Time Propagation of Partial Differential Equations Using the Short Iterative Lanczos Method and Finite-Element Discrete Variable Representation

Published

February 12, 2016

Author(s)

Barry I. Schneider, Klaus Bartschat, Xiaoxu Guan

Abstract

The Short Iterative Lanczos (SIL) method has been combined with the Finite-Element Discrete Variable Representation (FE-DVR) to yield a powerful approach to solving the time-dependent Schrödinger equation. It has been applied to the interaction of short, intense laser radiation (attosecond pulses) to describe the single and double ionization of atoms and molecules, but the approach is not limited to this particular application. The paper describes the algorithms in some detail and how they have been successfully ported to the Intel Phi coprocessors. While further experimentation is needed, the current results provide reasonable evidence that by suitably modifying the code to combine MPI, OpenMP, and compiler offload directives, one can achieve significant improvement in performance from these coprocessors for problems such as the above.

Citation

Advances In Quantum Chemistry

Pub Type

Journals

Keywords

time-dependent Schro¿dinger equation, attosecond pulses, short-iterative Lanczos method, finite-element discrete variable method, numerical solution of PDE, high performance computing, Phi coprocessors

Citation

Schneider, B. , Bartschat, K. and Guan, X. (2016), Time Propagation of Partial Differential Equations Using the Short Iterative Lanczos Method and Finite-Element Discrete Variable Representation, Advances In Quantum Chemistry (Accessed October 1, 2025)