title: Optimizing the FEDVR-TDCC code for exploring the quantum dynamics of two-electron systems in intense laser pulses.
abstract: To efficiently solve the three-dimensional (3D) time-dependent linear and nonlinear Schrödinger equation, we have developed a large-scale parallel code RSP-FEDVR [B. I. Schneider, L. A. Collins, and S. X. Hu, Phys. Rev. E 73, 036708 (2006)], which combines the finite-element discrete variable representation (FEDVR) with the real-space product algorithm. Using the similar algorithm, we have derived an accurate approach to solve the time-dependent close-coupling (TDCC) equation for exploring two-electron dynamics in linearly polarized intense laser pulses. However, when the number (N) of partial waves used for the TDCC expansion increases, the FEDVR-TDCC code unfortunately slows down, because the potential-matrix operation scales as ∼O(N2) . In this paper, we show that the full potential-matrix operation can be decomposed into a series of small-matrix operations utilizing the sparse property of the [N×N] potential matrix. Such optimization speeds up the FEDVR-TDCC code by an order of magnitude for N=256 . This may facilitate the ultimate solution to the 3D two-electron quantum dynamics in ultrashort intense optical laser pulses, where a large number of partial waves are required.
authors.affiliation: Laboratory for Laser Energetics, University of Rochester, 250 E. River Road, Rochester, New York 14623, USA. shu@lle.rochester.edu
authors.forename: S X
authors.initials: SX
authors.lastname: Hu