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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Victor A. Kovtunenko

4 High-order topological expansions for Helmholtz problems in 2D

Victor A. Kovtunenko, Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstraße 36, 8010 Graz, Austria; and, Lavrent’ev Institute of Hydrodynamics, Sibirian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia, victor.kovtunenko@uni-graz.at

Abstract: Methods of topological analysis are inherently related to singular perturbations. For topology variation, a trial geometric object put in a test domain is examined by reducing the object size from a finite to an infinitesimal one. Based on the singular perturbation of the forward Helmholtz problem, a topology optimization approach, which is ...

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