Friday, November 14, 2025 3:30 pm
-
4:30 pm
EST (GMT -05:00)
Title: Parameter robust preconditioning
| Speaker: | Sander Rhebergen |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: The discretization of a partial differential equation (PDE) results in a linear system and iterative solvers are typically used to solve these linear systems, especially if these linear systems are large. Krylov subspace methods are an important class of iterative methods but for these methods to be effective they must be combined with a preconditioner. However, finding a good preconditioner for a given discretization of a PDE is a nontrivial task and so in the first part of this talk I will summarize some useful results from the literature that use a Functional Analysis framework to identify preconditioners for symmetric PDEs.
Many PDEs depend on parameters such as viscosity, permeability, a discrete time-step, etc. and these parameters can have a large effect on the convergence of preconditioned Krylov subspace methods if they are not properly accounted for by the preconditioner. In the second part of this talk I will show how the Functional Analysis framework is used to identify preconditioners such that the convergence of a preconditioned Krylov subspace method is robust with respect to these parameters.
In the final part of this talk I will discuss discretizations that allow for static condensation. Static condensation is the process of eliminating certain degrees of freedom from the linear system with the purpose of reducing the size of the linear system. The main question I will answer is: If one has a parameter robust preconditioner for a linear system before static condensation, is the preconditioner still parameter robust after static condensation?