An adaptive high-order piecewise polynomial based sparse grid collocation method with applications

JOURNAL OF COMPUTATIONAL PHYSICS

卷:433

Article

Tao, Zhanjing¹  Jiang, Yan²  Cheng, Yingda³ 

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[3] Michigan State Univ, Dept Computat Math Sci & Engn, Dept Math, E Lansing, MI 48824 USA

关键词: High-dimensional model;    Adaptive sparse grid;    Piecewise polynomial;    Collocation method;    Multiresolution analysis;   

DOI  :  10.1016/j.jcp.2020.109770

来源: Elsevier

【 摘 要 】

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well studied in the literature. The contribution of this work is the introduction of a systematic framework for collocation onto high-order piecewise polynomial space that is allowed to be discontinuous. We consider both Lagrange and Hermite interpolation methods on nested collocation points. Our construction includes a wide range of function space, including those used in sparse grid continuous finite element method. Error estimates are provided, and the numerical results in function interpolation, integration and some benchmark problems in uncertainty quantification are used to compare different collocation schemes. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free