Abstract
The application of High Performance Computing to Quantum Chemical (QC) calculations faces many challenges. A central step is the solution of the generalized eigenvalue problem of a Hamilton matrix. Although in many cases its execution time is small relative to other numerical tasks, its complexity of \(\mathcal{O}(N^3)\) is higher, thus more significant in larger applications. For parallel QC codes, it therefore is advantageous to have a scalable solver for this step.
We investigate the case where the symmetry of a molecule leads to a block-diagonal matrix structure, which complicates an efficient use of available parallel eigensolvers. We present a technique which employs a malleable parallel task scheduling (MPTS) algorithm to schedule instances of sequential and parallel eigensolver routines from LAPACK and ScaLAPACK. In this way, an efficient use of hardware resources is guaranteed while overall scalability is facilitated. Finally, we evaluate the proposed technique for electronic structure calculations of real chemical systems. For the systems considered, the performance was improved by factors of up to 8.4, compared to the previously used, non-malleable parallel scheduling approach.
Chapter PDF
References
Altmann, S.L., Herzig, P.: Point-group theory tables. Clarendon, Oxford (1994)
Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., Sorensen, D.: LAPACK’s user’s guide. SIAM, Philadelphia (1992)
Belling, T., Grauschopf, T., Krüger, S., Mayer, M., Nörtemann, F., Staufer, M., Zenger, C., Rösch, N.: High performance scientific and engineering computing. In: Bungartz, H.J., Durst, F., Zenger, C. (eds.) Lecture notes in Computational Science and Engineering, vol. 8, pp. 439–453 (1999)
Belling, T., Grauschopf, T., Krüger, S., Nörtemann, F., Staufer, M., Mayer, M., Nasluzov, V.A., Birkenheuer, U., Hu, A., Matveev, A.V., Shor, A.V., Fuchs-Rohr, M.S.K., Neyman, K.M., Ganyushin, D.I., Kerdcharoen, T., Woiterski, A., Majumder, S., Rösch, N.: ParaGauss, version 3.1. Tech. rep., Technische Universität München (2006)
Bischof, C., Müller, M.S., Knüpfer, A., Jurenz, M., Lieber, M., Brunst, H., Mix, H., Nagel, W.E.: Developing scalable applications with Vampir, VampirServer and VampirTrace. In: Proc. of ParCo 2007, pp. 113–120 (2007)
Blackford, L.S., Choi, J., Cleary, A., D’Azeuedo, E., Demmel, J., Dhillon, I., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C., Dongarra, J.: ScaLAPACK user’s guide. SIAM, Philadelphia (1997)
Blazewicz, J., Ecker, K., Pesch, E., Schmidt, G., Weglarz, J.: Handbook on scheduling: from theory to applications. Springer, Heidelberg (2007)
Blazewicz, J., Kovalyov, M.Y., Machowiak, M., Trystram, D., Weglarz, J.: Scheduling malleable tasks on parallel processors to minimize the makespan. Ann. Oper. Res. 129, 65–80 (2004)
Decker, T., Lücking, T., Monien, B.: A 5/4-approximation algorithm for scheduling identical malleable tasks. Theor. Comput. Sci. 361(2), 226–240 (2006)
Demmel, J., Stanley, K.: The performance of finding eigenvalues and eigenvectors of dense symmetric matrices on distributed memory computers. In: Proc. seventh SIAM conf. on parallel processing for scientific computing, pp. 528–533 (1995)
Dunlap, B.I., Rösch, N.: The Gaussian-type orbitals density-functional approach to finite systems. Adv. Quantum Chem. 21, 317–339 (1990)
Garey, M., Johnson, D.: Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman and Company, New York (1979)
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)
Graham, R.: Bounds on multiprocessing timing anomalities. SIAM J. Appl. Math. 17, 263–269 (1969)
Hein, J.: Improved parallel performance of SIESTA for the HPCx Phase2 system. Tech. rep., The University of Edinburgh (2004)
Jansen, K.: Scheduling malleable parallel tasks: an asymptotic fully polynomial time approximation scheme. Algorithmica 39, 59–81 (2004)
Koch, W., Holthausen, M.C.: A chemist’s guide to density functional theory. Wiley-VCH, Weinheim (2001)
Ludwig, W., Tiwari, P.: Scheduling malleable and nonmalleable parallel tasks. In: SODA 1994, pp. 167–176 (1994)
Mounié, G., Rapine, C., Trystram, D.: Efficient approximation algorithms for scheduling malleable tasks. In: SPAA 1999, pp. 23–32 (1999)
Mounié, G., Rapine, C., Trystram, D.: A 3/2-approximation algorithm for scheduling independent monotonic malleable tasks. SIAM J. Comp. 37(2), 401–412 (2007)
National supercomputer HLRB-II, http://www.lrz-muenchen.de/
Steinberg, A.: A strip-packing algorithm with absolute performance bound 2. SIAM J. Comp. 26(2), 401–409 (1997)
Turek, J., Wolf, J., Yu, P.: Approximate algorithms for scheduling parallelizable tasks. In: SPAA 1992, pp. 323–332 (1992)
Ward, R.C., Bai, Y., Pratt, J.: Performance of parallel eigensolvers on electronic structure calculations II. Tech. rep., The University of Tennessee (2006)
Yudanov, I.V., Matveev, A.V., Neyman, K.M., Rösch, N.: How the C-O bond breaks during methanol decomposition on nanocrystallites of palladium catalysts. J. Am. Chem. Soc. 130, 9342–9352 (2008)
Yudanov, I.V., Metzner, M., Genest, A., Rösch, N.: Size-dependence of adsorption properties of metal nanoparticles: a density functional study on Pd nanoclusters. J. Phys. Chem. C 112, 20269–20275 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Roderus, M., Berariu, A., Bungartz, HJ., Krüger, S., Matveev, A., Rösch, N. (2010). Scheduling Parallel Eigenvalue Computations in a Quantum Chemistry Code. In: D’Ambra, P., Guarracino, M., Talia, D. (eds) Euro-Par 2010 - Parallel Processing. Euro-Par 2010. Lecture Notes in Computer Science, vol 6272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15291-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-15291-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15290-0
Online ISBN: 978-3-642-15291-7
eBook Packages: Computer ScienceComputer Science (R0)