GUPEA >

Faculty of Science / Naturvetenskapliga fakulteten >

Department of Mathematical Sciences / Institutionen för matematiska vetenskaper >

Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper >

Please use this identifier to cite or link to this item:
`http://hdl.handle.net/2077/31247` |

**Files in This Item:**

File | Description | Size | Format | |
---|---|---|---|---|

gupea_2077_31247_1.pdf | The thesis | 551Kb | Adobe PDF | View/Open |

gupea_2077_31247_2.pdf | The abstract | 49Kb | Adobe PDF | View/Open |

Title: | The Dirac Equation: Numerical and Asymptotic Analysis |

Authors: | Almanasreh, Hasan |

E-mail: | almanasr@chalmers.se |

Issue Date: | 28-Nov-2012 |

University: | Göteborgs universitet. Naturvetenskapliga fakulteten |

Institution: | Department of Mathematical Sciences ; Institutionen för matematiska vetenskaper |

Parts of work: | Paper I: Stabilized finite element method for the radial Dirac equation. Hasan Almanasreh, Sten Salomonson, and Nils Svanstedt. Submitted Paper II: $hp$-Cloud approximation of the Dirac eigenvalue problem: The way of stability. Hasan Almanasreh. Manuscript Paper III: G-convergence of Dirac operators. Hasan Almanasreh and Nils Svanstedt. Published in Journal of Function Spaces and Applications VIEW ARTICLE Paper IV: On G-convergence of positive self-adjoint operators. Hasan Almanasreh. Submitted Paper V: Strong convergence of wave operators for a family of Dirac operators. Hasan Almanasreh. Submitted paper VI: Existence and asymptotics of wave operators for self-adjoint operators. Hasan Almanasreh. Manuscript |

Date of Defence: | 2012-12-20 |

Disputation: | December 20, 2012, at 10.15 in room Pascal, Deparment of Mathematical Sciences, Chalmers Tvärgata 3, Gothenburg. |

Degree: | Doctor of Philosophy |

Publication type: | Doctoral thesis |

Keywords: | Dirac operator, eigenvalue problem, finite element method, spurious eigenvalues, Petrov-Galerkin, cubic Hermite basis functions, stability parameter, meshfree method, $hp$-cloud, intrinsic enrichment, G-convergence, $\Gamma$-convergence, scattering theory, identification, wave operator, stationary approach |

Abstract: | The thesis consists of three parts, although each part belongs to a specific subject area in mathematics, they are considered as subfields of the perturbation theory. The main objective of the presented work is the study of the Dirac operator; the first part concerns the treatment of the spurious eigenvalues in the computation of the discrete spectrum. The second part considers G-convergence theory for positive definite parts of a family of Dirac operators and general positive definite self-adjo... more |

ISBN: | 978-91-628-8593-9 |

URI: | http://hdl.handle.net/2077/31247 |

Appears in Collections: | Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper |