Volume 18, Issue 1
Review Article: Stochastic Collocation on Unstructured Multivariate Meshes

Akil Narayan & Tao Zhou

Commun. Comput. Phys., 18 (2015), pp. 1-36.

Published online: 2018-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for leastsquares 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 unstructured 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.

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@Article{CiCP-18-1, author = {}, title = {Review Article: Stochastic Collocation on Unstructured Multivariate Meshes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {1}, pages = {1--36}, abstract = {

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for leastsquares 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 unstructured 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020215.070515a}, url = {http://global-sci.org/intro/article_detail/cicp/11016.html} }
TY - JOUR T1 - Review Article: Stochastic Collocation on Unstructured Multivariate Meshes JO - Communications in Computational Physics VL - 1 SP - 1 EP - 36 PY - 2018 DA - 2018/04 SN - 18 DO - http://dor.org/10.4208/cicp.020215.070515a UR - https://global-sci.org/intro/cicp/11016.html KW - AB -

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for leastsquares 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 unstructured 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.

Akil Narayan & Tao Zhou. (2020). Review Article: Stochastic Collocation on Unstructured Multivariate Meshes. Communications in Computational Physics. 18 (1). 1-36. doi:10.4208/cicp.020215.070515a
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