45 citations · 88 across the 7 of their papers we have counts for
4 papers · 1 filter
Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces
Sharif Rahman
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogo…
A Galerkin Isogeometric Method for Karhunen-Loeve Approximation of Random Fields
Sharif Rahman
This paper marks the debut of a Galerkin isogeometric method for solving a Fredholm integral eigenvalue problem, enabling random field discretization by means of the Karhunen-Loeve…
A Polynomial Chaos Expansion in Dependent Random Variables
Sharif Rahman
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike ex…
Mathematical Properties of Polynomial Dimensional Decomposition
Sharif Rahman
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of rando…