Multiresolution scheme for Time-Dependent Schrödinger Equation

This paper is devoted to a multiresolution approach for solving laser-molecule Time-Dependent Schrödinger Equations (TDSE) in strong and high frequency fields. It is well known that short and intense laser-molecule interactions lead to complex nonlinear phenomena that necessitate an accurate numerical approximation of the TDSE. In particular, intense electric fields rapidly delocalize molecule wavefunctions so that their support can vary a lot during the interaction. In this kind of physical configurations, mesh adaption is a usual compromise between precision and computational efficiency. We then propose to explore numerically mesh adaptation for TDSE using a multiresolution analysis coupled with a Crank-Nicolson-like scheme. We then discuss the efficiency and the drawbacks of such a strategy.