My scientific interests include numerical analysis, multigrid methods, numerical linear algebra with application to solving partial differential equations and Computational Fluid Dynamics.
The current scientific projects I am involved:
German Scientific Research Foundation and Russian Foundation for Basic Research project “Robust and efficient solution strategies for generalized incompressible Navier-Stokes equations”, 2006-2008 (co-PI with S.Turek from Dortmund TU)
The Russian Foundation for Basic Research project "Novel computational technologies for hydrodynamic problems with free interior boundary" (2008-2010)
The Russian Foundation for Basic Research project "Development and analysis of numerical methods for Navier-Stokes type equations" (2008-2010)
An ongoing cooperation with Arnold Reusken and the Inst. of Geometry and Applied Mathematics of RWTH University of Aachen is partially supported within SFB 540 interdisciplinary project. Currently we are very interested in analysis of multi-phase flows and interface phenomena.
I am authoring two textbooks in multigrid and domain decpmposition methods: Lections and exercises in multigrid methods " Fizmatlit: Moscow 2005 and Short course on multigrid and domain decomposition methods, Moscow State University: MAKS-Press, Moscow, 2007 (joint with Yu.V.Vassilevski) (Both texts are in Russian)