Stochastic Collocation on Unstructured Multivariate Meshes (Communications in Computational Physics, 2018)
Collocation has become a standard tool for approximation of parameterizedsystems in the uncertainty quantification (UQ) community. Techniques for least-squaresregularization, compressive sampling recovery, and interpolatory reconstructionare becoming standard tools used in a variety of applications. Selection of a collocationmesh is frequently a challenge, but methods that construct geometrically unstructuredcollocation meshes have shown great potential due to attractive theoreticalproperties and direct, simple generation and implementation. We investigate propertiesof these meshes, presenting stability and accuracy results that can be used asguides for generating stochastic collocation grids in multiple dimensions.