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

Fedorov, M. V. and Flad, H.-J. and Chuev, G. N. and Grasedyck, L. and Khoromskij, B. N. (2007) A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. Computing, 80 (1). pp. 47-73. ISSN 0010-485X

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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.