The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
The numerical computation of connecting orbits in dynamical systems: a rational spectral approach
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
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Global discrete artificial boundary conditions for time-dependent wave propagation
Journal of Computational Physics
Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
Nonreflecting boundary condition for time-dependent multiple scattering
Journal of Computational Physics
Journal of Computational Physics
Local nonreflecting boundary condition for time-dependent multiple scattering
Journal of Computational Physics
Hi-index | 31.46 |
An exact non-reflecting boundary conditions based on a boundary integral equation or a modified Kirchhoff-type formula is derived for exterior three-dimensional wave equations. The Kirchhoff-type non-reflecting boundary condition is originally proposed by L. Ting and M.J. Miksis [J. Acoust. Soc. Am. 80 (1986) 1825] and numerically tested by D. Givoli and D. Cohen [J. Comput. Phys. 117 (1995) 102] for a spherically symmetric problem. The computational advantage of Ting Miksis boundary condition is that its temporal non-locality is limited to a fixed amount of past information. However, a long-time instability is exhibited in testing numerical solutions by using a standard nondissipative finite-difference scheme. The main purpose of this work is to present a new exact boundary condition and to eliminate the long-time instability. The proposed exact boundary condition can be considered as a limit case of Ting-Miksis boundary condition when the two artificial boundaries used in their method approach each other. Our boundary condition is actually a boundary integral equation on a single artificial boundary for wave equations, which is to be solved in conjunction with the interior wave equation. The new boundary condition needs only one artificial boundary, which can be of any shape, i.e., sphere, cubic surface, etc. It keeps all merits of the original Kirchhoff boundary condition such as restricting the temporal non-locality, free of numerical evaluation of any special functions and so on. Numerical approximation to the artificial boundary condition on cubic surface is derived and three-dimensional numerical tests are carried out on the cubic computational domain.