# Domain decomposition based algorithms for some inverse problems

Palansuriya, Charaka Jeewana (2000) *Domain decomposition based algorithms for some inverse problems.* PhD thesis, University of Greenwich.

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## Abstract

The work presented in this thesis develop algorithms to solve inverse problems where source terms are unknown. The algorithms are developed 011frameworks provided by domain decomposition methods and the numerical schemes use finite volume and finite difference discretisations.

Three algorithms are developed in the context of a metal cutting problem. The algorithms require measurement data within the physical body in order to retrieve the temperature field and the unknown source terms. It is shown that the algorithms can retrieve both the temperature field and the unknown source accurately. Applicability of the algorithms to other problems is shown by using one of the algorithms to solve a welding problem.

Presence of untreated noisy measurement data can severely affect the accuracy of the retrieved source. It is illustrated that a simple noise treatment procedure such as a least squares method can remedy this situation. The algorithms are implemented 011parallel computing platforms to reduce the execution time. By exploiting domain and data parallelism within the algorithms significant performance improvements are achieved. It is also shown that by exploiting mathematical properties such as change of nonlinearity further performance improvements can be made.

Item Type: | Thesis (PhD) |
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Additional Information: | uk.bl.ethos.550051 |

Uncontrolled Keywords: | domain decomposition methods, inverse problems, mathematics |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

School / Department / Research Groups: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

Last Modified: | 20 Jul 2012 15:39 |

URI: | http://gala.gre.ac.uk/id/eprint/8226 |

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