Comparison of Clenshaw–Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs

by Fabio Nobile, L. Tamellini, Raul Tempone

Year: 2015

Bibliography

F. Nobile, L. Tamellini, R. Tempone, Comparison of Clenshaw–Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs, International Conference on Spectral and High-Order Methods 2014 (ICOSAHOM'14), Salt Lake City, Utah, USA, June 23-27, 2014. Spectral and High Order Methods for Partial Differential Equations. Volume 106 of the series Lecture Notes in Computational Science and Engineering, pp 475-482. Springer, 2015

Abstract

In this work we compare numerically different families of nested quadrature points, i.e. the classic Clenshaw–Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests that the performances of both families are essentially comparable within such framework.

ISSN:1439-7358 / DOI 10.1007/978-3-319-19800-2_44

Keywords

Uncertainty Quantification PDEs with random data linear elliptic equations Stochastic collocation methods Sparse grids approximation Leja points Clenshaw–Curtis points