Numerical integration of the time-dependent Schrödinger equation for laser-driven helium

The full time-dependent Schrödinger equation for 2-electron atoms in intense laser fields is solved using a mixed finite-difference/basis set approach. We discuss Krylov subspace techniques for the propagation of the equation in time, and numerical methods for optimizing the description of the system on a finite-difference lattice. We describe the implementation of a parallelized code based on these numerical methods, and review performance and scaling results of the code on the Cray T3D/E.