Algorithms for Area Preserving Flows

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, th...

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Published inSIAM journal on scientific computing Vol. 33; no. 5; pp. 2382 - 2401
Main Authors Kublik, Catherine, Esedolu, Selim, Fessler, Jeffrey A.
Format Journal Article
LanguageEnglish
Published United States Society for Industrial and Applied Mathematics 01.01.2011
Subjects
Algorithms
Applied mathematics
Crystals
Interfaces
Velocity
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ISSN1064-8275
1095-7197
DOI10.1137/100815542

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Summary:We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.
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ISSN:1064-8275
1095-7197
DOI:10.1137/100815542