"An algebraic multigrid method in problems of computational physics"
Volkov K.N., Deryugin Yu.N., Emelyanov V.N., Kozelkov A.S., and Teterina I.V.

Implementation features and application of the algebraic multigrid methods to the solution of systems of difference equations resulting from the discretization of partial differential equations are considered. A number of approaches to the generation of C/F coarsening (standard coarsening and RS-coarsening), to the interpolation (direct interpolation, indirect interpolation, standard interpolation, and amg1r5 interpolation), and to the smoothing (iterative schemes) are discussed. Different storing formats for sparse matrices are used to calculate the Galerkin products. The results of numerical solving several model equations of mathematical physics are reported. The efficiency of the proposed approach is compared when using different components of the computational procedure.

Keywords: multigrid methods, interpolation, smoothing, computational physics.

  • Volkov K.N. – Ustinov Baltic State Technical University, Faculty of Power Engineering; ulitsa Pervaya Krasnoarmeiskaya 1, St. Petersburg, 190005, Russia; Ph.D., Leading Scientist, e-mail: dsci@mail.ru
  • Deryugin Yu.N. – Russian Federal Nuclear Center, All-Russian Institute of Experimental Physics; prospekt Mira 37, Sarov, 607188, Russia; Professor, Head of Department, e-mail: askozelkov@mail.ru
  • Emelyanov V.N. – Ustinov Baltic State Technical University, Faculty of Power Engineering; ulitsa Pervaya Krasnoarmeiskaya 1, St. Petersburg, 190005, Russia; Professor, e-mail: vlademelyanov@gmail.com
  • Kozelkov A.S. – Russian Federal Nuclear Center, All-Russian Institute of Experimental Physics; prospekt Mira 37, Sarov, 607188, Russia; Ph.D., Head of Laboratory, e-mail: askozelkov@mail.ru
  • Teterina I.V. – Ustinov Baltic State Technical University, Faculty of Power Engineering; ulitsa Pervaya Krasnoarmeiskaya 1, St. Petersburg, 190005, Russia; Associate Professor, e-mail: yaiv@mail.ru