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…