Geodesic
Parallel modeling of a blood flow through a cava-filter with a captured thrombus
Matematičeskoe modelirovanie, Tome 17 (2005) no. 11, pp. 3-15 
Yu. V. Vassilevski; S. A. Kapranov. Parallel modeling of a blood flow through a cava-filter with a captured thrombus. Matematičeskoe modelirovanie, Tome 17 (2005) no. 11, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2005_17_11_a0/
@article{MM_2005_17_11_a0,
     author = {Yu. V. Vassilevski and S. A. Kapranov},
     title = {Parallel modeling of a~blood flow through a~cava-filter with a~captured thrombus},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--15},
     year = {2005},
     volume = {17},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_11_a0/}
}
TY  - JOUR
AU  - Yu. V. Vassilevski
AU  - S. A. Kapranov
TI  - Parallel modeling of a blood flow through a cava-filter with a captured thrombus
JO  - Matematičeskoe modelirovanie
PY  - 2005
SP  - 3
EP  - 15
VL  - 17
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/MM_2005_17_11_a0/
LA  - ru
ID  - MM_2005_17_11_a0
ER  - 
%0 Journal Article
%A Yu. V. Vassilevski
%A S. A. Kapranov
%T Parallel modeling of a blood flow through a cava-filter with a captured thrombus
%J Matematičeskoe modelirovanie
%D 2005
%P 3-15
%V 17
%N 11
%U http://geodesic.mathdoc.fr/item/MM_2005_17_11_a0/
%G ru
%F MM_2005_17_11_a0

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

We consider basic aspects of numerical simulation of a blood flow through a cava-filter with a captured thrombus. Complicated geometrical features of the model require a large number of computational nodes. The efficient solution of large linear systems is possible due to the usage of contemporary parallel methods with low arithmetic complexity. We present an algorithmical and technological basis for a parallel 3D simulator of viscous flows including both discretization and solution methods.

[1] Prokubovskii V. I., Kapranov S. A., “Endovaskulyarnaya profilaktika tromboembolii legochnoi arterii”, Flebologiya, eds. V. S. Savelev, Meditsina, M., 2001, 359–375

[2] Savelev V. S., Prokubovskii V. I., Kapranov S. A., “Endovaskulyarnaya khirurgiya v profilaktike tromboembolii legochnoi arterii i lechenii ostrykh venoznykh trombozov”, Khirurgiya, 2003, no. 2, 6–11 | MR

[3] Ichikura K., Yamada N., Oota M. et al., “Clinical experience retrievable vena cava filters for prevention of pulmonary thromboembolism”, J. Cardiol., 40 (2002), 267–273

[4] Asch M. R., “Initial experience in humans with a new retrievable inferior vena cava filter”, Radiology, 225 (2002), 835–844 | DOI | MR

[5] Prokubovskii V. I., Kapranov S. A., Moskalenko E. P., “Anatomicheskie i gemodinamicheskie izmeneniya nizhnei poloi veny pri profilaktike tromboembolii legochnoi arterii”, Angiologiya i sosudistaya khirurgiya, 9:2 (2003), 51–60

[6] Kobel'kov G. and V. Valedinskiy, “On the inequality $\|p\|_{L_2}\le c\|\nabla p\|_{W_2^{-1}}$ and its finite dimensional image”, Sov. J. Numer. Anal. Math. Modelling, 1 (1986), 189–200 | DOI | MR

[7] Garbey M., Kuznetsov Yu., Vassilevski Yu., “Parallel Schwarz method for a convection-diffusion problem”, SIAM J. Sci. Comp., 22 (2000), 891–916 | DOI | MR | Zbl

[8] Garbey M., Kuznetsov Yu., Vassilevski Yu., Parallel Schwarz Method for Convection-Diffusion Constituent of the Navier–Stokes Solver, Proceedings of ParCFD-98 conference, Taiwan, 1998

[9] Marchuk G., Kuznetsov Yu., Matsokin A., “Fictitious Domain and Domain Decomposition Methods”, Sov. J. Numer. Anal. Math. Modelling, 1 (1986), 3–35 | DOI | MR | Zbl

[10] Rossi T., Toivanen J., “A Parallel Fast Direct Solver for the Discrete Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension”, SIAM J. Sci. Comp., 20 (1999), 1778–1793 | DOI | MR | Zbl

[11] Tromeur-Dervout D., Résolution des Equations de Navier–Stokes en Formulation Vitesse Tourbillon sur Systèmes multiprocesseurs à Mémoire Distribuée, Thesis, Univ. Paris VI, 1993

[12] Garbey M., Vassilevski Yu., “A parallel solver for unsteady incompressible 3D Navier–Stokes equations”, Parallel Computing, 27 (2001), 363–389 | DOI | MR | Zbl