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arXiv · 2112.02211

An iterative solver for the HPS discretization applied to three dimensional Helmholtz problems

José Pablo Lucero Lorca·Natalie Beams·Damien Beecroft·Adrianna Gillman
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Abstract

This manuscript presents an efficient solver for the linear system that arises from the Hierarchical Poincaré-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.

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José Pablo Lucero Lorca, Natalie Beams, Damien Beecroft, Adrianna Gillman. 2023-01-16. An iterative solver for the HPS discretization applied to three dimensional Helmholtz problems. https://arxiv.org/abs/2112.02211

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