Gene Golub Symposium
Preconditioned Iterative Methods for Sequences of Linear Systems
Eric de Sturler, Virginia Tech
Many large, nonlinear and/or time-dependent problems, such as porous medium flow, the design of structural systems, and tomography, lead to sequences of linear and nonlinear algebraic systems. The nonlinear systems can be solved by Newton or quasi-Newton methods, leading to an additional sequence of linear problems. The solution of such systems is typically the bottleneck in simulations and optimizations. I will present a set of techniques to solve such problems efficiently. The key to efficient solvers is to update and reuse, hence recycle, the generated search spaces and preconditioners, and, for nonlinear problems, modify the Newton scheme such as to exploit this optimally.
