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Approximation of partitions of least perimeter by \(\Gamma\)-convergence: around Kelvin’s conjecture. (English) Zbl 1261.49009

Summary: A numerical process to approximate optimal partitions in any dimension is reported. The key idea of the method is to relax the problem into a functional framework based on the famous result of \(\Gamma\)-convergence obtained by Modica and Mortolla.

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
65K10 Numerical optimization and variational techniques
52C23 Quasicrystals and aperiodic tilings in discrete geometry

Software:

KELLEY
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References:

[1] DOI: 10.1007/978-3-642-57186-2_3
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