Optimizing the FEDVR-TDCC code for exploring the quantum dynamics of two-electron systems in intense laser pulses

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.