Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene (Communications in Computational Physics, 2023)
In this paper, we derive the frozen Gaussian approximation (FGA) for computing 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 strainedgraphene surfaces. We present numerical comparisons of the Dirac solutions on curvedand flat spaces, illustrating the focusing effect of graphene surfaces, as well as qualitative comparisons with a tight-binding model. A CPU-time comparison shows thatFGA becomes more efficient than an IMEX pseudospectral method when the semiclassical parameter is small.