Numerical simulations of crystalline motion by mean curvature with Allen-Cahn relaxation

Maurizio Paolini, R. Goglione

Risultato della ricerca: Contributo in libroContributo a convegno


In this paper we present some numerical simulations of motion by mean curvature associated to an underlying anisotropy of crystalline type. Such anisotropies are characterized by a Frank diagram (and consequently a Wulff shape) of polygonal type. Our simulations are based on an Allen-Cahn type regularization, performed in the context of a Finsler geometry. The choice of a nonregular double well potential leads to a double obstacle formulation that allows us to exploit the dynamic mesh algorithm, thus reducing considerably the computational cost. A number of simulations show the robustness of our discretization process, which is capable to deal with situations (presence of a generic forcing term) that are critical for other known numerical techniques.
Lingua originaleEnglish
Titolo della pubblicazione ospiteFree boundary problems, theory and applications, Pitman Res. Notes Math. Ser., 363
Numero di pagine14
Stato di pubblicazionePubblicato - 1996
EventoFree Boundary Problems '95 - Zakopane
Durata: 11 giu 199518 giu 1995


WorkshopFree Boundary Problems '95


  • anisotropic allen-cahn equation
  • crystalline mean curvature


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