Abstract
We introduce a new algorithm that exploits the relationship between the determinants of a sequence of matrices that appear in the calculation of many-electron wave function overlaps, yielding a considerable reduction of the theoretical cost. The resulting enhanced algorithm is embarrassingly parallel and our comparison against the (embarrassingly parallel version of) original algorithm, on a computer node with 40 physical cores, shows acceleration factors which are close to 7 for the largest problems, consistent with the theoretical difference.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Anzt, H., Dongarra, J., Flegar, G., Quintana-Ortí, E.S.: Variable-size batched LU for small matrices and its integration into block-Jacobi preconditioning. In: 2017 46th International Conference on Parallel Processing (ICPP), pp. 91–100 (2017). https://doi.org/10.1109/ICPP.2017.18
Dirac, P.A.M.: A new notation for quantum mechanics. Math. Proc. Cambridge Philos. Soc. 35(3), 416–418 (1939). https://doi.org/10.1017/S0305004100021162
Dong, T., Haidar, A., Luszczek, P., Harris, J.A., Tomov, S., Dongarra, J.: Lu factorization of small matrices: accelerating batched DGETRF on the GPU. In: 2014 IEEE International Conference on High Performance Computing and Communications, 2014 IEEE 6th Internatinal Symposium on Cyberspace Safety and Security, 2014 IEEE 11th International Conference on Embedded Software and Systems (HPCC, CSS, ICESS), pp. 157–160, August 2014. https://doi.org/10.1109/HPCC.2014.30
Golub, G.H., Loan, C.F.V.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)
Hammes-Schiffer, S., Tully, J.C.: Proton transfer in solution: molecular dynamics with quantum transitions. J. Chem. Phys. 101(6), 4657–4667 (1994). https://doi.org/10.1063/1.467455
Li, S.L., Truhlar, D.G., Schmidt, M.W., Gordon, M.S.: Model space diabatization for quantum photochemistry. J. Chem. Phys. 142(6), 064106 (2015)
Plasser, F., Ruckenbauer, M., Mai, S., Oppel, M., Marquetand, P., González, L.: Efficient and flexible computation of many-electron wave function overlaps. J. Chem. Theory Comput. 12(3), 1207–1219 (2016)
Quintana-Ortí, E.S., Van De Geijn, R.A.: Updating an LU factorization with pivoting. ACM Trans. Math. Softw. 35(2), 11:1–11:16 (2008)
Sapunar, M.: Natural transition orbitals for CIS type wave functions. https://github.com/marin-sapunar/cis_nto. Accessed 24 Oct 2019
Sapunar, M., Piteša, T., Davidović, D., Došlić, N.: Highly efficient algorithms for CIS type excited state wave function overlaps. J. Chem. Theory Comput. 15, 3461–3469 (2019)
Tully, J.C.: Molecular dynamics with electronic transitions. J. Chem. Phys. 93(2), 1061–1071 (1990). https://doi.org/10.1063/1.459170
Acknowledgement
This research was performed under project HPC-EUROPA3 (INFRAIA-2016-1-730897) and supported by Croatian Science Fundation under grant HRZZ IP-2016-06-1142, the Foundation of the Croatian Academy of Science and Arts, and the European Regional Development Fund under grant KK.01.1.1.01.0009 (DATACROSS). Enrique S. Quintana-Ortí was supported by project TIN2017-82972-R of the MINECO and FEDER. The authors gratefully acknowledge the computer resources provided by the Juelich Supercomputing center, and to BSC where the initial testings and the code development were performed.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Davidović, D., Quintana-Ortí, E.S. (2020). Structure-Aware Calculation of Many-Electron Wave Function Overlaps on Multicore Processors. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham. https://doi.org/10.1007/978-3-030-43229-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-43229-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43228-7
Online ISBN: 978-3-030-43229-4
eBook Packages: Computer ScienceComputer Science (R0)