Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data

P Benner, S Dolgov, A Onwunta, M Stoll - Computer Methods in Applied …, 2016 - Elsevier
We consider the numerical simulation of an optimal control problem constrained by the
unsteady Stokes–Brinkman equation involving random data. More precisely, we treat the …

A rapid and efficient isogeometric design space exploration framework with application to structural mechanics

J Benzaken, AJ Herrema, MC Hsu, JA Evans - Computer Methods in …, 2017 - Elsevier
In this paper, we present an isogeometric analysis framework for design space exploration.
While the methodology is presented in the setting of structural mechanics, it is applicable to …

Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs

P Benner, A Onwunta, M Stoll - SIAM Journal on Matrix Analysis and …, 2016 - SIAM
The goal of this paper is the efficient numerical simulation of optimization problems
governed by either steady-state or unsteady partial differential equations involving random …

A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations

K Lee, HC Elman - SIAM Journal on Scientific Computing, 2017 - SIAM
In this study, we consider the numerical solution of large systems of linear equations
obtained from the stochastic Galerkin formulation of stochastic partial differential equations …

On the convergence of Krylov methods with low-rank truncations

D Palitta, P Kürschner - Numerical Algorithms, 2021 - Springer
Low-rank Krylov methods are one of the few options available in the literature to address the
numerical solution of large-scale general linear matrix equations. These routines amount to …

Tensorial parametric model order reduction of nonlinear dynamical systems

AV Mamonov, MA Olshanskii - SIAM Journal on Scientific Computing, 2024 - SIAM
For a nonlinear dynamical system that depends on parameters, this paper introduces a
novel tensorial reduced-order model (TROM). The reduced model is projection-based, and …

Fast solution of three‐dimensional elliptic equations with randomly generated jum** coefficients by using tensor‐structured preconditioners

BN Khoromskij, V Khoromskaia - Numerical Linear Algebra with …, 2023 - Wiley Online Library
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic
elliptic problems in random media in ℝ d R^ d, d= 2, 3 d= 2, 3. Both the two‐dimensional …

Interpolatory tensorial reduced order models for parametric dynamical systems

AV Mamonov, MA Olshanskii - Computer Methods in Applied Mechanics …, 2022 - Elsevier
The paper introduces a reduced order model (ROM) for numerical integration of a dynamical
system which depends on multiple parameters. The ROM is a projection of the dynamical …

Low‐rank solution of an optimal control problem constrained by random Navier‐Stokes equations

P Benner, S Dolgov, A Onwunta… - International Journal for …, 2020 - Wiley Online Library
We develop a low‐rank tensor decomposition algorithm for the numerical solution of a
distributed optimal control problem constrained by two‐dimensional time‐dependent Navier …

A Low-rank solver for the Navier--Stokes equations with uncertain viscosity

K Lee, HC Elman, B Sousedik - SIAM/ASA Journal on Uncertainty …, 2019 - SIAM
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 …