# Research Group

**Possible Thesis Topics:**

Both MSc and PhD theses are extensive pieces of work that take full-time commitment over several months/years. They are also deeply personal decisions by each student. Here are nevertheless some suggestions for possible research topics, which the program is particularly qualified to supervise. In the following, a list of general topics that are available for either MSc or PhD thesis is provided. The topics are organized by general research themes in my research area. If some of these topics interest you, then please feel free to contact me at yucelh[at]metu.edu.tr. I am always looking for motivated and talented MSc and Ph.D. students interested in my research.

**Low Rank Approximations for Stochastic Partial Differential Equations***Qualifications*: implementation of finite element method in Matlab, knowledge of basic probability, numerical techniques for linear systems

**Phase Field Models including elasticity and temperature***Qualifications*: implementation of finite element method in Matlab or programming expertise in open source finite element softwares, e.g., FEnicCS, knowledge of basic numeric techniques

**Deep Neural Network for Partial Differential Equations***Qualifications*: programming expertise in python, numeric of PDEs

**Current MSc/Ph.D. Students:**

**Pelin Çiloğlu**, Ph.D. student- Stochastic discontinuous Galerkin methods for optimal control problems with random coefficients
- BS: Department of Mathematics, METU, 2015

**Mustafa Kütük**, Ph.D. student- Deep neural network for stochastic partial differential equations
- MSc: Departments of Electrical and Electronics Engineering, METU, 2018
- BS: Departments of Electrical and Electronics Engineering, Dokuz Eylül University, 2014

**Mehmet Alp Üreten**, Ph.D. student- Multilevel Monte Carlo simulations for optimal control problems with random coefficients
- MSc: Scientific Computing, Institute of Applied Mathematics, METU, 2018
- BS: Department of Mathematics, METU, 2014

**Sıtkı Can Toraman**, MSc student- Stochastic momentum methods for optimal control problems with uncertain coefficients
- BS: Department of Physics, METU, 2019

**Past MSc/Ph.D. Students:**

**Eda Oktay (MSc Graduate)**: Reevaluating Spectral Partitioning for Unsymmetric Matrices, September 2020.(jointly supervised with Murat Manguoğlu (*Advisor*), Department of Computer Engineering, METU).**Halil Kaya****(PhD Graduate)**: Development of a Discrete Adjoint-Based Aerodynamic Shape optimization for Natural Laminar Flows, August 2020 (jointly supervised with İ. Hakkı Tuncer (*Advisor*), Department of Aerospace Engineering, METU).**Mehmet Alp Üreten (MSc Graduate)**: Numerical Studies of Korteweg-de Vries Equation with Random Input Data, September 2018 (jointly supervised with Ömür Uğur (Co-A*dvisor*), IAM, METU).**Özgür M. Arslantaş****(MSc Graduate)**: Multigrid Methods for Optimal Control Problems Governed by Convection-Diffusion Equations, 2015 (jointly supervised with Bülent Karasözen (*Advisor*), IAM, METU).

**News:**

**November 04, 2020:**P. Çiloğlu, H. Yücel, “Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations”, Submitted.**September 10, 2019:**Mustafa Kütük gives a research talk, titled “Hyperspectral Target Detection by using Superpixels and Signature Based Methods” in BEYOND 2019: Computational Science and Engineering Conference**.****September 10, 2019:**Pelin Çiloğlu gives a research talk, titled “Discontinuous Galerkin Methods for Convection Diffusion Equations with Random Coefficients” in BEYOND 2019: Computational Science and Engineering Conference.**October 21, 2018:**Pelin Çiloğlu gives a research talk, titled “Discontinuous Galerkin Methods for Unsteady Convection Diffusion Equation with Random Coefficients” in BEYOND: Workshop on Computational Science and Engineering**.****September 24, 2018:**Pelin Çiloğlu gives a research talk, titled “Unsteady Convection Diffusion Equation with Random Input Data” in the Chemnitz FE Symposium 2018.**September 03, 2018**: M. Alp Üreten successfully defends his Master thesis, titled “Numerical Studies of Korteweg-de Vries Equation with Random Input Data”.

**Group Meetings: **

We regularly come together to discuss the relevant topics in the scope of my research group. Each person give a talk related to his/her research interests. If you are interested to join the meetings, please feel free to contact me at yucelh[at]metu.edu.tr.