A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Perfectly matched absorbing layers for the paraxial equations
Journal of Computational Physics
Discrete transparent boundary conditions for Schrödinger-type equations
Journal of Computational Physics
Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics
Journal of Computational Physics
Absorbing Boundary Conditions for the Schrödinger Equation
SIAM Journal on Scientific Computing
A comparison of transparent boundary conditions for the Fresnel equation
Journal of Computational Physics
Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A perfectly matched layer approach to the nonlinear Schrödinger wave equations
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Journal of Computational Physics
Applied Numerical Mathematics
On the stability of boundary conditions for molecular dynamics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
A local high-order doubly asymptotic open boundary for diffusion in a semi-infinite layer
Journal of Computational Physics
Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains
Mathematics and Computers in Simulation
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings
Journal of Computational Physics
Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
SIAM Journal on Scientific Computing
Original article: Lanczos-Chebyshev pseudospectral methods for wave-propagation problems
Mathematics and Computers in Simulation
Transient Schrödinger-Poisson simulations of a high-frequency resonant tunneling diode oscillator
Journal of Computational Physics
Hi-index | 31.50 |
This paper addresses the problem of the construction of stable approximation schemes for the one-dimensional linear Schrödinger equation set in an unbounded domain. After a study of the initial boundary-value problem in a bounded domain with a transparent boundary condition, some unconditionally stable discretization schemes are developed for this kind of problem. The main difficulty is linked to the involvement of a fractional integral operator defining the transparent operator. The proposed semi-discretization of this operator yields with a very different point of view the one proposed by Yevick, Friese and Schmidt [J. Comput. Phys. 168 (2001) 433]. Two possible choices of transparent boundary conditions based on the Dirichlet-Neumann (DN) and Neumann-Dirichlet (ND) operators are presented. To preserve the stability of the fully discrete scheme, conform Galerkin finite element methods are employed for the spatial discretization. Finally, some numerical tests are performed to study the respective accuracy of the different schemes.