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Elena N. Akimova

Elena N. Akimova
http://parallel.ru/russia/people/akimova.html
Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation

Department of  Ill-Posed Problems of Analysis and Applications, Leading Researcher

PhD (Phys., Math.), Professor

ScopusID: 15838749500

ORCID ID: 0000-0002-4462-5817

Scientific interests: Numerical Methods, Parallel Algorithms, Mathematical Modeling, Integral Equations, Ill-Posed Problems, Inverse Geophysical Problems, Elasticity Problems, Multiprocessor Systems, High Performance Computing.

Scientific achievements: The main direction of scientific research is the construction and  investigation of  direct and iterative methods and parallel algorithms, and  their application to solving (on multiprocessor computing systems) mathematical physics problems:  linear and nonlinear inverse gravimetry and magnetometry problems, multicomponent diffusion problems, three-dimensional elasticity and elastic-plastic problems. The parallel direct methods for solving linear systems with band and block matrices have been constructed and  the stability theorems for  parallel algorithms with respect to relations on  the coefficients of the original systems have been proved. The effective stable parallel iterative algorithms for solving the  inverse gravimetry problem of  density reconstruction and the structural inverse gravimetry and magnetometry problems of contact surface reconstruction have been developed.

Main publications:

  1. Akimova E.N. Parallel algorithms for solving the three-dimensional elasticity problem and sparse linear systems // Far Eastern mathematical journal. 2001. Vol. 2. No. 2. P. 10–28.
  2. Akimova E.N., Vasin V.V. Stable parallel algorithms for solving the inverse gravimetry and magnetometry problems // International Journal Engineering Modelling. 2004. Vol. 17. No. 1-2. P. 13–19.
  3. Akimova E.N.,  Gorbachev I.I., Popov V.V.  Multicomponent diffusion problems solving by   matrix sweep algorithm // Mathematical modeling. 2005. Vol. 17. No. 9. P. 85–92.
  4. Akimova E.N., Gemaidinov D.V.  Parallel algorithms for solving the gravity problem about finding the density in the layer // Trudy Inst. Mat. i Mekh. UrO RAN. 2007. Vol. 13, no. 3. P. 3–21.
  5. Akimova E.N. Parallel algorithm for solving the system with fivediagonal matrices and study its stability // Vestnik of Lobachevsky University of Nizhni Novgorod. 2009. No. 2. P. 135–140. 
  6. Akimova E.N., Belousov D.V. Parallel algorithms for solving linear systems with block-tridiagonal matrices on multi-core CPU with GPU // Journal of Computational Science. 2012.  Vol. 3. Issue 6. P. 445–449. DOI: 10.1016/j.jocs.2012.08.004
  7. Akimova E.N., Martyshko P.S., Misilov V.E. Algorithms for solving the structural gravity problem in a multilayer medium // Doklady Earth Sciences. 2013. Vol. 453.  Part 2. P. 1278–1281. DOI: 10.1134/S1028334X13120180
  8. Akimova E.N., Belousov D.V., Misilov V.E. Algorithms for solving inverse geophysical problems on parallel computing systems // Numerical Analysis and Application. 2013. Vol. 6. No. 2. P. 98–110. DOI: 10.1134/S199542391302002X
  9. Akimova E.N., Misilov V.E., Skurydina A.F., Tretyakov A.I. Gradient Methods for Solving Inverse Gravimetry and Magnetometry Problems on the Uran Supercomputer // Numerical Methods and Programming. 2015. Vol. 16. Part.1. P. 155–164.
  10. Martyshko P.S., Akimova E.N., Misilov V.E. Solving the Structural Inverse Gravity Problem by the Modified Gradient Methods // Izvestiya, Physics of the Solid Earth. 2016. Vol. 52. No. 5. P. 704–708. DOI: 10.1134/S1069351316050098