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Sparse Grid Quadrature Rules Based on Conformal Mappings

  • P. Jantsch
  • C. G. WebsterEmail author
Conference paper
  • 402 Downloads
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 123)

Abstract

In this work, we demonstrate the extension of quadrature approximations, built from conformal mapping of interpolatory rules, to sparse grid quadrature in the multidimensional setting. In one dimension, computation of an integral involving an analytic function using these transformed quadrature rules can improve the convergence rate by a factor approaching π∕2 versus classical interpolatory quadrature (Hale and Trefethen, SIAM J Numer Anal 46:930–948, 2008). For the computation of high-dimensional integrals with analytic integrands, we implement the transformed quadrature rules in the sparse grid setting, and we show that in certain settings, the convergence improvement can be exponential with growing dimension. Numerical examples demonstrate the benefits and drawbacks of the approach, as predicted by the theory.

Keywords

Sparse Grid Sparse Grid Quadrature Rule Conformal Mapping Interpolatory Quadrature High-dimensional Integrals 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of TennesseeKnoxvilleUSA
  2. 2.Oak Ridge National LaboratoryOak RidgeUSA

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