"Acceleration of parallel algorithms for solving three-dimensional boundary value problems on quasi-structured grids"
Klimonov I.A., Korneev V.D., and Sveshnikov V.M.

This paper is devoted to the acceleration of the parallel solution of three-dimensional boundary value problems by the computational domain decomposition method into subdomains that are conjugated without overlapping. The decomposition is performed by a uniform parallelepipedal macrogrid. In each subdomain and on the interface, some structured subgrids are constructed. The union of these subgrids forms a quasi-structured grid on which the problem is solved. The parallelization is carried out using the MPI-technology. We propose and experimentally study the acceleration algorithm for an external iterative process on subdomains to solve a system of linear algebraic equations approximating the Poincare-Steklov equation on the interface. A number of numerical experiments are carried out on various quasi-structured grids and with various parameters of computational algorithms showing the acceleration of computations.

Keywords: boundary value problems, parallelization, quasi-structured grids, iterative process, initial approximation.

  • Klimonov I.A. – Novosibirsk State University, Faculty of Mechanics and Mathematics; ulitsa Pirogova 2, Novosibirsk, 630090, Russia; Graduate Student, e-mail: ilya.klimonov@gmail.com
  • Korneev V.D. – Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences; prospekt Lavrentyeva 6, Novosibirsk, 630090, Russia; Ph.D., Associate Professor, e-mail: korneev@ssd.sscc.ru
  • Sveshnikov V.M. – Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences; prospekt Lavrentyeva 6, Novosibirsk, 630090, Russia; Dr. Sci., Professor, Head of Laboratory, e-mail: victor@lapasrv.sscc.ru