Analysis of the quasicontinuum method and its application
<p>The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials.</p> <p>The thesis consists of two parts. The fir...
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| Format: | Thesis |
| Language: | English |
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2013
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| _version_ | 1797080965059706880 |
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| author | Wang, H |
| author2 | Suli, E |
| author_facet | Suli, E Wang, H |
| author_sort | Wang, H |
| collection | OXFORD |
| description | <p>The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials.</p> <p>The thesis consists of two parts. The first part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a specific energy based QC method which was recently developed.</p> <p>In the first part, we develop a unified framework for the a priori error estimates and present a new and simpler proof based on negative-norm estimates, which essentially extends previous results.</p> <p>In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh refinement algorithms based on these error estimators are formulated.</p> <p>In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates.</p> <p>The thesis is accompanied by a thorough introduction to the development of the QC methods and its numerical analysis, as well as an outlook of the future work in the conclusion.</p> |
| first_indexed | 2024-03-07T01:07:46Z |
| format | Thesis |
| id | oxford-uuid:8bef60f0-74f1-44f5-bcbe-d64d4afad15f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:07:46Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:8bef60f0-74f1-44f5-bcbe-d64d4afad15f2022-03-26T22:41:27ZAnalysis of the quasicontinuum method and its applicationThesishttp://purl.org/coar/resource_type/c_db06uuid:8bef60f0-74f1-44f5-bcbe-d64d4afad15fNumerical analysisMechanics of deformable solids (mathematics)Partial differential equationsMechanics of particles and systems (mathematics)EnglishOxford University Research Archive - Valet2013Wang, HSuli, EOrtner, C <p>The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials.</p> <p>The thesis consists of two parts. The first part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a specific energy based QC method which was recently developed.</p> <p>In the first part, we develop a unified framework for the a priori error estimates and present a new and simpler proof based on negative-norm estimates, which essentially extends previous results.</p> <p>In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh refinement algorithms based on these error estimators are formulated.</p> <p>In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates.</p> <p>The thesis is accompanied by a thorough introduction to the development of the QC methods and its numerical analysis, as well as an outlook of the future work in the conclusion.</p> |
| spellingShingle | Numerical analysis Mechanics of deformable solids (mathematics) Partial differential equations Mechanics of particles and systems (mathematics) Wang, H Analysis of the quasicontinuum method and its application |
| title | Analysis of the quasicontinuum method and its application |
| title_full | Analysis of the quasicontinuum method and its application |
| title_fullStr | Analysis of the quasicontinuum method and its application |
| title_full_unstemmed | Analysis of the quasicontinuum method and its application |
| title_short | Analysis of the quasicontinuum method and its application |
| title_sort | analysis of the quasicontinuum method and its application |
| topic | Numerical analysis Mechanics of deformable solids (mathematics) Partial differential equations Mechanics of particles and systems (mathematics) |
| work_keys_str_mv | AT wangh analysisofthequasicontinuummethodanditsapplication |