Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Abstract

Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schrödinger equation. Finite element discrete variables grid discretizations provide as efficient absorption as the corresponding finite elements basis set discretizations. This finding is at variance with results reported in literature [L. Tao et al., Phys. Rev. A 48, 063419 (2009)]. For finite differences, a new class of generalized $Q$-point schemes for non-equidistant grids is derived. Convergence of absorption is exponential $\sim Δx^{Q-1}$ and numerically robust. Local relative errors $\sim10^{-9}$ are achieved in a standard problem of strong-field ionization.