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

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

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​​
F. Nobile, L. Tamellini, R. Tempone
Uncertainty Quantification ; PDEs with random data ; linear elliptic equations ; Stochastic Collocation methods ; Sparse grids approximation ; Leja points ; Clenshaw–Curtis points
2015
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.
1439-7358 / DOI 10.1007/978-3-319-19800-2_44