Geodesic
Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 71-83 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 elliptic equations. We describe these schemes theoretically and also compare results of the numerical experiments based on exact solution using proposed schemes.
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 elliptic equations. We describe these schemes theoretically and also compare results of the numerical experiments based on exact solution using proposed schemes.
Classification : 35K20, 35K55, 65M08
Keywords: Mean curvature flow; level set equation; numerical solution; semi-implicit scheme; discrete duality finite volume method (DDFV) 
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Kotorová, Dana. Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 71-83. http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a4/

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