An iterative solver for the HPS discretization applied to three dimensional Helmholtz problems
Abstract
This manuscript presents an efficient solver for the linear system that arises from the Hierarchical Poincar\'e-Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. Previous work on the HPS method has tied it with a direct solver. This work is the first efficient iterative solver for the linear system that results from the HPS discretization. The solution technique utilizes GMRES coupled with a locally homogenized block-Jacobi preconditioner. The local nature of the discretization and preconditioner naturally yield the matrix-free application of the linear system. Numerical results illustrate the performance of the solution technique. This includes an experiment where a problem approximately 100 wavelengths in each direction that requires more than a billion unknowns to achieve approximately 4 digits of accuracy takes less than 20 minutes to solve.
Cite
@article{arxiv.2112.02211,
title = {An iterative solver for the HPS discretization applied to three dimensional Helmholtz problems},
author = {José Pablo Lucero Lorca and Natalie Beams and Damien Beecroft and Adrianna Gillman},
journal= {arXiv preprint arXiv:2112.02211},
year = {2023}
}