Abstract
The time-dependent Schrödinger equation (TDSE) describes the quantum dynamical nature of molecular processes. However, numerical simulations of this linear, high-dimensional partial differential equation (PDE) rapidly become computationally very demanding and massive-scale parallel computing is needed to tackle many interesting problems. We present recent improvements to our MPI and OpenMP parallelized code framework HAParaNDA for solving high-dimensional PDE problems like the TDSE. By using communication-efficient high-order finite difference methods and Lanczos time propagators, we are able to accurately and efficiently solve TDSE problems in up to five dimensions on medium-sized clusters. We report numerical experiments which show that the solver scales well up to at least 4096 computing cores, also on computer systems with commodity communication networks.
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Gustafsson, M., Kormann, K., Holmgren, S. (2012). Communication-Efficient Algorithms for Numerical Quantum Dynamics. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_36
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DOI: https://doi.org/10.1007/978-3-642-28145-7_36
Publisher Name: Springer, Berlin, Heidelberg
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