### 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.

Original language | English |
---|---|

Pages (from-to) | 47-73 |

Number of pages | 27 |

Journal | Computing |

Volume | 80 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2007 |

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### Keywords

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

### Cite this

*Computing*,

*80*(1), 47-73. https://doi.org/10.1007/s00607-007-0221-7

}

*Computing*, vol. 80, no. 1, pp. 47-73. https://doi.org/10.1007/s00607-007-0221-7

**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.

Research output: Contribution to journal › Article

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.

AU - Grasedyck, L.

AU - Khoromskij, B. N.

PY - 2007/5

Y1 - 2007/5

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

KW - simple fluids

KW - data-sparse matrix approximations

KW - simulations

KW - h-matrices

KW - fluids

KW - singularities

U2 - 10.1007/s00607-007-0221-7

DO - 10.1007/s00607-007-0221-7

M3 - Article

VL - 80

SP - 47

EP - 73

JO - Computing

JF - Computing

SN - 0010-485X

IS - 1

ER -