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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Low-Rank wavelet solver for the Ornstein-Zernike integral equation
Maxim V. Fedorov, Heinz-Jürgen Flad, Lars Grasedyck and Boris N. KhoromskijAbstract
A structured wavelet algorithm is developed to solve the Ornstein-Zernike integral equation for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank matrix approximations. The fundamental properties of wavelet bases such as 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 in a multilevel method, 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.
- Received:
- 15.06.05
- Published:
- 15.06.05
- MSC Codes:
- 65F50, 65F30, 46B28, 47A80
- PACS:
- 02.60.N, 61.20.Ne, 61.20.Gy
- Keywords:
- wavelets, ornstein-zernike equation, simple fluids, data-sparse matrix approximations