A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Nonreflecting boundary conditions based on Kirchhoff-type formulae
Journal of Computational Physics
Exact nonreflecting boundary conditions for the time dependent wave equation
SIAM Journal on Applied Mathematics
Nonreflecting boundary conditions for time-dependent scattering
Journal of Computational Physics
Nonreflecting boundary conditions for Maxwell's equations
Journal of Computational Physics
A formulation of asymptotic and exact boundary conditions using local operators
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Fast evaluation of three-dimensional transient wave fields using diagonal translation operators
Journal of Computational Physics
The Perfectly Matched Layer in Curvilinear Coordinates
SIAM Journal on Scientific Computing
Exact nonreflecting boundary condition for elastic waves
SIAM Journal on Applied Mathematics
Nonreflecting boundary conditions for elastodynamic scattering
Journal of Computational Physics
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
SIAM Journal on Numerical Analysis
Fast Convolution for Nonreflecting Boundary Conditions
SIAM Journal on Scientific Computing
Stability of perfectly matched layers, group velocities and anisotropic waves
Journal of Computational Physics
Exact boundary condition for time-dependent wave equation based on boundary integral
Journal of Computational Physics
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Local nonreflecting boundary condition for time-dependent multiple scattering
Journal of Computational Physics
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An exact nonreflecting boundary condition (NBC) is derived for the numerical solution of time-dependent multiple scattering problems in three space dimensions, where the scatterer consists of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. In fact, the computational work due to the NBC only requires a fraction of the computational work inside @W, due to any standard finite difference or finite element method, independently of the mesh size or the desired overall accuracy. Therefore, the overall numerical scheme retains the rate of convergence of the interior scheme without increasing the complexity of the total computational work. Moreover, the extra storage required depends only on the geometry and not on the final time. Numerical examples show that the NBC for multiple scattering is as accurate as the NBC for a single convex artificial boundary [M.J. Grote, J.B. Keller, Nonreflecting boundary conditions for time-dependent scattering, J. Comput. Phys. 127(1) (1996), 52-65], while being more efficient due to the reduced size of the computational domain.