Mathematical Sciences Department Numerical Methods Seminar: Sijing Liu, WPI
![Poster for Sijing Liu's Numerical Methods seminar: "Multigrid preconditioning for discontinuous Galerkin discretizations of an elliptic optimal control problem with a convection-dominated state equation." Thursday, Sept. 5th, 2024 Stratton hall 207 11:00 AM -12:00 PM](/sites/default/files/styles/1x_1000x576/public/2024-08/Sijing-Liu-Numerical-Methods--Seminar-9-5-2024.jpg?itok=O4yInvKe)
11:00 am to 12:00 pm
Thursday, September 5th, 2024
11:00 AM - 12:00 PM
Stratton Hall 207
Title: Multigrid preconditioning for discontinuous Galerkin discretizations of an elliptic optimal control problem with a convection-dominated state equation.
Abstract: We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter ϵ and regularization parameter β explicitly tracked. We then propose a multilevel preconditioner based on downwind ordering to solve the discretized system. The preconditioner only requires two approximate solves of single convection-dominated equations using multigrid methods. Moreover, for the strongly convection-dominated case, only two sweeps of block Gauss-Seidel iterations are needed. Numerical results are shown to support our findings.