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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 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.

MiS Preprint
53/2009

On the efficient convolution with the Newton potential

Wolfgang Hackbusch, Kishore Kumar Naraparaju and Jan Schneider

Abstract

The convolution $\int_{\mathbb{R}^{d}}\frac{1}{\left\Vert x-y\right\Vert }f(y)dy,$ where $f$ is smooth, except for some local singularities, arises for example in electronic structure calculations. An efficient convolution with the Newton potential in $d$ dimensions has been proposed in [3]. The convolution is approximated on a refined grid and additional approximations are introduced for efficient evaluation. This paper studies the performance of the method and a precise error analysis of the method is discussed.

Received:
Aug 28, 2009
Published:
Aug 28, 2009
Keywords:
convolution, Refined grid, Tensor product representation, Pointwise smoothness, 2-microlocal spaces

Related publications

inJournal
2010 Repository Open Access
Wolfgang Hackbusch, Kishore Kumar Naraparaju and Jan Schneider

On the efficient convolution with the Newton potential

In: Journal of numerical mathematics, 18 (2010) 4, pp. 257-280