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Novel results for the anisotropic sparse grid quadrature

Haji-Ali, Abdul-Lateef and Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus. (2018) Novel results for the anisotropic sparse grid quadrature. Journal of complexity, 47. pp. 62-85.

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Official URL: https://edoc.unibas.ch/64175/

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Abstract

This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error versus cost estimate of the proposed quadrature. In addition, we provide a novel and improved estimate for the cardinality of the underlying anisotropic index set. To validate the theoretical findings, we present several examples ranging from simple quadrature problems to diffusion problems on random domains. These examples demonstrate the remarkable convergence behavior of the anisotropic sparse grid quadrature in applications.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0885-064X
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
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Last Modified:12 Jul 2018 15:28
Deposited On:11 Jul 2018 14:53

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