zbMATH — the first resource for mathematics

Using piecewise polynomials for faster potential function evaluation. (English) Zbl 1182.65018
Summary: In many molecular dynamics simulation software packages and hardware implementations, piecewise polynomials are used to represent and compute pairwise potential functions efficiently. In this paper, we present three modifications applicable to most interpolations to increase their accuracy. The increased accuracy reduces the amount of data that needs to be stored for each interaction potential, making such interpolations more suitable for architectures with limited memory and/or cache or hardware implementations.
65D05 Numerical interpolation
65C05 Monte Carlo methods
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
Full Text: DOI
[1] Allen, M.P.; Tildesley, D.J., Computer simulation of liquids, (1987), Oxford Science Publications, Clarendon Press Oxford · Zbl 0703.68099
[2] Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A.E.; Berendsen, H.J.C., GROMACS: fast, flexible and free, Journal of computational chemistry, 26, 1701-1718, (2005)
[3] Kalé, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K., NAMD2: greater scalability for parallel molecular dynamics, Journal of computational physics, 151, 283-312, (1999) · Zbl 0948.92004
[4] IBM Systems and Technology Group, Cell Broadband Engine Programming Handbook, Including the PowerXCell 8i Processor, IBM Corporation, 2008.
[5] Andrea, T.A.; Swope, W.C.; Andersen, H.C., The role of long ranged forces in determining the structure and properties of liquid water, Journal of chemical physics, 79, 9, 4576-4584, (1983)
[6] D. van der Spoel, E. Lindahl, B. Hess, A.R. van Buuren, E. Apol, P.J. Meulenhoff, D.P. Tieleman, A.L.T.M. Sijbers, K.A. Feenstra, R. van Drunen, H.J.C. Berendsen, GROMACS User Manual version 3.3, www.gromacs.org, 2005.
[7] M. Tiji, N. Tetsu, Y. Ohno, N. Futatsugi, A. Suenaga, N. Takada, A. Konagaya, Protein explorer: a petaflops special-purpose computer system for molecular dynamics simulations, in: Proceedings of the ACM/IEEE SC2003 Conference (SC’03), 2003, p. 15.
[8] K.J. Bowers, E. Chow, H. Xu, R.O. Dror, M.P. Eastwood, B.A. Gregersen, J.L. Klepeis, I. Kolossváry, M.A. Moraes, F.D. Sacerdoti, J.K. Salmon, Y. Shan, D.E. Shaw, Scalable algorithms for molecular dynamics simulations on commodity clusters, in: Proceedings of the ACM/IEEE Conference on Supercomputing (SC06), Tampa, Florida, 2006, p. 84.
[9] D.E. Shaw Research, Desmond User’s Guide, September 1987.
[10] R.H. Larson, J.K. Salmon, R.O. Dror, M.M. Deneroff, C. Young, J. Grossman, Y. Shan, J.L. Klepeis, D.E. Shaw, High-throughput pairwise point interactions in Anton, a specialized machine for molecular dynamics simulation, in: Proceedings of the 14th Annual International Symposium on High-Performance Computer Architecture (HPCA ’08), Salt Lake City, Utah, 2008, pp. 331-342.
[11] Fox, L.; Parker, I.B., Chebyshev polynomials in numerical analysis, (1968), Oxford University Press London · Zbl 0153.17502
[12] Clenshaw, C.W., A note on the summation of Chebyshev series, Mathematical tables and other aids to computation, 9, 51, 118-120, (1955) · Zbl 0065.05403
[13] W.G. Horner, A new method of solving numerical equations of all orders, by continuous approximation, Philosophical Transactions of the Royal Society of London (1819) 308-335.
[14] J. Wetzel, E. Shiha, C. May, B. Frey, J. Furukawa, G. Frazier, PowerPC User Instruction Set Architecture, Book I, IBM, January 2005.
[15] Hunt, N.G.; Cohen, F.E., Fast lookup tables for interatomic interactions, Journal of computational chemistry, 17, 16, 1857-1862, (1996)
[16] Berendsen, H.J.C., Simulating the physical world, (2007), Cambridge University Press Cambridge, UK
[17] Brent, R.P., Algorithms for minimization without derivatives, (1973), Prentice-Hall LinkEnglewood Cliffs, N.J. · Zbl 0245.65032
[18] Berendsen, H.J.C.; Grigera, J.R.; Straatsma, T.P., The missing term in effective pair potentials, Journal of physical chemistry, 91, 6269-6271, (1987)
[19] Intel C++ Compiler Professional Edition 11.1 for Linux, http://software.intel.com/en-us/intel-compilers/.
[20] Intel VTune Performance Analyzer 9.1 for Linux, http://software.intel.com/en-us/intel-vtune/.
[21] Barker, K.J.; Davis, K.; Hoisie, A.; Kerbyson, D.J.; Lang, M.; Pakin, S.; Sancho, J.C., Entering the petaflop era: the architecture and performance of roadrunner, (), 1-11
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.