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

Authors:
M. V. Fedorov;H. -J. Flad;G. N. Chuev;L. Grasedyck;B. N. Khoromskij
Affiliations:
University of Cambridge, Department of Chemistry, Lensfield Road, CB2 1EW, Cambridge, UK;Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22–26, 04103, Leipzig, Germany;Biophysics of RAS, Institute of Theoretical and Experimental, Institutskaya str. 3, 142 290, Pushchino, Russia;Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22–26, 04103, Leipzig, Germany;Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22–26, 04103, Leipzig, Germany
Venue:
Computing
Year:
2007

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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.