**Eric de Sturler**

**Virginia Tech**

**Room: **UNIV 301

Oct 24, 2012 3:30 PM EDT

We will discuss a range of challenging applications in which we need to solve a long sequence of linear systems. Examples of such applications are parameterized linear systems arising in acoustics, model reduction, and nonlinear parametric inversion; topology optimization and optimal design;evolutionary problems involving mesh refinement and derefinement; and methods in computational physics like the quantum Monte Carlo method for solid state physics simulations.

For a sequence of linear systems we may have to compute a sequence of preconditioners that yield fast convergence for each linear systems.However, computing many preconditioners from scratch may be prohibitively expensive or at best a waste of computational resources. We discuss several methods for efficiently updating the required preconditioners and show experimental results for several applications.