Speaker
Adrianna Gillman, UC Boulder
Abstract
Nested dissection-type direct solvers have been demonstrated to be very efficient for two dimensional problems discretized with the HPS method. Unfortunately, these solvers struggle for three dimensional problems due to the curse of dimensionality. In this talk, we present two techniques that are making progress towards efficient solvers for three dimensional problems. The first is an efficient preconditioned for high frequency Helmholtz problems. The second is a hybrid solver. This solver utilizes direct solver techniques to reduce the size of the system that needs to be solved. It is can effectively “compress” out local features that increase iteration counts. Numerical results illustrate the potential of these two methods.