Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene

In this paper, we derive the frozen Gaussian approximation (FGA) for com-puting the solution to the Dirac equation in curved space in the semi-classical regime. The latter equation is used in particular for modeling electronic scattering on strained graphene surfaces. We present numerical comparisons of the Dirac solutions on curved and flat spaces, illustrating the focusing effect of graphene surfaces, as well as quali-tative comparisons with a tight-binding model. A CPU-time comparison shows that FGA becomes more efficient than an IMEX pseudospectral method when the semiclas-sical parameter is small.