Papers › Phase field approach to optimal packing problems and related Cheeger clusters
Phase field approach to optimal packing problems and related Cheeger clusters
Beniamin Bogosel, Dorin Bucur, Ilaria Fragala
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In a fixed domain of Rᴺ we study the asymptotic behaviour of optimal clusters associated to α-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter α converges to the "critical" value ((N-1)/N) _+, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute α-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions.
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