1. Solving linear systems in fluid dynamics P. Aaron Lott Applied Mathematics and Scientific Computation Program University of Maryland

3. Non-zero structure of 2D Poisson Operator Using a Spectral Element Discretization

5. Incompressible Navier Stokes Equations

6. Discretized Steady Navier Stokes Each time step requires a Nonlinear Solve Each Nonlinear Solve requires a Linear solve Each Linear Solve can be expensive - Need efficient scalable solvers

7. Preconditioning

8. Preconditioner for Steady Navier Stokes Equations Choose P_F as an inexpensive approximation to F Choose P_S as an inexpensive approximation to the Schur complement of the system matrix

10. References High-Order Methods for Incompressible Fluid Flow. Deville Fischer and Mund Spectral/hp Element Methods for Computational Fluid Dynamics. Karniadakis and Sherwin Spectral Methods Fundamentals in Single Domains. Canuto Hussaini Quarteroni Zang Finite Element Methods and Fast Iterative Solvers with applications in incompressible fluid dynamics. Elman Silverster and Wathen Iterative Methods for Sparse Linear Systems. Saad

11. Opportunities/Resources Burgers Program in Fluid Dynamics Center for Scientific Computation and Mathematical Modeling AMSC Faculty Research Interests AMSC Wiki (CFD)