27 citations · 123 across the 18 of their papers we have counts for
20 papers
Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem
Howard C. Elman, Jiaxing Liang, Tonatiuh Sánchez-Vizuet
The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equa…
An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models
Kayla D. Davie, Howard C. Elman
We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, t…
Surrogate Approximation of the Grad-Shafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids
Howard C. Elman, Jiaxing Liang, Tonatiuh Sánchez-Vizuet
In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces…
On Surrogate Learning for Linear Stability Assessment of Navier-Stokes Equations with Stochastic Viscosity
Bedřich Sousedík, Howard C. Elman, Kookjin Lee +1
We study linear stability of solutions to the Navier\textendash Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a~sto…
Novel Deep neural networks for solving Bayesian statistical inverse
Harbir Antil, Howard C Elman, Akwum Onwunta +1
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MC…
Alternating Energy Minimization Methods for Multi-term Matrix Equations
Kookjin Lee, Howard C. Elman, Catherine E. Powell +1
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solut…
Reduced-order modeling for nonlinear Bayesian statistical inverse problems
Howard C. Elman, Akwum Onwunta
Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial d…
A Low-rank Solver for the Stochastic Unsteady Navier-Stokes Problem
Howard C. Elman, Tengfei Su
We study a low-rank iterative solver for the unsteady Navier-Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochast…
Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media
Q. M. Bui, H. C. Elman
Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems…
Low-Rank Solution Methods for Stochastic Eigenvalue Problems
Howard C. Elman, Tengfei Su
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochas…
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…
An adaptive reduced basis collocation method based on PCM ANOVA decomposition for anisotropic stochastic PDEs
Heyrim Cho, Howard C. Elman
The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic co…
Collocation Methods for Exploring Perturbations in Linear Stability Analysis
Howard C. Elman, David J. Silvester
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical…
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 Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem
Howard C. Elman, Tengfei Su
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of…
Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media
Quan M. Bui, Howard C. Elman, J. D. Moulton
Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process…
Numerical Solution of the Steady-State Navier-Stokes Equations using Empirical Interpolation Methods
Howard C. Elman, Virginia Forstall
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline s…
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…
Inverse subspace iteration for spectral stochastic finite element methods
Bedřich Sousedík, Howard C. Elman
We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator,…
Stochastic Galerkin methods for the steady-state Navier-Stokes equations
Bedřich Sousedík, Howard C. Elman
We study the steady-state Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in…