Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations

Date

2021-09-06

Author

Çiloğlu, Pelin
Yücel, Hamdullah

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

302
views

0
downloads

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 few years.In this talk, 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, whereas discontinuous Galerkin method is used to discretize spatial domain due to its local mass conservativity. To address the curse of dimensionality of Stochastic Galerkin method, we take advantage of the low--rank Krylov subspace methods, which reduce both the storage requirements and the computational complexity by exploiting a Kronecker--product structure of system matrices. The efficiency of the proposed methodology is illustrated by numerical experiments on the benchmark problems.

URI

https://www.chemnitz-am.de/cfem2021/talks/ciloglu_pelin.pdf
https://hdl.handle.net/11511/92481

Conference Name

Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Stability analysis of constraints in flexible multibody systems dynamics İder, Sıtkı Kemal (Elsevier BV, 1990-1) Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use...
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...
Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS Kalayci, Betul; Ozmen, Ayse; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01) Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on s...
Monte Carlo analysis of ridged waveguides with transformation media Ozgun, Ozlem; Kuzuoğlu, Mustafa (Wiley, 2013-07-01) A computational model is presented for Monte Carlo simulation of waveguides with ridges, by combining the principles of transformation electromagnetics and the finite methods (such as finite element or finite difference methods). The principle idea is to place a transformation medium around the ridge structure, so that a single and easy-to-generate mesh can be used for each realization of the Monte Carlo simulation. Hence, this approach leads to less computational resources. The technique is validated by me...
Domain Structured Dynamics: Unpredictability, chaos, randomness, fractals, differential equations and neural networks Akhmet, Marat (Institute of Physics Publishing (IOP), 2021-03-01) Domain structured dynamics introduces a way for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract similarity dynamics. Then a labeling procedure is designed to determine the domain structured dynamics. The results follow the Pythagorean doctrine, considering finite number of indices for the labeling, with potential to become universal in future. The immediate power of the approach for f...

Citation Formats

P. Çiloğlu and H. Yücel, “Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations,” presented at the Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations, Chemnitz, Almanya, 2021, Accessed: 00, 2021. [Online]. Available: https://www.chemnitz-am.de/cfem2021/talks/ciloglu_pelin.pdf.