A fast solver for the Ornstein-Zernike equations

C. Tim Kelley; B. Montgomery Pettitt

doi:10.1016/j.jcp.2003.12.006

A fast solver for the Ornstein-Zernike equations

C. Tim Kelley, B. Montgomery Pettitt

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

17 Scopus citations

Abstract

In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.

Original language	English (US)
Pages (from-to)	491-501
Number of pages	11
Journal	Journal of Computational Physics
Volume	197
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2003.12.006
State	Published - Jul 1 2004
Externally published	Yes

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2003.12.006

Cite this

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title = "A fast solver for the Ornstein-Zernike equations",

abstract = "In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.",

author = "Kelley, {C. Tim} and Pettitt, {B. Montgomery}",

note = "Funding Information: The research of CTK was partially supported by National Science Foundation Grants DMS-0070641 and DMS-0209695. The research of BMP was supported in part by the NIH and the Robert A. Welch Foundation. The authors are grateful to Dr. Dimitry A. Tikhonov for his comments on an earlier version of the manuscript.",

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AU - Pettitt, B. Montgomery

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N2 - In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.

AB - In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.

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A fast solver for the Ornstein-Zernike equations

Abstract

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