Title: Practical and Optimal Iterative Methods for Large Scale Systems Including Maxwell Equations        

Speaker: Professor Jinchao Xu, Pennsylvania State University       

Date/Time: Wednesday, May 2, 2007, 1:00 – 2:00 pm

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: In this talk, we will present a number of recent results on optimally efficient iterative methods for large scale algebraic systems arising from the discretization of various (linear and nonlinear) partial differential equations.   After a brief introduction to several basic ideas and techniques of modern iterative methods such as how a discretized Poisson (and its variants) equation can be efficiently solved by some practical and optimal algebraic multigrid (AMG) methods, we will demonstrate how more complicated systems can be reduced to the solution of a number of Poisson-like equations and hence can be solved by optimal algorithms in a very practical setting.  In particular, we will show, both theoretically and numerically, that a three dimensional Maxwell equation can be optimally preconditioned by four Poisson-like equations together with some additional simple point relaxations such as the Gauss-Seidel method.  We will specifically demonstrate that our new methods are robust with respect to possible large jumps and/or degeneracy in the coefficients of Maxwell equations and relevant diffusion-type equations.  We will further present a related but a general technique on the design of robust iterative methods for nearly singular systems and illustrate how this technique can be applied to various problems such as general saddle point problems, porous media, Newtonian and non-Newtonian fluid flows and their couplings.

CSRI POC: Ray Tuminaro, (925) 294-2564