A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation
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...
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| Format: | Article |
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Society of Exploration Geophysicists
2018
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| Online Access: | http://hdl.handle.net/1721.1/115980 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1811070548813283328 |
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| author | Nunez, Leonardo Zepeda Taus, Matthias F Demanet, Laurent |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Nunez, Leonardo Zepeda Taus, Matthias F Demanet, Laurent |
| author_sort | Nunez, Leonardo Zepeda |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T08:37:47Z |
| format | Article |
| id | mit-1721.1/115980 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T08:37:47Z |
| publishDate | 2018 |
| publisher | Society of Exploration Geophysicists |
| record_format | dspace |
| spelling | mit-1721.1/1159802022-09-30T10:07:03Z A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation Nunez, Leonardo Zepeda Taus, Matthias F Demanet, Laurent Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Department of Mathematics Taus, Matthias F Demanet, Laurent 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 2018-05-30T17:42:05Z 2018-05-30T17:42:05Z 2016-09 2018-05-17T17:29:21Z Article http://purl.org/eprint/type/ConferencePaper 1949-4645 http://hdl.handle.net/1721.1/115980 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 https://orcid.org/0000-0001-7052-5097 http://dx.doi.org/10.1190/SEGAM2016-13848017.1 SEG Technical Program Expanded Abstracts 2016 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Society of Exploration Geophysicists MIT Web Domain |
| spellingShingle | Nunez, Leonardo Zepeda Taus, Matthias F Demanet, Laurent A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title | A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title_full | A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title_fullStr | A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title_full_unstemmed | A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title_short | A short note on a fast and high-order hybridizable discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation |
| title_sort | short note on a fast and high order hybridizable discontinuous galerkin solver for the 2d high frequency helmholtz equation |
| url | http://hdl.handle.net/1721.1/115980 https://orcid.org/0000-0001-7052-5097 |
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