Past Event: Oden Institute Seminar

Matrix-free solvers for high-order discretizations on modern architectures

Will Pazner, Fernbach Postdoctoral Fellow, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory

Abstract

High-order numerical methods promise higher fidelity and more predictive power when compared with traditional low-order methods. Furthermore, many properties of these methods make them well-suited for modern computer architectures. However, the use of these methods also introduces several new challenges. For example, in the time-dependent setting, high-order spatial discretizations can result in severe time step restrictions, motivating the use of implicit solvers. The resulting systems are large and often ill-conditioned, posing a challenge for traditional solvers. In this talk, I will discuss the development of efficient solvers and preconditioners designed specifically for high-order finite element and discontinuous Galerkin methods. These methods will then be applied to relevant problems in compressible and incompressible flow. Bio Will Pazner is the Sidney Fernbach Postdoctoral Fellow at Lawrence Livermore National Laboratory's Center for Applied Scientific Computing. He received his Ph.D. from Brown University in 2018, where he was co-supervised by Prof. Per-Olof Persson and Prof. Chi-Wang Shu. Will was a postdoctoral scholar at UC Berkeley, and is an affiliate of the Mathematics Group at Lawrence Berkeley National Laboratory.