Geodesic
On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 375-391 
A. O. Kazakov. On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 375-391. http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a2/
@article{SJVM_2018_21_4_a2,
     author = {A. O. Kazakov},
     title = {On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {375--391},
     year = {2018},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a2/}
}
TY  - JOUR
AU  - A. O. Kazakov
TI  - On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2018
SP  - 375
EP  - 391
VL  - 21
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a2/
LA  - ru
ID  - SJVM_2018_21_4_a2
ER  - 
%0 Journal Article
%A A. O. Kazakov
%T On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2018
%P 375-391
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a2/
%G ru
%F SJVM_2018_21_4_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Grid-characteristic method for the numerical simulation of wave processes in continuum mechanics was initially proposed and successfully applied to periodic hexagonal computational grids. Later, it was proposed to adapt this method to non-periodic triangle and tetrahedral grids, and a broad computational experience has been gained by now. However, this approach encounters some challenges with the calculation of border and contact points when applied to various grid configurations in the areas with complex geometries. In this paper, the method limitations, which cause the problems is considered, and some improvements to overcome them are proposed.

[1] Magomedov K. M., Kholodov A. S., “O postroenii raznostnykh skhem dlya uravnenii giperbolicheskogo tipa na osnove kharakteristicheskikh sootnoshenii”, Zhurn. vychisl. matem. i mat. fiziki, 9:2 (1969), 373–386 | MR | Zbl

[2] Petrov I. B., Kholodov A. S., “Chislennoe issledovanie nekotorykh dinamicheskikh zadach mekhaniki deformiruemogo tvërdogo tela setochno-kharakteristicheskim metodom”, Zhurn. vychisl. matem. i mat. fiziki, 24:5 (1984), 722–739 | MR | Zbl

[3] Golubev V. I., Petrov I. B., Khokhlov N. I., Shul'ts K. I., “Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes”, Computational Mathematics and Mathematical Physics, 55:3 (2015), 509–518 | DOI | MR | Zbl

[4] Golubev V. I., Petrov I. B., Khokhlov N. I., “Compact grid-characteristic schemes ofhigher orders of accuracy for a 3D linear transport equation”, Mathematical Models and Computer Simulations, 8:5 (2016), 577–584 | DOI | MR

[5] Favorskaya A. V., Petrov I. B., Khokhlov N. I., “Numerical modeling of wave processes during shelf seismic exploration”, Proc. Computer Science, 96 (2016), 920–929 | DOI

[6] Magomedov K. M., Kholodov A. S., Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988 | MR

[7] Agapov P. I., Chelnokov F. B., “Sravnitelnyi analiz raznostnykh skhem dlya chislennogo resheniya dvumernykh zadach mekhaniki deformiruemogo tverdogo tela”, Modelirovanie i obrabotka informatsii, MFTI, M., 2003, 19–27

[8] Chelnokov F. B., “Yavnoe predstavlenie setochno-kharakteristicheskikh skhem dlya uravnenii uprugosti v dvumernom i trekhmernom prostranstvakh”, Matem. modelirovanie, 18:6 (2006), 96–108 | MR | Zbl

[9] Petrov I. B., Favorskaya A. V., Muratov M. V., Biryukov V. A., Sannikov A. V., “Grid-characteristic method on unstructured tetrahedral grids”, Doklady Mathematics, 90:3 (2014), 781–783 | DOI | MR | Zbl

[10] Beklemysheva K. A., Danilov A. A., Petrov I. B., Salamatova V. Yu., Vassilevski Y. V., Vasyukov A. V., “Virtual blunt injury of human thorax: Age-dependent response of vascular system”, Russ. J. of Numerical Analysis and Mathematical Modelling, 30:5 (2015), 259–268 | DOI | MR | Zbl

[11] CGAL. Computational Geometry Algorithms Library, http://www.cgal.org

[12] Flototto J., “2D and surface function interpolation”, CGAL, CGAL User and Reference Manual, 4.8 ed., 2016

[13] Devillers O., Pion S., Teillaud M., “Walking in a triangulation”, Proc. 17th Comp. Geom. (SCG/SoCG 2001), ACM Press, 2001, 106–114, INRIA, RR-4120 | Zbl

[14] Beklemysheva K. A., Grigoriev G. K., Kulberg N. S., Kazakov A. O., Petrov I. B., Salamatova V. Yu., Vassilevski Yu. V., Vasyukov A. V., “Transcranial ultrasound of cerebral vessels in silico: Proof of concept”, Russ. J. of Numerical Analysis and Mathematical Modelling, 31:5 (2016), 317–328 | MR | Zbl