PhD Comprehensive Seminar | Esteban Henriquez, A Robust Preconditioning Strategy for the Hybridizable Discontinuous Galerkin Method

Wednesday, August 28, 2024 9:00 am - 10:00 am EDT (GMT -04:00)

Candidate

Esteban Henriquez | Applied Mathematics, University of Waterloo

Title

A Robust Preconditioning Strategy for the Hybridizable Discontinuous Galerkin Method

Abstract

The Hybridizable Discontinuous Galerkin (HDG) method has emerged as a powerful numerical technique for solving partial differential equations (PDEs). It combines the flexibility of discontinuous Galerkin (DG) methods with improved computational efficiency. By introducing hybrid variables on the element boundaries, the HDG method effectively reduces the global system size while maintaining high-order accuracy and local conservation properties.

In this seminar, we introduce a novel general preconditioning strategy for the condensed reduced system of HDG discretizations. We demonstrate the theoretical robustness of the preconditioners and validate our findings through numerical experiments. Applications of the HDG method preconditioning to Darcy flow, Stokes flow and Biot consolidation models are presented, showing the effectiveness and versatility of the proposed approach.