[PAST EVENT] Mathematics Colloquium: Mengying Xiao (W&M)
Title: Algebraic splitting methods for solving saddle point problems arising in computational fluid dynamics
Abstract: We study an efficient numerical method for solving difficult `saddle point' linear systems that arise at every time step in the discretization of incompressible flow problems, including those modeled by the Navier-Stokes equations (e.g. water, oil, air under 220 mph) and magnetohydrodynamics (flows on conducting fluids). By combining an algebraic splitting of the block saddle point matrix, a particular approximation of the Schur complement system, and an incremental version of the associated time stepping algorithm, we are able to decompose the linear systems into smaller pieces that are easier to solve. We prove that the approximations made in the solve process are third (or fourth) order, and so are appropriate for use with second order time stepping methods. Numerical tests are performed which verify excellent performance of the methods on a variety of test problems.