53 citations · 149 across the 23 of their papers we have counts for
6 papers · 1 filter
Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
Bedřich Sousedík, Kookjin Lee
We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model p…
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
Kookjin Lee, Kevin Carlberg
Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such a…
Inexact Methods for Symmetric Stochastic Eigenvalue Problems
Kookjin Lee, Bedřich Sousedík
We study two inexact methods for solutions of random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetri…
A Low-rank solver for the Navier--Stokes equations with uncertain viscosity
Kookjin Lee, Howard C. Elman, Bedřich Sousedík
We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linear…
Stochastic Least-Squares Petrov-Galerkin Method for Parameterized Linear Systems
Kookjin Lee, Kevin Carlberg, Howard C. Elman
We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input para…
A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations
Kookjin Lee, Howard C. Elman
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equation…