The minimization of the functional G(v)=H(Sv)+∫∂Ω m·v-∫Ω k·v is related to various geometrical type problems in calculus of variations, such as the minimal partition of a set, the segmentation of images, and the search for sets with prescribed curvature. The functional G is first regularized and next discretized by means of piecewise linear finite elements with numerical quadratures, thus allowing its actual minimization on a computer. The discrete functionals converge to G in the sense of Γ-convergence, which implies the convergence of the discrete minima to a minimum of G. Various numerical experiments illustrate the behaviour of the numerical algorithm.
Bellettini, G., Paolini, M., Verdi, C. (1990). Numerical minimization of geometrical type problems related to calculus of variations. CALCOLO, 27(3-4), 251-278 [10.1007/BF02575797].
Numerical minimization of geometrical type problems related to calculus of variations
BELLETTINI, GIOVANNI;
1990-01-01
Abstract
The minimization of the functional G(v)=H(Sv)+∫∂Ω m·v-∫Ω k·v is related to various geometrical type problems in calculus of variations, such as the minimal partition of a set, the segmentation of images, and the search for sets with prescribed curvature. The functional G is first regularized and next discretized by means of piecewise linear finite elements with numerical quadratures, thus allowing its actual minimization on a computer. The discrete functionals converge to G in the sense of Γ-convergence, which implies the convergence of the discrete minima to a minimum of G. Various numerical experiments illustrate the behaviour of the numerical algorithm.File | Dimensione | Formato | |
---|---|---|---|
1990_Bellettini_Paolini_Verdi_Calcolo.pdf
non disponibili
Tipologia:
PDF editoriale
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
6.67 MB
Formato
Adobe PDF
|
6.67 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/1017405