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  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  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.
Keywords: Uncertainty quantification ; Curse of dimensionality ; Generalized sparse grid ; Hierarchical surpluses ; Reduced basis method ; Adaptive greedy algorithm ; Weighted a posteriori error bound
Record created on 2015-09-28, modified on 2016-08-09