A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers

Xavier Antoine (1, 2) , Emmanuel Lorin (3, 4)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 School of Mathematics and Statistics [Ottawa]
4 CRM - Centre de Recherches Mathématiques [Montréal]

A simple time-splitting pseudospectral method for the computation of the Dirac equation with Perfectly Matched Layers is proposed. Within this approach, basic and widely used FFT-based solvers can be adapted without much effort to compute Initial Boundary Value Problems for the time-dependent Dirac equation with absorbing boundary layers. Some numerical examples from laser-physics are proposed to illustrate the method.

Mots clés: pseudospectral approximation; time-splitting; high-order accuracy; Perfectly Matched Layers; Dirac equation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Xavier Antoine, Emmanuel Lorin. A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. Journal of Computational Physics, 2019, 395, pp.583-601. ⟨10.1016/j.jcp.2019.06.020⟩. ⟨hal-02340843⟩