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

2018 
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.
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