CCM Colloquium: Adrianna GIllman (CU Boulder)

Wednesday Dec 4, 2024, 10:00 AM → 11:00 AM America/New_York

Title:  Efficient Helmholtz Solvers for the Sparse System That Arises from the HPS Discretization

Abstract: Numerical results indicated that the Hierarchical Poincare-Steklov (HPS) discretization effectively solves two-dimensional Helmholtz problems even in the high-frequency regime.  The efficiency of the method is thanks to its nested dissection-inspired direct solver.  Unfortunately, while the discretization extends easily to three-dimensional problems, the direct solver's natural extension is often considered too slow to be practical.  This talk presents alternative methods for solving the linear system that arises from the HPS discretization.  The methods utilize both sparse direct solver and iterative solver techniques.  This combination allows them to be easily parallelized.  Preliminary numerical results will be presented.