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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 5, Pages 796–821 (Mi zvmmf10893)  

This article is cited in 1 scientific paper (total in 1 paper)

A $KP_1$ scheme for acceleration of inner iterations for the transport equation in 3D geometry consistent with nodal schemes: 2. Splitting method for solving the $P_1$ system for acceleration corrections

A. M. Voloshchenko

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Abstract: An algorithm is proposed for solving the ${{P}_{1}}$ system for acceleration corrections that arises in constructing a $K{{P}_{1}}$ scheme for accelerating the convergence of inner iterations consistent with the nodal LD (Linear Discontinues) and LB (Linear Best) schemes of third and fourth-order accuracy in space for the transport equation in three-dimensional $r,\vartheta,z$ geometry. The algorithm is based on a cyclic splitting method combined with the through-computation algorithm for solving auxiliary two-point equations system. A modification of the algorithm is considered for three-dimensional $x,y,z$ geometry.

Key words: splitting method, $KP_1$ acceleration scheme, transport equation, nodal schemes.

DOI: https://doi.org/10.1134/S0044466919050156


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:5, 751–774

Bibliographic databases:

UDC: 519.6:536.71
Received: 17.09.2018
Revised: 12.12.2018
Accepted:11.01.2019

Citation: A. M. Voloshchenko, “A $KP_1$ scheme for acceleration of inner iterations for the transport equation in 3D geometry consistent with nodal schemes: 2. Splitting method for solving the $P_1$ system for acceleration corrections”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 796–821; Comput. Math. Math. Phys., 59:5 (2019), 751–774

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. V. Shilkov, “Primenenie modelnykh uravnenii dlya iteratsionnogo rascheta polei neitronov i fotonov v veschestve”, Preprinty IPM im. M. V. Keldysha, 2020, 129, 36 pp.  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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