The objective of this paper is to give a general overview of recent research activities on non-
probabilistic finite element analysis and its application for the representation of parametric …

In this paper, we provide a review of statistical methods that are useful in conducting
computer experiments. Our focus is on the task of metamodeling, which is driven by the goal …

Radial basis function methods are modern ways to approximate multivariate functions,
especially in the absence of grid data. They have been known, tested and analysed for …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

The goal of the research reported here is to develop rigorous optimization algorithms to
apply to some engineering design problems for which direct application of traditional …

DURING the last two decades, giant strides have been achieved in many aspects of
computational engineering and sciences. Higher-order mathematical models, better …

We study polynomial interpolation on ad-dimensional cube, where d is large. We suggest to
use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

Compactly supported smooth piecewise polynomial functions provide an efficient tool for the
approximation of curves and surfaces and other smooth functions of one and several …

We consider the problem of Lagrange polynomial interpolation in high or countably infinite
dimension, motivated by the fast computation of solutions to partial differential equations …