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Quadrature Strategies for Constructing Polynomial Approximations
Pranay Seshadri, Gianluca Iaccarino, Tiziano Ghisu
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated…
Data-driven dimensional analysis: algorithms for unique and relevant dimensionless groups
Paul G. Constantine, Zachary del Rosario, Gianluca Iaccarino
Classical dimensional analysis has two limitations: (i) the computed dimensionless groups are not unique, and (ii) the analysis does not measure relative importance of the dimensio…
Many physical laws are ridge functions
Paul G. Constantine, Zachary del Rosario, Gianluca Iaccarino
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws a…
An Efficient Non-Intrusive Uncertainty Propagation Method for Stochastic Multi-Physics Models
Akshay Mittal, Gianluca Iaccarino
Multi-physics models governed by coupled partial differential equation (PDE) systems, are naturally suited for partitioned, or modular numerical solution strategies. Although widel…
An Efficient Intrusive Uncertainty Propagation Method For Multi-Physics System With Random Inputs
Akshay Mittal, Gianluca Iaccarino
Coupled partial differential equation (PDE) systems, which often represent multi-physics models, are naturally suited for modular numerical solution methods. However, several chall…
Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet
Paul Constantine, Michael Emory, Johan Larsson +1
We present a computational analysis of the reactive flow in a hypersonic scramjet engine with focus on effects of uncertainties in the operating conditions. We employ a novel metho…
Factorizing the Stochastic Galerkin System
Paul G. Constantine, David F. Gleich, Gianluca Iaccarino
Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochast…
Spectral Methods for Parameterized Matrix Equations
Paul G. Constantine, David F. Gleich, Gianluca Iaccarino
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of…