Multigrid methods for optimal control problems governed by convection-diffusion equations

---

Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Scientific Computing, Turkey

Approval Date: 2015

Student: ÖZGÜN MURAT ARSLANTAŞ

Co-Supervisor: BÜLENT KARASÖZEN, HAMDULLAH YÜCEL

Abstract:

Linear-quadratic optimal control problems governed by partial differential equations proved themselves important through their use in many real life applications. In order to solve the large scale linear system of equations that results from optimality conditions of the optimization problem, efficient solvers are required. For this purpose, multigrid methods, with an ordering technique to deal with the dominating convection, can be good candidates. This thesis investigates an application of the multigrid methods for the linear-quadratic optimal control problems governed by convection-diffusion equation, discretized by a discontinuous Galerkin method, namely, symmetric interior penalty Galerkin (SIPG) method. Further, an ordering technique called Downwind Numbering is proposed to reduce the number of iteration in multigrid approach