Schedule Aug 30, 2006
Advanced Time Dependent Computational Methods Using a Finite Element DVR Basis
Dr. Barry Schneider, NSF & KITP

The interaction of intense, short pulse lasers with atoms and molecules is best treated by propagating an initial state forward in time using the time dependent Schrodinger equation. In order to accomplish this it is essential to find computationally efficient techniques to discretize the spatial coordinates as well as to propagate the typically very large set of algebraic equations that results from the discretization procedure. The authors have developed a computational approach using a Finite Element Discrete Variable Method which scales linearly with the size of the basis set and can propagate the wavefunction in O(N) operations. In addition, the method only requires that basis functions or grid points at the boundaries of the elements communicate at each timestep. This allows us to parallelize the method using standard message passing techniques with high efficiency. The result is a numerical approach which scales linearly with the number of processors. I will describe the methodology in some detail and demonstrate the efficacy of the approach on a number of problems using up to 1000 processors. To date, we have observed linear scaling with both the number of processors as well as the number of finite elements in a variety of problems including the interaction of a circularly polarized laser pulse with atomic hydrogen.

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