Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients,



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 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 for Robust Deterministic Optimal Control
Çiloğlu, Pelin; Yücel, Hamdullah (2022-03-25)
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 surplus processes with VaR AND CVaR simulations in actuarial applications
Şimşek, Meral; Uğur, Ömür; Kestel, Sevtap Ayşe; Department of Actuarial Sciences (2016)
The theory of ruin is a substantial study for those who are interested in financial survival probability based on the patterns imposed by the surplus process, which determines the insurer’s capital balance at a given time. In other words, fluctuations in aggregate claims as well as premiums in such processes can be secured by a certain capital. In this study, we simulate various surplus processes under different claim sizedistribution assumptions and extend the analyses by adding perturbation of a Brownian mo...
Citation Formats
P. Çiloğlu and H. Yücel, “Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients,” presented at the SIAM Conference on Uncertainty Quantification (UQ22), Georgia, Amerika Birleşik Devletleri, 2022, Accessed: 00, 2022. [Online]. Available: