Stochastic Collocation on Unstructured Multivariate Meshes. (3rd July 2015)

• Record Type: Journal Article
• Authors: Narayan, Akil; Zhou, Tao
• Is Part Of: Communications in computational physics. Volume 18:Number 1(2015:Jul.)
• Page Start: 1
• Page End: 36
• Publication Date: 2015-07-03
• Subjects: Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.020215.070515a
• Languages: English
• ISSNs: 1815-2406

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometrically <italic>unstructured</italic> collocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.</p> </abstract>