A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. Application to quantum relativistic laser physics

X Antoine (1, 2) , E Lorin (3, 4)

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

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

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

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

X Antoine, E Lorin. A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. Application to quantum relativistic laser physics. 2018. ⟨hal-01929065⟩