Fast Projected Convolution of Piecewise Linear Functions on Non-equidistant Grids

W. Hackbusch ()
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W. Hackbusch: Max-Planck-Institut Mathematik in den Naturwissenschaften

A chapter in From Nano to Space, 2008, pp 145-160 from Springer

Abstract: Abstract Usually, the fast evaluation of a convolution integral f ℝ f(y)g(x−y)dy requires that the functions f, g are discretised on an equidistant grid in order to apply FFT. Here we discuss the efficient performance of the convolution in locally refined grids. More precisely, f and g are assumed to be piecewise linear and the convolution result is projected into the space of linear functions in a given locally refined grid. Under certain conditions, the overall costs are still O(N logN), where N is the sum of the dimensions of the subspaces containing f, g and the resulting function.

Keywords: Piecewise Linear Function; Level Number; Discrete Convolution; Equidistant Grid; Population Balance Model (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74238-8_12

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DOI: 10.1007/978-3-540-74238-8_12

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