Numerical Analysis Seminar

Date: October 25, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Giorgio Bornia, Texas Tech

Title: Some questions arising in PDE-constrained optimal control and numerical linear algebra

Abstract: The talk will be divided in two parts. In the first one, we address some issues arising in a certain class of boundary optimization problems. Common boundary optimal control problems yield a mismatch between the regularity of solutions on the domain and their boundary data. We discuss a reformulation of these problems with a lifting approach whose goal is to fix this regularity mismatch. Moreover, this approach provides additional benefits when applied to constraints characterized by compatibility conditions on the boundary data, such as those arising for the incompressible Navier-Stokes equations. In the second part of the talk, we discuss an analysis of preconditioning schemes for the numerical solution of Rayleigh-Bénard convection problems discretized with inf-sup stable finite element spaces. The analysis is carried out using a notion of field-of-values (FOV) equivalence between the preconditioner and the system matrix. Numerical results are discussed for both topics.