期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 433, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2020.109770
关键词
High-dimensional model; Adaptive sparse grid; Piecewise polynomial; Collocation method; Multiresolution analysis
资金
- NSFC [11901555, 12001231]
- NSF [DMS-1453661, DMS-1720023]
This paper introduces an adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space, including Lagrange and Hermite interpolation methods. Error estimates are provided, and numerical results are used to compare different collocation schemes in function interpolation, integration, and uncertainty quantification benchmark problems.
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.
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