A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation
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SEG_HDG_polarized_traces.pdf
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553.66 KB
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Author(s)
Nunez, Leonardo Zepeda
Taus, Matthias F
Demanet, Laurent
Date Issued
September 2016
Journal
SEG Technical Program Expanded Abstracts 2016
Publisher
Society of Exploration Geophysicists
Citation
Taus, Matthias et al. “A Short Note on a Fast and High-Order Hybridizable Discontinuous Galerkin Solver for the 2D High-Frequency Helmholtz Equation.” SEG Technical Program Expanded Abstracts 2016 (September 2016): 3835-3840 © 2016 SEG
Version
Author's final manuscript
Abstract
The method of polarized traces provides the first documented algorithm with truly scalable complexity for the highfrequency Helmholtz equation, i.e., with a runtime sublinear in the number of volume unknowns in a parallel environment. However, previous versions of this method were either restricted to a low order of accuracy, or suffered from computationally unfavorable boundary reduction to ρ(p) interfaces in the p-th order case. In this note we rectify this issue by proposing a high-order method of polarized traces with compact reduction to two, rather than ρ(p), interfaces. This method is based on a primal Hybridizable Discontinuous Galerkin (HDG) discretization in a domain decomposition setting. In addition, HDG is a welcome upgrade for the method of polarized traces, since it can be made to work with flexible meshes that align with discontinuous coefficients, and it allows for adaptive refinement in h and p. High order of accuracy is very important for attenuation of the pollution error, even in settings when the medium is not smooth. We provide some examples to corroborate the convergence and complexity claims. Keywords: finite element; frequency-domain; numerical; acoustic; wave equation
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1190/SEGAM2016-13848017.1
