Skip Navigation


IMA Journal of Numerical Analysis Advance Access originally published online on October 3, 2008
IMA Journal of Numerical Analysis 2009 29(4):960-985; doi:10.1093/imanum/drn047
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
29/4/960    most recent
drn047v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Hackbusch, W.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Convolution of hp-functions on locally refined grids

W. Hackbusch{dagger}

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22–26, D-04103 Leipzig, Germany

{dagger} Email: wh{at}mis.mpg.de

Received on 31 May 2007. Revised on 18 June 2008.


  Abstract

Usually, the fast evaluation of a convolution integral Formula requires that the functions f and 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 O(p2N log N), 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.

Key Words: convolution integral; hp-finite elements; nonuniform grids; local refinement


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.