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# Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

- Handle URI:
- http://hdl.handle.net/10754/597549
- Title:
- Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
- Authors:
- Abstract:
- We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.
- Citation:
- Bramble JH, Pasciak JE, Trenev D (2010) Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem. Math Comp 79: 2079–2079. Available: http://dx.doi.org/10.1090/s0025-5718-10-02355-0.
- Publisher:
- Journal:
- KAUST Grant Number:
- Issue Date:
- 2010
- DOI:
- 10.1090/s0025-5718-10-02355-0
- Type:
- Article
- ISSN:
- 0025-5718
- Sponsors:
- This work was supported in part by the National Science Foundation throughGrant DMS-0609544 and in part by award number KUS-C1-016-04 made by KingAbdulla University of Science and Technology (KAUST).

- Appears in Collections:
- Publications Acknowledging KAUST Support

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.contributor.author | Bramble, James H. | en |

dc.contributor.author | Pasciak, Joseph E. | en |

dc.contributor.author | Trenev, Dimitar | en |

dc.date.accessioned | 2016-02-25T12:41:51Z | en |

dc.date.available | 2016-02-25T12:41:51Z | en |

dc.date.issued | 2010 | en |

dc.identifier.citation | Bramble JH, Pasciak JE, Trenev D (2010) Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem. Math Comp 79: 2079–2079. Available: http://dx.doi.org/10.1090/s0025-5718-10-02355-0. | en |

dc.identifier.issn | 0025-5718 | en |

dc.identifier.doi | 10.1090/s0025-5718-10-02355-0 | en |

dc.identifier.uri | http://hdl.handle.net/10754/597549 | en |

dc.description.abstract | We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society. | en |

dc.description.sponsorship | This work was supported in part by the National Science Foundation throughGrant DMS-0609544 and in part by award number KUS-C1-016-04 made by KingAbdulla University of Science and Technology (KAUST). | en |

dc.publisher | American Mathematical Society (AMS) | en |

dc.subject | Elastic wave problem | en |

dc.subject | Elastic waves scattering | en |

dc.subject | Helmholtz equation | en |

dc.subject | PML layer | en |

dc.title | Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem | en |

dc.type | Article | en |

dc.identifier.journal | Mathematics of Computation | en |

dc.contributor.institution | Texas A and M University, College Station, United States | en |

kaust.grant.number | KUS-C1-016-04 | en |

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