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A SIMPLE, FAST AND STABILIZED FLOWING FINITE VOLUME METHOD FOR SOLVING GENERAL CURVE EVOLUTION EQUATIONS (810)
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BibTeX
@MISC{Mikula810asimple,,
author = {Karol Mikula and Martin Bala ˇzovjech},
title = {A SIMPLE, FAST AND STABILIZED FLOWING FINITE VOLUME METHOD FOR SOLVING GENERAL CURVE EVOLUTION EQUATIONS},
year = {810}
}
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Abstract
Abstract. A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial differential equation for updating the position vector of evolving family of plane curves. A curve can be evolved in the normal direction by a combination of fourth order terms related to the intrinsic Laplacian of the curvature, second order terms related to the curvature, first order terms related to anisotropy and by a given external velocity field. The evolution is numerically stabilized by an asymptotically uniform tangential redistribution of grid points yielding the first order intrinsic advective terms in the governing system of equations. By using a semi-implicit in time discretization it can be numerically approximated by a solution to linear penta-diagonal systems of equations (in presence of the fourth order terms) or tri-diagonal systems (in the case of the second order terms). Various numerical experiments of plane curve evolutions, including, in particular, nonlinear, anisotropic and regularized backward curvature flows, surface diffusion and Willmore flows, are presented and discussed.
Keyphrases
second order term fourth order term surface diffusion various numerical experiment regularized backward curvature normal direction general plane curve evolution time discretization new simple lagrangian method intrinsic partial differential equation grid point plane curve evolution finite volume discretization willmore flow plane curve intrinsic laplacian uniform tangential redistribution efficiency property favorable stability external velocity field penta-diagonal system tri-diagonal system first order term first order intrinsic advective term position vector
