Hybridized Discontinuous Galerkin Methods for Wave Propagation
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their perfor...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Science+Business Media
2019
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| Online Access: | https://hdl.handle.net/1721.1/122780 |
| _version_ | 1826203716195188736 |
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| author | Fernandez del Campo, Pablo Christophe, A. Terrana, Sebastien Nguyen, Ngoc C. Peraire, Jaime |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Fernandez del Campo, Pablo Christophe, A. Terrana, Sebastien Nguyen, Ngoc C. Peraire, Jaime |
| author_sort | Fernandez del Campo, Pablo |
| collection | MIT |
| description | We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems. Keywords: Hybridized discontinuous Galerkin methods, Wave propagation, Fluids, Solids, Electromagnetism |
| first_indexed | 2024-09-23T12:41:56Z |
| format | Article |
| id | mit-1721.1/122780 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:41:56Z |
| publishDate | 2019 |
| publisher | Springer Science+Business Media |
| record_format | dspace |
| spelling | mit-1721.1/1227802022-10-01T10:35:44Z Hybridized Discontinuous Galerkin Methods for Wave Propagation Fernandez del Campo, Pablo Christophe, A. Terrana, Sebastien Nguyen, Ngoc C. Peraire, Jaime Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Theoretical Computer Science General Engineering Computational Theory and Mathematics Software We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems. Keywords: Hybridized discontinuous Galerkin methods, Wave propagation, Fluids, Solids, Electromagnetism United States. Air Force. Office of Scientific Research (FA9550-15-1-0276 and FA9550-16-1-0214) United States. National Aeronautics and Space Administration (NNX16AP15A) Pratt & Whitney Aircraft Group Fundacio Caixa de Pensions Massachusetts Institute of Technology. Office of Graduate Education. 2019-11-06T20:22:46Z 2019-11-06T20:22:46Z 2018-09-05 2017-12 2019-10-30T17:39:40Z Article http://purl.org/eprint/type/JournalArticle 0885-7474 1573-7691 https://hdl.handle.net/1721.1/122780 Fernandez, P. et al. "Hybridized Discontinuous Galerkin Methods for Wave Propagation." Journal of Scientific Computing, vol.77, 3 (December 2018): 1566-1604. © 2018 Springer Science+Business Media en https://doi.org/10.1007/s10915-018-0811-x Journal of Scientific Computing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Science+Business Media arXiv |
| spellingShingle | Theoretical Computer Science General Engineering Computational Theory and Mathematics Software Fernandez del Campo, Pablo Christophe, A. Terrana, Sebastien Nguyen, Ngoc C. Peraire, Jaime Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title | Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title_full | Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title_fullStr | Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title_full_unstemmed | Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title_short | Hybridized Discontinuous Galerkin Methods for Wave Propagation |
| title_sort | hybridized discontinuous galerkin methods for wave propagation |
| topic | Theoretical Computer Science General Engineering Computational Theory and Mathematics Software |
| url | https://hdl.handle.net/1721.1/122780 |
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