecting (transparent) boundary conditions in two dimensional direct scattering problems. This work is an extension of Keller, Givoli, and Grote's work on such conditions which required that the shape of the boundary be quite specific, i.e. circular or elliptical. The condition is enforced via the Dirichlet-Neumann operator (DNO) which, on general boundaries, presents the main difficulty in the method. The implementation is performed by one of two perturbative methods (where the perturbation parameter measures the deformation of the general geometry from a canonical one). A rigorous proof of the analyticity for the DNO with respect to this perturbation parameter is presented. Numerical results show both perturbative methods are fast and accurate, and can enable significant computational savings.