A structured low-rank wavelet solver for the Ornstein-Zernike integral equation

M. V. Fedorov, H.-J. Flad, G. N. Chuev, L. Grasedyck, B. N. Khoromskij

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In this article, we present a new structured wavelet algorithm to solve the Ornstein-Zernike integral equation for simple liquids. This algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank approximations of the obtained convolution matrices. The fundamental properties of wavelet bases such as the interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets and Newton-Raphson algorithm, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.

LanguageEnglish
Pages47-73
Number of pages27
JournalComputing
Volume80
Issue number1
DOIs
Publication statusPublished - May 2007

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Ornstein-Zernike Equation
Integral equations
Integral Equations
Wavelets
Newton-Raphson Algorithm
Low-rank Approximation
Radial Distribution Function
Wavelet Bases
Hybrid Algorithm
Orthogonality
Wavelet Transform
Convolution
Interpolate
Liquid
Discrete wavelet transforms
Iteration
Distribution functions
Interpolation
Liquids

Keywords

  • wavelets
  • Ornstein-Zernike equation
  • simple fluids
  • data-sparse matrix approximations
  • simulations
  • h-matrices
  • fluids
  • singularities

Cite this

Fedorov, M. V. ; Flad, H.-J. ; Chuev, G. N. ; Grasedyck, L. ; Khoromskij, B. N. / A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. In: Computing. 2007 ; Vol. 80, No. 1. pp. 47-73.
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abstract = "In this article, we present a new structured wavelet algorithm to solve the Ornstein-Zernike integral equation for simple liquids. This algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank approximations of the obtained convolution matrices. The fundamental properties of wavelet bases such as the interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets and Newton-Raphson algorithm, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.",
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A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. / Fedorov, M. V.; Flad, H.-J.; Chuev, G. N.; Grasedyck, L.; Khoromskij, B. N.

In: Computing, Vol. 80, No. 1, 05.2007, p. 47-73.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A structured low-rank wavelet solver for the Ornstein-Zernike integral equation

AU - Fedorov, M. V.

AU - Flad, H.-J.

AU - Chuev, G. N.

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AU - Khoromskij, B. N.

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N2 - In this article, we present a new structured wavelet algorithm to solve the Ornstein-Zernike integral equation for simple liquids. This algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank approximations of the obtained convolution matrices. The fundamental properties of wavelet bases such as the interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets and Newton-Raphson algorithm, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.

AB - In this article, we present a new structured wavelet algorithm to solve the Ornstein-Zernike integral equation for simple liquids. This algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank approximations of the obtained convolution matrices. The fundamental properties of wavelet bases such as the interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets and Newton-Raphson algorithm, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.

KW - wavelets

KW - Ornstein-Zernike equation

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KW - simulations

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KW - fluids

KW - singularities

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