Paper Info
Title
Domain Decomposition Method and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrödinger Equation with Ionization and Recombination by Intense Electric Field.
Abstract
This paper is devoted to the efficient computation of the time dependent Schrödinger equation for quantum particles subject to intense electromagnetic fields including ionization and recombination of electrons with their parent ion. The proposed approach is based on a domain decomposition technique, allowing a fine computation of the wavefunction in the vicinity of the nuclei located in a domain \(\Omega _1\) and a fast computation in a roughly meshed domain \(\Omega _2\) far from the nuclei where the electrons are assumed free. The key ingredients in the method are (i) well designed transmission boundary conditions on \(\partial \Omega _1\) (resp. \(\partial \Omega _2\)) in order to estimate the part of the wavefunction “leaving” Domain \(\Omega _1\) (resp. \(\Omega _2\)), (ii) a Schwarz waveform relaxation algorithm to accurately reconstruct the solution. The developed method makes it possible for electrons to travel from one domain to another without loosing accuracy, when the frontier or the overlapping region between two domains is crossed by the wavefunction.
Year
DOI
Venue
2015
10.1007/s10915-014-9902-5
Journal of Scientific Computing
Keywords
Field
DocType
Schrödinger equation, Non-reflecting boundary conditions, Domain decomposition method, Schwarz waveform relaxation, Laser, Ionization
Boundary value problem,Mathematical optimization,Ionization,Mathematical analysis,Quantum mechanics,Schrödinger equation,Wave function,Omega,Electromagnetic field,Domain decomposition methods,Physics,Electron
Journal
Volume
Issue
ISSN
64
3
1573-7691
Citations 
PageRank 
References 
7
0.58
8
Authors
3
Name
Order
Citations
PageRank
Xavier Antoine125132.52
Emmanuel Lorin25513.13
André D. Bandrauk3439.52