Novel results for the anisotropic sparse grid quadrature

Author: 

Haji-Ali, AL
Harbrecht, H
Peters, MD
Siebenmorgen, M

Publication Date: 

1 January 2018

Journal: 

Journal of Complexity

Last Updated: 

2018-03-14T11:43:44.68+00:00

DOI: 

10.1016/j.jco.2018.02.003

abstract: 

© 2018 Elsevier Inc. 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.

Symplectic id: 

823574

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article