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
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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 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 -