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Structure-Aware Calculation of Many-Electron Wave Function Overlaps on Multicore Processors

  • Davor DavidovićEmail author
  • Enrique S. Quintana-Ortí
Conference paper
  • 114 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12043)

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.

Keywords

Wave functions LU factorization Multicore processors 

Notes

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.

References

  1. 1.
    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
  2. 2.
    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/S0305004100021162MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    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
  4. 4.
    Golub, G.H., Loan, C.F.V.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  5. 5.
    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/10.1063/1.467455CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sapunar, M.: Natural transition orbitals for CIS type wave functions. https://github.com/marin-sapunar/cis_nto. Accessed 24 Oct 2019
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Tully, J.C.: Molecular dynamics with electronic transitions. J. Chem. Phys. 93(2), 1061–1071 (1990).  https://doi.org/10.1063/1.459170CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Centre for Informatics and ComputingRuđer Bošković InstituteZagrebCroatia
  2. 2.Depto. de Informática de Sistemas y ComputadoresUniversitat Politècnica de ValènciaValènciaSpain

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