Stochastic collocation on unstructured multivariate meshes

TL;DR

This paper investigates unstructured multivariate meshes for stochastic collocation, providing stability and accuracy insights to improve the generation of collocation grids in uncertainty quantification applications.

Contribution

It offers new theoretical analysis of unstructured meshes, guiding their effective construction for multivariate stochastic collocation in UQ.

Findings

Stability results for unstructured meshes

Accuracy bounds for multivariate collocation

Guidelines for mesh generation in multiple dimensions

Abstract

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 "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.