Title:  Efficient Solutions of Large Saddle-Point Systems

Abstract:  Summer projects are great; here is one such project. Linear systems of saddle-point type arise in a range of applications including optimization, mixed finite-element methods for mechanics and fluid dynamics, economics, and finance (basically everywhere). Due to their indefiniteness and generally unfavorable spectral properties, such systems are difficult to solve, particularly when their dimension is very large. In some applications - for example, when simulating fluid flow over large periods of time - such systems have to be solved many times over the course of a single run, and the linear solver rapidly becomes a major bottleneck. For this reason, finding an efficient and scalable solver is of the utmost importance. In this project, we examined various solution strategies for saddle-point systems.