Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions
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The Ohio State University / OhioLINK
2020
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu15747977131334222021-08-03T07:13:25Z Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions Wang, Guanqian Mathematics In this thesis we test some known algorithms and propose some new algorithms for the computation of the mean curvature flow under topological changes. For the known algorithms, we test Level Set Method, Phase Field Method and Energy Minimization. We also propose two new algorithms: Energy Penalized Minimization Algorithm and Multilevel Energy Minimization Algorithm. The thesis consists of three parts. In the first part, to study the random initial condition, we set up several sensitive benchmark initial conditions with topological changes and finds that different interaction lengths may lead to different evolution patterns. Secondly, we propose the energy penalized minimization algorithm, which can solve those benchmark problems very well. Further, the newly proposed energy penalized minimization algorithm can carry out the evolution of random initial conditions very well. At last, we propose a multilevel energy minimization algorithm, which can be more tolerant when there is an unsatisfying initial guess. 2020-03-06 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422 http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Wang, Guanqian Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| author |
Wang, Guanqian |
| author_facet |
Wang, Guanqian |
| author_sort |
Wang, Guanqian |
| title |
Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| title_short |
Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| title_full |
Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| title_fullStr |
Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| title_full_unstemmed |
Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions |
| title_sort |
some optimization algorithms for the mean curvature flow under rough initial conditions |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2020 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422 |
| work_keys_str_mv |
AT wangguanqian someoptimizationalgorithmsforthemeancurvatureflowunderroughinitialconditions |
| _version_ |
1719456714535731200 |