Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms
Author(s)Hussain, Mohammad Tariq
Massachusetts Institute of Technology. Computation for Design and Optimization Program.
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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 ...
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).
DepartmentMassachusetts Institute of Technology. Computation for Design and Optimization Program.; Massachusetts Institute of Technology. Computation for Design and Optimization Program
Massachusetts Institute of Technology
Computation for Design and Optimization Program.