DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Andrei Draganescu, UMBC

**Title: ***
Multigrid preconditioners for linear systems arising in PDE
constrained optimization
*

**Abstract:**
We will discuss the problem of finding optimal order multigrid
preconditioners for linear systems involved in the solution process of
large-scale, distributed optimal control problems constrained by
partial differential equations. Multigrid methods have long been
associated with large-scale linear systems, the paradigm being that
the solution process can be significantly accelerated by using
multiple resolutions of the same problem. However, the exact
embodiment of the multigrid paradigm depends strongly on the class of
problems considered, with multigrid methods for differential equations
(elliptic, parabolic, flow problems) being significantly different
from methods for PDE constrained optimization problems, where the
linear systems often resemble integral equations. In this talk we will
present a number of model problems for which we were able to construct
optimal order multigrid preconditioners, as well as problems where we
have been less successful. The test-problems include (a) linear and
semi-linear elliptic constrained problems, (b) optimal control
problems constrained by Stokes flow (both (a) and (b) without
control-constraints), and (c) control-constrained problems with
linear-elliptic PDE constraints.

**Time:** Friday, Sept. 30, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491