Absorbing boundary conditions are derived for the Klein-Gordon and Dirac equations modeling quantum particles subject to a classical electromagnetic field in high frequency regime. The proposed approach is based on the approximation of pseudo-differential operators using techniques developed by Antoine, Barucq and Besse. Numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
This is a joint work with X. Antoine (Univ. Lorraine) and J. Sater (Carleton Univ.).