Abstract
Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudopartides whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally-intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This work contributes a strategy for improving the performance of wavepacket simulations using the QTM on message-passing systems. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling is employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel efficiencies of up to 90% when simulating a free particle.
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References
D. Bohm. 1952. āA Suggested Interpretation of the Quantum Theory In Terms of Hidden Variables.ā Physical Review 85,No. 2, January:166ā193.
Lopreore, C. L. and R. W. Wyatt. 1999. āQuantum Wavepacket Dynamics With Trajectories.ā Physical Review Letters 82, No. 26, June:5190ā5193.
Brook, R. G.; P. E. Oppenheimer; C. A. Weatherford; I. Banicescu; J. Zhu. 2001. āSolving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method.ā International Journal of Quantum Chemistry 85, Nos. 4ā5, October: 263ā271.
Brook, R. G.; P. E. Oppenheimer; C. A. Weatherford; I. Banicescu; J. Zhu. 2002. āAccuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrƶdinger Equationā Journal of Molecular Structure (Theochem) 592, April: 69ā77.
Vadapalli, R. K.; C. A. Weatherford; I. Banicescu; R. L. Carin; J. Zhu. 2003. āTransient Effect of a Free Particle Wave Packet in the Hydrodynamic Formulation of the Time-dependent Schrƶdinger Equation.ā International Journal of Quantum Chemistry 94, Issue 1: 1ā6.
Carino, R. L.; R. K. Vadapalli; I. Banicescu; C. A. Weatherford; J. Zhu. 2002. āWavepacket Dynamics Using the Quantum Trajectory Method on Message-Passing Systems.ā Proceedings of the ITAMP Workshop on Computational Approaches to Time-Dependent Quantum Dynamics, (to be published in the Journal of Molecular Science).
Carino, R. L.; I. Banicescu; R. K. Vadapalli; T. Dubreus; C. A. Weatherford; J. Zhu. 2003. āWavepacket Simulations Using the Quantum Trajectory Method With Loop Scheduling.ā Proceedings of the High Performance Computing Symposium (HPC) 2003, (Orlando, FL, March 30-April 3). Society for Computer Simulation, 93ā99.
Kruskal, C. and A. Weiss. 1985. āAllocating Independent Subtasks on Parallel Processors.ā IEEE Trans. Software Eng SE-11, No. 10, October: 1001ā1016.
Polychronopoulos, C. and D. Kuck. 1987. āGuided Self-Scheduling: A Practical Scheduling Scheme for Parallel Supercomputers.ā IEEE Trans on Computers C-36, No. 12, December: 1425ā1439.
Flynn Hummel, S., E. Schonberg; L. E. Flynn. 1992. āFactoring: A Method for Scheduling Parallel Loops.ā Communications of the ACM 35, No. 8, August:90ā101.
Banicescu, I. and S. F. Hummel. 1995. āBalancing Processor Loads and Exploiting Data Locality in N-Body Simulations.ā Proceedings of the 1995 ACM/IEEE Supercomputing Conference,(San Diego, CA, December 3ā8). ACM/IEEE, http://www.supercomp.org/sc95/proceedings/ 594_BHUM/SC95.HTM.
Flynn Hummel, S.; J. Schmidt; R. N. Uma; J. Wein. 1996. āLoad-Sharing in Heterogeneous Systems via Weighted Factoring.ā SPAA ā86: Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures, (Padua, Italy, June 24ā26). ACM, 318ā328.
Banicescu, I. and V. Velusamy. 2001. āPerformance of Scheduling Scientific Applications with Adaptive Weighted Factoring.ā Proceedings of the 15th International Parallel and Distributed Processing Symposium (IPDPS-01), 10th Heterogeneous Computing Workshop, (San Francisco, CA, April 23ā27). IEEE Computer Society Press, on CD-ROM.
Banicescu, I., V. Velusamy and J. Devaprasad. 2003. āOn the Scalability of Dynamic Scheduling Scientific Applications with Adaptive Weighted Factoring.ā Cluster Computing, The Journal of Networks, Software Tools and Applications 6, July:215ā226.
Cariiio, R. L. and I. Banicescu. 2002. āDynamic scheduling parallel loops with variable iterate execution times.ā Proceedings of the 16th International Parallel and Distributed Processing Symposium (IPDPS-02) - Workshop on Parallel and Distributed Scientific and Engineering Applications, (Ft. Lauderdale, FL, April 15ā19). IEEE Computer Society Press, on CD-ROM.
Cariiio, R. L. and I. Banicescu. 2002. āLoad Balancing Parallel Loops on Message-Passing Systems.ā Proceedings of the 14th TASTED International Conference on Parallel and Distributed Computing and Systems, S. G. Akl and T Gonzales (Eds) (Cambridge MA, Nov. 4ā6). ACTA Press, 362ā367.
Banicescu, I. and Z. Liu. 2000. āAdaptive Factoring: A Dynamic Scheduling Method Tuned to the Rate of Weight Changes.ā Proceedings of the High Performance Computing Symposium (HPC) 2000, (Washington DC, April 16ā20). Society for Computer Simulation, 122ā129.
Banicescu, I. and V. Velusamy. 2002. āLoad Balancing Highly Irregular Computations with the Adaptive Factoring.ā Proceedings of the 16th International Parallel and Distributed Processing Symposium (IPDPS-02) - Heterogeneous Computing Workshop, (Ft. Lauderdale, FL, April 15ā19). IEEE Computer Society Press, on CD-ROM.
Carino, R. L. and I. Banicescu. 2003. āA Load Balancing Tool for Distributed Parallel Loops.ā Proceedings of the International Workshop on Challenges of Large Applications in Distributed Environments (CLADE) 2003, (Seattle WA, June 21). IEEE Computer Society Press, 39ā46.
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CariƱo, R.L., Banicescu, I., Vadapalli, R.K., Weatherford, C.A., Zhu, J. (2004). Message-Passing Parallel Adaptive Quantum Trajectory Method. In: Yang, L.T., Pan, Y. (eds) High Performance Scientific and Engineering Computing. The Springer International Series in Engineering and Computer Science, vol 750. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5402-5_9
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DOI: https://doi.org/10.1007/978-1-4757-5402-5_9
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