Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation
Mathematics of Computation
Absorbing boundary conditions for diffusion equations
Numerische Mathematik
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Absorbing Boundary Conditions for the Schrödinger Equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
Local spectral time splitting method for first- and second-order partial differential equations
Journal of Computational Physics
Absorbing Boundary Conditions for One-dimensional Nonlinear Schrödinger Equations
Numerische Mathematik
Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
Journal of Computational Physics
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In this paper, we present an adaptive approach to design the artificial boundary conditions for the two-level Schrodinger equation with conical crossings on the unbounded domain. We use the windowed Fourier transform to obtain the local wave number information in the vicinity of artificial boundaries, and adopt the operator splitting method to obtain an adaptive local artificial boundary condition. Then reduce the original problem into an initial boundary value problem on the bounded computational domain, which can be solved by the finite difference method. By this numerical method, we observe the surface hopping phenomena of the two-level Schrodinger equation with conical crossings. Several numerical examples are provided to show the accuracy and convergence of the proposed method.