Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2008
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| Online Access: | http://hdl.handle.net/1721.1/42455 |
| _version_ | 1826209620902805504 |
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| author | Hussain, Mohammad Tariq |
| author2 | Gilbert Strang. |
| author_facet | Gilbert Strang. Hussain, Mohammad Tariq |
| author_sort | Hussain, Mohammad Tariq |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. |
| first_indexed | 2024-09-23T14:25:21Z |
| format | Thesis |
| id | mit-1721.1/42455 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:25:21Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/424552019-04-12T21:24:29Z Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms Hussain, Mohammad Tariq Gilbert Strang. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Computation for Design and Optimization Program. Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. In title on t.p., "L" appears as italic letters and "[infinity]" appears as the symbol. Includes bibliographical references (leaves 47-48). The Cheeger constant h(Q) of a domain Q is defined as the minimum value of ...... with D varying over all smooth sub-domains of Q. The D that achieves this minimum is called the Cheeger set of Q. We present some analytical and numerical work on the Cheeger set for the unit cube ... using the ...and the ... norms for measuring IIDII. We look at the equivalent max-flow min-cut problem for continuum flows, and use it to get numerical results for the problem. We then use these results to suggest analytical solutions to the problem and optimize these shapes using calculus and numerical methods. Finally we make some observations about the general shapes we get, and how they can be derived using an algorithm similar to the one for finding Cheeger sets for domains in ... by Mohammad Tariq Hussain. S.M. 2008-09-03T15:43:12Z 2008-09-03T15:43:12Z 2008 2008 Thesis http://hdl.handle.net/1721.1/42455 240704675 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 48 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Computation for Design and Optimization Program. Hussain, Mohammad Tariq Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title | Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title_full | Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title_fullStr | Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title_full_unstemmed | Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title_short | Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms |
| title_sort | cheeger sets for unit cube analytical and numerical solutions for l infinity and l² norms |
| topic | Computation for Design and Optimization Program. |
| url | http://hdl.handle.net/1721.1/42455 |
| work_keys_str_mv | AT hussainmohammadtariq cheegersetsforunitcubeanalyticalandnumericalsolutionsforlinfinityandl2norms |