| Title:
|
Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes (English) |
| Author:
|
Kotorová, Dana |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
71-83 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Mean curvature flow |
| Keyword:
|
level set equation |
| Keyword:
|
numerical solution |
| Keyword:
|
semi-implicit scheme |
| Keyword:
|
discrete duality finite volume method (DDFV) |
| MSC:
|
35K20 |
| MSC:
|
35K55 |
| MSC:
|
65M08 |
| idZBL:
|
Zbl 06417001 |
| idMR:
|
MR3331007 |
| . |
| Date available:
|
2014-12-16T15:00:42Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144040 |
| . |
| Reference:
|
[1] Andreianov, B., Bendahmare, M., Karlsen, K. H.: A Gradient Reconstruction Formula for Finite Volume Schemes and Discrete Duality. In: Finite Volume For Complex Applications, Problems And Perspectives. 5th International Conference, Wiley, London, 2008, 161–168. MR 2451403 |
| Reference:
|
[2] Andreianov, B., Boyer, F., Hubert, F.: Discrete duality finite volume schemes for Leray–Lions type elliptic problems on general 2D meshes. Numerical Methods PDE 23, 1 (2007), 145–195. Zbl 1111.65101, MR 2275464, 10.1002/num.20170 |
| Reference:
|
[3] Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations. Algoritmy 2009 (2009), 51–60. Zbl 1171.65441 |
| Reference:
|
[4] Evans, L. C., Spruck, J.: Motion of the level sets by mean curvature I. J. Differential Geometry 3 (1991), 635–681. MR 1100206 |
| Reference:
|
[5] Eymard, R., Gallouë, T., Herbin, R.: Finite volume methods. Handbook of Numerical Analysis (Ph., Ciarlet, J. L., Lions, eds.), 3 (2000), 713–1018. MR 1804748 |
| Reference:
|
[6] Handlovičová, A., Kotorová, D.: Stability of the semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2D. Tatra Mountains Mathematical Publications, accepted. |
| Reference:
|
[7] Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes. Journal of Computational Physics 228, 16 (2009), 5763–5786. Zbl 1168.76340, MR 2542915, 10.1016/j.jcp.2009.05.002 |
| Reference:
|
[8] Kotorová, D.: Discrete duality finite volume scheme for the curvature-driven level set equation. Acta Polytechnica Hungarica 8, 3 (2011), 7–12. |
| Reference:
|
[9] Kotorová, D.: Discrete duality finite volume scheme for the curvature driven level set equation in 3D. In: Advances in architectural, civil and environmental engineering [electronic source]: 22nd Annual PhD Student Conference, Nakl. STU, Bratislava, 2012, 33–39. |
| Reference:
|
[10] Kotorová, D.: 3D numerical schemes for the level set equation based on discrete duality finite volumes. to appear. |
| Reference:
|
[11] Sethian, J. A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridge University Press, New York, 1999. MR 1700751 |
| . |
