DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Aaron Lott, NIST

**Title: ***
Fast Solvers for Models of Fluid Flow with Spectral Elements
*

**Abstract:**
Numerical simulation of fluid dynamics allows for improved prediction and design of natural and engineered systems such as those involving air, water and blood. Such systems routinely involve dynamics that occur on disparate length and time scales due to variations in inertial and viscous forces. In order to numerically simulate these dynamics, intricate mathematical modeling and computational methods are required.
Numerical solvers for use in fluid simulations have traditionally been based on fast Poisson solvers. Recent advances in solution techniques for convection-diffusion systems based on multigrid and domain decomposition strategies have enabled the development of new and efficient techniques for simulating fluid systems. We will introduce a new technique for solving convection-diffusion systems based on a spectral element discretization and discuss how this can be used as a building block as part of a block preconditioning strategy for solving steady incompressible fluid flow problems. Our technique is centered on domain decomposition which uses fast diagonalization to efficiently compute dense subdomain interiors.

**Time:** Friday, Dec. 4, 2009, 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