Scientific Computing Seminar

Date:

Friday, April 9, 2004

Time:

1:00pm-2:00pm

Location:

50A-5132

Seminar Speaker:

Ernesto Prudencio
Department of Computer Science
University of Colorado at Boulder, Boulder, CO 80309
http://www.cs.colorado.edu/~prudenci

Title:

Parallel Linear and Nonlinear Domain Decomposition Methods for PDE-Constrained Optimization

Abstract:

In this talk I will discuss the application of Schwarz preconditioners, both linear and nonlinear, to the parallel numerical solution of optimization problems constrained by partial differential equations. Preconditioners constitute a key element for the robustness, efficiency and scalability of algorithms. Numerical experiments for the Lagrange-Newton-Krylov-Schwarz (LNKSz) method are performed in the context of optimal flow control. The objective is to minimize turbulence of two-dimensional steady-state flows, the constraints are represented by incompressible viscous Navier-Stokes equations in velocity-vorticity formulation, and fluid velocities at the boundary give the controls. After the derivation of the Karush-Kuhn-Tucker system from the Lagrangian functional, Newton's method with line search is applied, using an augmented Lagrangian merit function. A one-level linear Schwarz preconditioned GMRES method is used at each Newton step for the solution of the linearized KKT systems. Numerical results are reported for different combinations of Reynolds number, meshsize and number of processors. The Schwarz preconditioner is also tested for different overlappings, on both full and restricted versions and for both forward and optimization problems. I will also briefly talk about the structure of the parallel code developed, in C/C++ and over PETSc and MPI, for such numerical experiments.

Sponsor of Seminar:

Osni Marques

Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov