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

Maurizio Paolini, 27408, BRESCIA - Dipartimento di Matematica e fisica 'Niccolò Tartaglia', FISICHE E NATURALI FACOLTA' DI SCIENZE MATEMATICHE, R. Goglione

Risultato della ricerca: Contributo in libroContributo a convegno

Abstract

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
Pagine203-216
Numero di pagine14
Stato di pubblicazionePubblicato - 1996
EventoFree Boundary Problems '95 - Zakopane
Durata: 11 giu 199518 giu 1995

Workshop

WorkshopFree Boundary Problems '95
CittàZakopane
Periodo11/6/9518/6/95

Keywords

  • anisotropic allen-cahn equation
  • crystalline mean curvature

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