Geodesic
Multigrid for finite-element discretizations of the equations of aerodynamics
Matematičeskoe modelirovanie, Tome 23 (2011) no. 1, pp. 115-131.

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

A multigrid algorithm for the solution of finite element stabilized discretization of compressible fluid dynamics equations on unstructured grids is described. Solution of the stationary problems is seached by time-stepping and a linearization of the non-linear discrete systems leads to a very large system of linear equations. These systems are ill-conditioned and require efficient computational procedures. The numerical experiments for Navier–Stokes and Euler systems are presented. The method can be easily included in a parallel library as preconditioner.
Keywords: multigrid, preconditioner, finite-element method, unstructured grids. 
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V. T. Zhukov; O. B. Feodoritova. Multigrid for finite-element discretizations of the equations of aerodynamics. Matematičeskoe modelirovanie, Tome 23 (2011) no. 1, pp. 115-131. http://geodesic.mathdoc.fr/item/MM_2011_23_1_a9/

[1] Smith B. F., Bjorstad P. E., Gropp W. D., Domain decomposition, Cambridge University Press, 1996 | MR

[2] Zhukov V. T., Feodoritova O. B., Yang D. P., “Iteratsionnye algoritmy dlya skhem konechnykh elementov vysokogo poryadka”, Matem. modelirovanie, 16:7 (2004), 117–128 | Zbl

[3] Martynov A. A., Medvedev S. Yu., “Nadezhnyi sposob postroeniya setok s vytyanutymi yacheikami”, Postroenie raschetnykh setok: teoriya i prilozheniya, eds. S. A. Ivanenko, V. A. Garanzha, VTs RAN, Moskva, 2002, 266–276

[4] Venkattakrishnan V., Almaras S., Kamenetskii D., Johnson F., Higher Order Schemes for the Compressible Navier–Stokes Equations, AIAA-2003-3987, 2003

[5] Saad Y., Iterative Methods for sparse linear systems, PWS Publishing company, 1996 | Zbl

[6] Hughes T. J. R., “Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier–Stokes equations”, Int. J. for Numerical Methods in Fluids, 7:11 (1987), 1261–1275 | DOI | MR | Zbl

[7] Trottenberg U., Oosterlee C. W., Schuller A., Multigrid, ACADEMIC PRESS, 2001 | MR | Zbl

[8] Landau L. D., Lifshits E. M., Mekhanika sploshnykh sred, Tekh.-Teor. Izdat., M., 1954

[9] ParMETIS – Parallel Graph Partitioning and Fill-reducing Matrix Ordering http://glaros.dtc.umn.edu/gkhome/views/metis/