Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation

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

doi:10.1016/S0166-1280(02)00228-2

Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation

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

Mississippi State University
Florida A&M University
Florida Agricultural and Mechanical University

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

Abstract

This work examines the accuracy of a parallel moving least squares algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm solves the associated linear least squares problems using either normal equations or QR factorization. The accuracy of the algorithm is studied for both the free particle and the harmonic oscillator, and the results of a series of experiments designed to determine the spatial and temporal dependence of the accuracies are presented. In closing, a few qualitative observations concerning the performance of the algorithm are offered for consideration.

Original language	American English
Journal	Journal of Molecular Structure: THEOCHEM
Volume	592
DOIs	https://doi.org/10.1016/S0166-1280(02)00228-2
State	Published - Sep 13 2002

Keywords

Hydrodynamic formulation
Quantum mechanics
Parallel MLS algorithm
Wave-packet method

Disciplines

Mathematics
Physical Chemistry

Access to Document

10.1016/S0166-1280(02)00228-2License: CC BY

http://www.sciencedirect.com/science/article/pii/S0166128002002282

Cite this

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title = "Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schr{\"o}dinger Equation",

abstract = " This work examines the accuracy of a parallel moving least squares algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm solves the associated linear least squares problems using either normal equations or QR factorization. The accuracy of the algorithm is studied for both the free particle and the harmonic oscillator, and the results of a series of experiments designed to determine the spatial and temporal dependence of the accuracies are presented. In closing, a few qualitative observations concerning the performance of the algorithm are offered for consideration.",

keywords = "Hydrodynamic formulation, Quantum mechanics, Parallel MLS algorithm, Wave-packet method",

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. (2002). Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schr{\"o}dinger Equation. Journal of Molecular Structure: THEOCHEM, 592(1-3), 69 -77, doi: 10.1016/S0166-1280(02)00228-2.",

year = "2002",

month = sep,

day = "13",

doi = "10.1016/S0166-1280(02)00228-2",

language = "American English",

volume = "592",

journal = "Journal of Molecular Structure: THEOCHEM",

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TY - JOUR

T1 - Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation

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. (2002). Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation. Journal of Molecular Structure: THEOCHEM, 592(1-3), 69 -77, doi: 10.1016/S0166-1280(02)00228-2.

PY - 2002/9/13

Y1 - 2002/9/13

N2 - This work examines the accuracy of a parallel moving least squares algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm solves the associated linear least squares problems using either normal equations or QR factorization. The accuracy of the algorithm is studied for both the free particle and the harmonic oscillator, and the results of a series of experiments designed to determine the spatial and temporal dependence of the accuracies are presented. In closing, a few qualitative observations concerning the performance of the algorithm are offered for consideration.

AB - This work examines the accuracy of a parallel moving least squares algorithm for solving the governing equations of the hydrodynamic formulation of quantum mechanics. The algorithm solves the associated linear least squares problems using either normal equations or QR factorization. The accuracy of the algorithm is studied for both the free particle and the harmonic oscillator, and the results of a series of experiments designed to determine the spatial and temporal dependence of the accuracies are presented. In closing, a few qualitative observations concerning the performance of the algorithm are offered for consideration.

KW - Hydrodynamic formulation

KW - Quantum mechanics

KW - Parallel MLS algorithm

KW - Wave-packet method

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/60

UR - http://www.sciencedirect.com/science/article/pii/S0166128002002282

U2 - 10.1016/S0166-1280(02)00228-2

DO - 10.1016/S0166-1280(02)00228-2

M3 - Article

VL - 592

JO - Journal of Molecular Structure: THEOCHEM

JF - Journal of Molecular Structure: THEOCHEM

ER -

Accuracy Studies of a Parallel Algorithm for Solving the Hydrodynamic Formulation of the Time-dependent Schrödinger Equation

Abstract

Keywords

Disciplines

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