Stochastic Discontinuous Galerkin Methods for Robust Deterministic Optimal Control

Date

2022-03-25

Author

Çiloğlu, Pelin
Yücel, Hamdullah

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https://hdl.handle.net/11511/96879

Conference Name

The SFB Spring School 2022

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Graduate School of Applied Mathematics, Conference / Seminar

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Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients Çiloğlu, Pelin; Yücel, Hamdullah (2023-04-01) We investigate a numerical behavior of robust deterministic optimal control problem subject to a convection-diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing uncertainties into a large system of deterministic problems, is applied to discretize the stochastic domain, while a discontinuous Galerkin method is preferred for the spatial discretization due to its better convergence behavior for optimization problems governed by conve...
Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations Çiloğlu, Pelin; Yücel, Hamdullah (2021-09-06) To simulate complex kinds of behavior in physical systems, one makes predictions and hypotheses about certain outputs of interest with the help of simulation of mathematical models. However, due to the lack of knowledge or inherent variability in the model parameters, such real-problems formulated by mathematical models generally come with uncertainty concerning computed quantities. Therefore, the idea of uncertainty quantification (UQ) has become a powerful tool for modeling physical phenomena in the last ...
Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients, Çiloğlu, Pelin; Yücel, Hamdullah (2022-04-12)
Stochastic Momentum Methods For Optimal Control Problems Governed By Convection-diffusion Equations With Uncertain Coefficients Toraman, Sıtkı Can; Yücel, Hamdullah; Department of Scientific Computing (2022-1-6) Many physical phenomena such as the flow of an aircraft, heating process, or wave propagation are modeled mathematically by differential equations, in particular partial differential equations (PDEs). Analytical solutions to PDEs are often unknown or very hard to obtain. Because of that, we simulate such systems by numerical methods such as finite difference, finite volume, finite element, etc. When we want to control the behavior of certain system components, such as the shape of a wing of an aircraft or a...
Stochastic discontinuous Galerkin methods with low–rank solvers for convection diffusion equations Çiloğlu, Pelin; Yücel, Hamdullah (2022-02-01) We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas discontinuous Galerkin method is used to discretize spatial domain due to its local mass conservativity. A priori error estimates of the stationary problem and stability...

Citation Formats

P. Çiloğlu and H. Yücel, “Stochastic Discontinuous Galerkin Methods for Robust Deterministic Optimal Control,” presented at the The SFB Spring School 2022, Potsdam, Almanya, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/96879.