Colloquium| Institute of Mathematical Sciences
Time: Tuesday, October 15th, 2024 , 09:00-10:00
Location: IMS, RS408
Speaker: David Silvester
About the Speaker: David Silvester is best known for his work on finite element methods, fast iterative solvers for fluid dynamics, and uncertainty quantification. He has more than 65 refereed publications on topics such as iterative solution of Stokes and Navier–Stokes systems, preconditioning, and error estimation in finite element methods. Silvester's books include Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics and Essential Partial Differential Equations (co-authored with David F. Griffiths and John W. Dold).
David Silvester has served as the elected President of the UK and Republic of Ireland section of the Society for Industrial and Applied Mathematics (2009–2011). He became a Fellow of the Society for Industrial and Applied Mathematics in 2023.
Abstract: This talk describes efficient preconditioned iterative solvers for incompressible flow problems discretised by an enriched Taylor–Hood mixed approximation, in which the usual pressure space is augmented by a piecewise constant pressure to ensure local mass conservation. The enrichment process causes over-specification of the pressure, which complicates the design and implementation of efficient solvers for the resulting linear systems. We describe the impact of this choice of pressure space on the matrices involved. We also show how to recover effective solvers for Stokes problems, with a preconditioner based on the singular pressure mass matrix, and for Oseen systems arising from linearised Navier–Stokes equations, by using a two-stage pressure convection–diffusion strategy.
This is joint work with Jennifer Pestana.
Colloquium talk (involves technical material, mostly linear algebra)
Reference
https://arxiv.org/abs/2303.10233