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Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method
International Journal of Quantum Chemistry
  • R. Glenn Brook, Mississippi State University
  • Paul E. Oppenheimera, Florida A&M University
  • Charles A. Weatherford, Florida Agricultural and Mechanical University
  • Ioana Banicescu, Mississippi State University
  • Jianping Zhu, Cleveland State University
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This article documents the first implementation of a parallel algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm employs a quantum trajectory method (QTM) based on the serial algorithm introduced by Wyatt and Lopreore. The OpenMP API is employed to parallelize the code across the quantum trajectories in a shared memory environment. An outline of the parallel algorithm is provided; the analytical solution for a moving free particle is used to verify the solution obtained by the parallel algorithm. Further validation against several of the results obtained by Wyatt and Lopreore is also provided. The parallel speedups and runtimes are presented, and several performance issues are noted. Finally, the results of a preliminary accuracy study examining a moving free particle are provided.

Contract grant sponsor: National Science Foundation. Contract grant numbers: NSF ITR/ACS Award # ACI0081303 and Award # EEC-9730381.

Citation Information
Brook, G., Oppenheimer, P., Weatherford, C. A., Banicescu, I., and Zhu, J. (2001). Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method. International Journal of Quantum Chemistry, 85(4-5), 263 - 271, doi: 10.1002/qua.1509.