Department of Computational Mathematics
- History of the department
- The department is based at the same time with the opening of the Institute of Mathematics, March 18, 1988. The first head of the department of computational mathematics has been a correspondent member of Academy of Sciences of the Republic Bashkortostan Ph.D. Valentin Timofeevich Ivanov. Since 1992 the department was headed by Dr. Marat Davidovich Ramazanov. Since 2008 - by Dr. Yavdat Shavkatovich Il'yasov.
- Main research themes
- The main topic of research in 1988-1992 - heat and mass transfer problems with application to the calculations of aluminum smelting electrolysis baths, electrical protection pipeline corrosion problems and geophysical exploration.
- Since 1992, the main task - the theory of approximate calculation of multidimensional integrals. We consider the problem of constructing cubature formulas with lattice of nodes.
Properties of the integrands are given by membership in certain functional spaces. The quality of the cubature formula determined by the norm of the error functional in the dual space. We solve the problem of minimizing this norm by the coefficients of the cubature formula and all sorts of lattices. We have developed algorithms for constructing asymptotically optimal cubature formulas for bounded domains with smooth boundaries.
This line of research originates from the works of academician S.L. Sobolev in 1960-1980 years, see , . About development of research in this direction see the papers , , .
- In the 2003-2008 Department participated in the programs № 17 and № 14 of the Presidium of RAS "Parallel computing on multiprocessor systems". Under this program studied: cubature formulas, Navier-Stokes calculations of discontinuous solutions of hyperbolic equations, inverse problems of chemical kinetics.
- Reports of the Department are presented on the page "ОВМ" reports (in Russian).
- Studies of the Department supported by the following grants of RFBR and RAS Presidium
- 96-01-00959-а, "Theory and applications of lattice cubature formulas", 1996 - 1998.
- 99-01-00799-а, "The theory of approximate calculation of multidimensional integrals", 1999 - 2001.
- 02-01-01167-а, "The theory of approximate calculation of multidimensional integrals", 2002 - 2004.
- 03-07-90077-в, "Creation of libraries of programs for personal and supercomputers", 2003 - 2005.
- 06-01-00597-а, "Libraries of programs for PC and multiprocessor systems", 2006 - 2008.
- 09-01-00349-а, "Parallel algorithms and programs for the numerical solution of integral equations based on lattice cubature formulas", 2009 - 2011;
- The project "The standard programs of parallel computing of model problems" in the Basic Research Program of the Presidium of RAS for 2003 - 2005, № 17 "Fundamental Problems of Informatics and Information Technologies". Section II «Parallel computing and multiprocessor systems.
- The project "The standard programs of parallel computing of model problems" in the Basic Research Program of the Presidium of RAS for 2006 - 2008, № 14 "Fundamental Problems of Informatics and Information Technologies". Section II "High-performance computing and multiprocessor systems".
- Conference "Cubature formulas and their applications" - VII, Krasnoyarsk, 2003