Ten lectures on wavelets
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Fast Convolution for Nonreflecting Boundary Conditions
SIAM Journal on Scientific Computing
Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics
Journal of Scientific Computing
High-order non-reflecting boundary scheme for time-dependent waves
Journal of Computational Physics
Design of Absorbing Boundary Conditions for Schrödinger Equations in $\mathbbR$d
SIAM Journal on Numerical Analysis
Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations
Numerische Mathematik
Time-frequency localization operators: a geometric phase space approach
IEEE Transactions on Information Theory
A perfectly matched layer approach to the nonlinear Schrödinger wave equations
Journal of Computational Physics
Mathematics and Computers in Simulation
Hi-index | 31.46 |
We present a new algorithm, the time dependent phase space filter (TDPSF) which is used to solve time dependent nonlinear Schrodinger equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.