Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems

Abstract. We develop in this paper some efficient algorithms which are essential to implementations of spectral methods on the sparse grid by Smolyak's construction based on a nested quadrature. More precisely, we develop a fast algorithm for the discrete transform between the values at the sparse grid and the coefficients of expansion in a hierarchical basis; and by using the aforementioned fast transform, we construct two very efficient sparse spectral-Galerkin methods for a model elliptic equation. In particular, the Chebyshev

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Jie Shen, Haijun Yu
• Keywords: SIAMSC 2010, Sparse, Sparse Grid, Spectral Method