Displaying similar documents to “Dewetting dynamics of anisotropic particles: A level set numerical approach”

Fast numerical schemes related to curvature minimization: a brief and elementary review

Xue-Cheng Tai (2013)

Actes des rencontres du CIRM

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We will treat variational models that use Euler’s elastica and related higher order derivatives as regularizers. These models normally lead to higher order partial differential equations with complicated nonlinearities. It is difficult to solve these equations numerically. Recently, some fast numerical techniques have been proposed that can solve these equations with very good numerical speed. We will try to explain the essential ideas of these numerical techniques and point to some...

New efficient numerical method for 3D point cloud surface reconstruction by using level set methods

Kósa, Balázs, Haličková-Brehovská, Jana, Mikula, Karol

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In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency...

Simplifying numerical solution of constrained PDE systems through involutive completion

Bijan Mohammadi, Jukka Tuomela (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several...

Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes

Dana Kotorová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear...

Forced anisotropic mean curvature flow of graphs in relative geometry

Dieu Hung Hoang, Michal Beneš (2014)

Mathematica Bohemica

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The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.