Convolution of hp-functions on locally refined grids - extended version

Wolfgang Hackbusch

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Submission date: 11. Apr. 2007 (revised version: June 2007)
Pages: 26
published in: IMA journal of numerical analysis, 29 (2009) 4, p. 960-985 
DOI number (of the published article): 10.1093/imanum/drn047
Bibtex
with the following different title: Convolution of hp-functions on locally refined grids
MSC-Numbers: 44A35, 42A55
Keywords and phrases: convolution integral, hp-finite elements, non-uniform grids, local refinement
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Abstract:
Usually, the fast evaluation of a convolution integral requires that the functions f,g have a simple structure based on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the convolution of hp-functions in certain locally refined grids. More precisely, the convolution result is projected into some given hp-space (Galerkin approximation). The overall cost is where N is the sum of the dimensions of the subspaces containing f, g and the resulting function, while p is the maximal polynomial degree.