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arXiv · 2304.01728

Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence

Jacob Badger·Stefan Henneking·Socratis Petrides·Leszek Demkowicz
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Abstract

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12-26) and extends the convergence results from $\mathcal{O}(10^7)$ degrees of freedom (DOFs) to $\mathcal{O}(10^9)$ DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear dependence with respect to the wave frequency. The paper concludes with numerical results on hp-adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

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Jacob Badger, Stefan Henneking, Socratis Petrides, Leszek Demkowicz. 2023-04-04. Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence. https://arxiv.org/abs/2304.01728

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