CDS&E: Stochastic Isogeometric Analysis by Hierarchical B-Spline Sparse Grids

Sponsor:                          U.S. National Science Foundation

Project No.:                     CMMI-1607398

Duration:                         July 15, 2016 – June 30, 2021

Principal Investigator:    Professor Sharif Rahman

Graduate Student:          Messrs. Ramin Jahanbin and Steven Dixler



The objective of this project is to advance the theory of isogeometric analysis, accompanied by robust numerical algorithms, for uncertainty quantification of a high-dimensional response from complex materials and structures.  The proposed effort will involve: (1) new randomized non-uniform rational B-splines (NURBS) for the stochastic matrix equation and NURBS-based random field discretization for a material body; (2) new stochastic isogeometric methods entailing the hierarchical B-spline sparse grids for high-dimensional function interpolation; and (3) new formulae and scalable algorithms for predicting the statistical moments and probability density functions of a complex structural response.  The research will bridge geometric modeling, stress analysis, and stochastic simulation by interacting natively upon the same mathematical building blocks, forming a seamless uncertainty quantification pipeline of the future.  Due to innovative formulation of the sparse grid interpolation, the resulting stochastic method will be efficiently implemented regardless of the size of an uncertainty quantification problem.  New computational algorithms will be generated for efficiently estimating the statistical moments and probability density function of a structural response, including error estimates that will result in a rigorous assessment of the sparse grid approximation.  The overall effort will effectively integrate research, education, training, and outreach.