On the efficient convolution with the Newton potential

Wolfgang Hackbusch, Kishore Kumar Naraparaju, and Jan Schneider

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Submission date: 28. Aug. 2009
Pages: 19
published in: Journal of numerical mathematics, 18 (2010) 4, p. 257-280 
DOI number (of the published article): 10.1515/JNUM.2010.013
Bibtex
Keywords and phrases: convolution, Refined grid, Tensor product representation, Pointwise smoothness, 2-microlocal spaces
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Abstract:
The convolution 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.