A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods

In this work we develop an adaptive and reduced computational algorithm based on dimension-adaptive sparse grid approximation and reduced basis methods for solving highdimensional uncertainty quantification (UQ) problems. In order to tackle the computational challenge of "curse of dimensionality" commonly faced by these problems, we employ a dimension-adaptive tensor-product algorithm [16] and propose a verified version to enable effective removal of the stagnation phenomenon besides automatically detecting the importance and interaction of different dimensions. To reduce the heavy computational cost of UQ problems modelled by partial differential equations (PDE), we adopt a weighted reduced basis method [7] and develop an adaptive greedy algorithm in combination with the previous verified algorithm for efficient construction of an accurate reduced basis approximation. The efficiency and accuracy of the proposed algorithm are demonstrated by several numerical experiments. (C) 2015 Elsevier Inc. Allrightsreserved.


Published in:
Journal Of Computational Physics, 298, 176-193
Year:
2015
Publisher:
San Diego, Elsevier
ISSN:
0021-9991
Keywords:
Laboratories:




 Record created 2015-09-28, last modified 2018-09-13


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