Skip to Main Content
 

Global Search Box

 
 
 
 

ETD Abstract Container

Abstract Header

Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions

Abstract Details

2020, Master of Actuarial and Quantitative Risk Management, Ohio State University, Actuarial and Quantitative Risk Management.
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.
Chunsheng Ban (Advisor)
Yulong Xing (Committee Member)
36 p.

Recommended Citations

Citations

  • Wang, G. (2020). Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422

    APA Style (7th edition)

  • Wang, Guanqian. Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions. 2020. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422.

    MLA Style (8th edition)

  • Wang, Guanqian. "Some Optimization Algorithms for the Mean Curvature Flow Under Rough Initial Conditions." Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574797713133422

    Chicago Manual of Style (17th edition)