Geodesic
Conservative interpolation method between non-matching surface meshes
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2014), pp. 64-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we consider a problem of conservative interpolation data between non-matching surface meshes. We develop a new interpolation method based on voxel representation of the mesh followed by the evaluation of intersection area of each voxel with mesh cells. The mass of cells of the resulting mesh is represented through a linear combination of the known mass of parent cells. The method allows us to consider the problem of interpolation on curved surfaces when it is impossible to define the grid cells geometric intersection. The method was validated by numerical simulation of data interpolation based on various functions for the non-matching meshes describing plane and curved surfaces. The method of voxel interpolation was compared to the interpolation algorithm based on radial basis functions of different smoothness degree.
Mots-clés : conservative interpolation
Keywords: voxel mesh, non-matching surface mesh. 
@article{VUU_2014_4_a4,
     author = {A. S. Karavaev and S. P. Kopysov and I. M. Kuz'min},
     title = {Conservative interpolation method between non-matching surface meshes},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {64--75},
     year = {2014},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/}
}
TY  - JOUR
AU  - A. S. Karavaev
AU  - S. P. Kopysov
AU  - I. M. Kuz'min
TI  - Conservative interpolation method between non-matching surface meshes
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2014
SP  - 64
EP  - 75
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/
LA  - ru
ID  - VUU_2014_4_a4
ER  - 
%0 Journal Article
%A A. S. Karavaev
%A S. P. Kopysov
%A I. M. Kuz'min
%T Conservative interpolation method between non-matching surface meshes
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2014
%P 64-75
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/
%G ru
%F VUU_2014_4_a4
A. S. Karavaev; S. P. Kopysov; I. M. Kuz'min. Conservative interpolation method between non-matching surface meshes. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2014), pp. 64-75. http://geodesic.mathdoc.fr/item/VUU_2014_4_a4/

[1] Garimella R., Kucharik M., Shashkov M., “An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes”, Computers and Fluids, 36:2 (2007), 224–237 | DOI | MR | Zbl

[2] Berndt M., Breil J., Galera S., Kucharik M., Maire P., Shashkov M., “Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods”, Journal of Computational Physics, 230:17 (2011), 6664–6687 | DOI | Zbl

[3] Aganin A. A., Kuznetsov V. B., “Method of conservative interpolation for integral parameters of cells for arbitrary meshes”, Dinamika obolochek v potoke, 18, Kazan Physical Technical Institute of the Academy of Sciences of USSR, 1985, 144–160 (in Russian)

[4] Farrell P. E., Piggott M. D., Pain C. C., Gorman G. J., Wilson C. R., “Conservative interpolation between unstructured meshes via supermesh construction”, Computer Methods in Applied Mechanics and Engineering, 198:8 (2009), 2632–2642 | DOI | MR | Zbl

[5] Azarenok B. N., “A method for conservative remapping on hexahedral meshes”, Mathematical Models and Computer Simulations, 1:1 (2009), 51–63 | DOI | MR | Zbl

[6] Karavaev A. S., Kopysov S. P., “The method of unstructured hexahedral mesh generation from volumetric data”, Komp. Issled. Model., 5:1 (2013), 11–24 (in Russian)

[7] Paar C., Pelzl J., Preneel B., Understanding cryptography: a textbook for students and practitioners, Springer, Heidelberg–Dordrecht–London–New York, 2011, 372 pp.

[8] Buhmann M. D., Radial basis functions: theory and implementations, Cambridge University Press, Cambridge, 2004, 257 pp. | MR

[9] Kopysov S. P., Kuzmin I. M., Tonkov L. E., “Methods of mesh deformation for FSI problems”, Vychislitel'nye Metody i Programmirovanie, 14:3 (2013), 269–278 (in Russian)