

Preprint 81/2007
Efficient convolution with the Newton potential in d dimensions
Wolfgang Hackbusch
Contact the author: Please use for correspondence this email.
Submission date: 04. Sep. 2007 (revised version: July 2008)
Pages: 30
published in: Numerische Mathematik, 110 (2008) 4, p. 449-489
DOI number (of the published article): 10.1007/s00211-008-0171-9
Bibtex
Keywords and phrases: newton potential, convolution, coulomb potential
Download full preprint: PDF (378 kB), PS ziped (337 kB)
Abstract:
The paper is concerned with the evaluation of the convolution integral
in
d dimensions (usually d=3), when f is given as piecewise polynomial of
possibly large degree, i.e., f may be considered as an hp-finite element
function. The underlying grid is locally refined using various levels of
dyadically organised grids. The result of the convolution is approximated in
the same kind of mesh. If f is given in tensor product form, the
d-dimensional convolution can be reduced to one-dimensional convolutions.
Although the details are given for the kernel
the basis techniques can be generalised to homogeneous kernels, e.g., the
fundamential solution
of the
d-dimensional Poisson equation.