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Generalized convolution quadrature with variable time stepping. Part II: Algorithm and numerical results


Lopez-Fernandez, Maria; Sauter, Stefan A (2015). Generalized convolution quadrature with variable time stepping. Part II: Algorithm and numerical results. Applied Numerical Mathematics, 94:88-105.

Abstract

In this paper we address the implementation of the Generalized Convolution Quadrature (gCQ) presented and analyzed by the authors in a previous paper for solving linear parabolic and hyperbolic convolution equations. Our main goal is to overcome the current restriction to uniform time steps of Lubich's Convolution Quadrature (CQ). A major challenge for the efficient realization of the new method is the evaluation of high-order divided differences for the transfer function in a fast and stable way. Our algorithm is based on contour integral representation of the numerical solution and quadrature in the complex plane. As the main application we consider the wave equation in exterior domains, which is formulated as a retarded boundary integral equation. We provide numerical experiments to illustrate the theoretical results.

Abstract

In this paper we address the implementation of the Generalized Convolution Quadrature (gCQ) presented and analyzed by the authors in a previous paper for solving linear parabolic and hyperbolic convolution equations. Our main goal is to overcome the current restriction to uniform time steps of Lubich's Convolution Quadrature (CQ). A major challenge for the efficient realization of the new method is the evaluation of high-order divided differences for the transfer function in a fast and stable way. Our algorithm is based on contour integral representation of the numerical solution and quadrature in the complex plane. As the main application we consider the wave equation in exterior domains, which is formulated as a retarded boundary integral equation. We provide numerical experiments to illustrate the theoretical results.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:August 2015
Deposited On:27 Jan 2016 09:43
Last Modified:08 Dec 2017 16:52
Publisher:Elsevier
ISSN:0168-9274
Publisher DOI:https://doi.org/10.1016/j.apnum.2015.03.004

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