Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method

R. Glenn Brook; Paul E. Oppenheimera; Charles A. Weatherford; Ioana Banicescu; Jianping Zhu

doi:10.1002/qua.1509

Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method

R. Glenn Brook, Paul E. Oppenheimera, Charles A. Weatherford, Ioana Banicescu, Jianping Zhu

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Journal	International Journal of Quantum Chemistry
Volume	85
DOIs	https://doi.org/10.1002/qua.1509
State	Published - Jan 1 2001

Keywords

Scattering theory
Wave-packet methods
Hydrodynamic formulation
Meshless methods
Quantum trajectory methods
Parallel algorithm

Disciplines

Mathematics
Physical Chemistry

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10.1002/qua.1509License: CC BY

http://onlinelibrary.wiley.com/doi/10.1002/qua.1509/abstract

Cite this

@article{6d4871476c484ab79a8e7873ddc4f90d,

title = "Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method",

abstract = "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.",

keywords = "Scattering theory, Wave-packet methods, Hydrodynamic formulation, Meshless methods, Quantum trajectory methods, Parallel algorithm",

author = "Brook, \{R. Glenn\} and Oppenheimera, \{Paul E.\} and Weatherford, \{Charles A.\} and Ioana Banicescu and Jianping Zhu",

note = "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.",

year = "2001",

month = jan,

day = "1",

doi = "10.1002/qua.1509",

language = "American English",

volume = "85",

journal = "International Journal of Quantum Chemistry",

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TY - JOUR

T1 - Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method

AU - Brook, R. Glenn

AU - Oppenheimera, Paul E.

AU - Weatherford, Charles A.

AU - Banicescu, Ioana

AU - Zhu, Jianping

N1 - 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.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

KW - Scattering theory

KW - Wave-packet methods

KW - Hydrodynamic formulation

KW - Meshless methods

KW - Quantum trajectory methods

KW - Parallel algorithm

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/61

UR - http://onlinelibrary.wiley.com/doi/10.1002/qua.1509/abstract

U2 - 10.1002/qua.1509

DO - 10.1002/qua.1509

M3 - Article

VL - 85

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

ER -

Solving the Hydrodynamic Formulation of Quantum Mechanics: A Parallel MLS Method

Abstract

Keywords

Disciplines

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