Analysis and application of a lower envelope method for sharp-interface multiphase problems

• Autorzy: Laurain Antoine

Identyfikatory

DOI

10.2478/candc-2024-0009

• Języki publikacji: EN

Abstrakty

EN

We introduce and analyze a lower envelope method (LEM) for the tracking of motion of interfaces in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides with exactly one of the functions. We show that a variety of complex lower-dimensional interfaces naturally appear in the process. The evolution of phases is then achieved by solving a set of transport equations. In the first part of the paper, we show several theoretical properties, give conditions to obtain a well-posed behaviour, and show that the level set method is a particular case of the LEM. In the second part, we propose a LEM-based numerical algorithm for multiphase shape optimization problems. We apply this algorithm to an inverse conductivity problem with three phases and present several numerical results.

Słowa kluczowe

EN

lower envelope method; shape optimization; multiphase; sharp-interface problems; electrical impedance tomography

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2024
• Tom: Vol. 53, No. 1
• Strony: 189--229
• Opis fizyczny: Bibliogr. 61 poz., rys.

Twórcy

autor

Laurain Antoine

• Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Str. 9, 45127 Essen, Germany

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