The Finite Element Discrete Variable Method (FEDVRM) for Solving the Time-Dependent Schroedinger Equation (TDSE)

The FEDVRM is an efficient approach to discretizing partial differential equations containing second-order or lower derivatives in space. The piecewise continuous nature of this representation, leading to sparse and structured matrices, combined with its ability to accurately represent matrix elements of local operators as their values on the grid, make it an extremely efficient spectral-element method. When combined with a time-propagation technique such as the short iterative Lanczos or real space propagation method, it is possible to parallelize the solution for the TDSE in a manner which scales linearly with the number of cpu cores. The method has been applied in up to six space and one time dimension ( i.e. the $H_2$ molecule in an intense laser field) and applications have been made demonstrating this linear scaling on a number of NSF supercomputers. The method will be described in some detail in the talk and will conclude with one or two illustrative examples.

Speaker Bio: Dr Barry I. Schneider (b. 1940 in Brooklyn, New York) is a staff member of the NIST Applied and Computational Mathematics Division. He is also a General Editor for the DLMF project. A graduate of the NYC Public Schools, he received his B.S. in chemistry from Brooklyn College, his M.S. in chemistry from Yale University and a Ph.D. in theoretical chemistry from the University of Chicago. Before coming to NIST in 2014, he was a postdoctoral research associate at the University of Southern California (1969-1970), and a staff member of the General Telephone and Electronics Laboratory (1970-1972). He joined the Theoretical Division of Los Alamos National Laboratory (1972-1991) and then the National Science Foundation (1991-2013 ). In early 2014, he came to NIST as a General Editor of the DLMF project. Schneider's current research interests span a broad number of areas of theoretical chemistry, atomic and molecular physics, numerical methods and high performance computing. His current principal focus is developing novel methods for the solution of the time dependent Schroedinger equation in ultra-short, and intense laser fields. He has authored or co-authored 130 refereed papers and books and has given numerous invited talks in the US and abroad. Schneider was awarded a Poste Rouge by the CNRS in 1980, was elected a Fellow of the American Physical Society (APS) in 1983 and received the prestigious Humboldt prize from the German government in 1987. He was a visiting scientist at NIST from 1995 to 2013 and spent a sabbatical year at NIST in 2000-2001. Schneider has served as Chair and Co-Chair of the APS Division of Computational Physics and Few Body Topical group and has been the organizer of a number of conferences and invited sessions here and abroad. He also serves as a reviewer for a variety of journals inside and outside the US.

Presentation Slides: PPT

Note: Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.