A Time-Space Adaptive Method for the Schrödinger Equation (Communications in Computational Physics, 2018)
In this paper, we present a discretization of the time-dependent Schrödingerequation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobattofinite elements in space. A truncated Galerkin orthogonality is used to obtain duality-baseda posteriori error estimates that address the temporal and the spatial error separately.Based on this theory, a space-time adaptive solver for the Schrödinger equationis devised. An efficient matrix-free implementation of the differential operator, suitedfor spectral elements, is used to enable computations for realistic configurations. Wedemonstrate the performance of the algorithm for the example of matter-field interaction.