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Fast and oblivious convolution quadrature

Please always quote using this URN:urn:nbn:de:0296-matheon-2127
  • We give an algorithm to compute N steps of a convolution quadrature approximation to a continuous temporal convolution using only O(N logN) multiplications and O(logN) active memory. The method does not require evaluations of the convolution kernel, but instead O(logN) evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integrodifferential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.

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Metadaten
Author:Achim Schädle, Maria Lopez Fernandez, Christian Lubich
URN:urn:nbn:de:0296-matheon-2127
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/01/13
Release Date:2005/01/24
Preprint Number:307
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