Nonintrusive Polynomial Chaos on Nested Unstructured Meshes

We present a novel method for construction of polynomial interpolation grids on arbitrary Euclidean geometries on which there is a probability density. These grids are eminently suitable for uncertainty quantification: they are constructed using the standard polynomial Chaos basis, they are nested so that refinement strategies can be employed, they are applicable for high-dimensional spaces. The construction of these grids is accomplished by combining the Least Orthogonal Interpolant formulation, allowing interpolation on an arbitrary distribution of nodes, and weighted Leja Sequence methods, allowing the well-behaved construction of nested approximation sequences.