THE SOFTWARE PACKAGE LOGOS. ALGEBRAIC MULTIGRID METHOD FOR SOLUTION OF LINEAR EQUATIONS SYSTEMS FROM CFD-PROBLEMS

Golubev A.A, Derjugin J.N, Zelenskij D.K, Kozelkov A.S, Lashkin S.V, Silaev D.P, Simonov P.G

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In the paper a software implementation of an algebraic multigrid method (AMG) with aggregative coarsening for solution of systems of linear equations was reviewed. Data and memory structure of the LOGOS, a software package for solving of CFD-problems by SIMPLE-method, were used during the implementation. V-, W-, F-cycles of multigrid method were considered for solution of systems of linear algebraic equations (SLAE). Face-by-cell storage format for a matrix and an adaptation of Gauss-Seidel method for efficient processing of the format were reviewed. Parallelization of algorithms of both smoothing and coarsening is examined in extra details. Also solution for a problem of parallel coarse level’s usage is presented. The problem was the following: because of small matrix size at coarse level’s time spent for data exchanges is longer comparing to the time of calculations. The paper contains results of test problems solutions, and comparison of results against other implementations of AMG.

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Голубев А.А, Дерюгин Ю.Н, Зеленский Д.К, Козелков А.С, Лашкин С.В, Силаев Д.П, Симонов П.Г ПАКЕТ ПРОГРАММ ЛОГОС. АЛГЕБРАИЧЕСКИЙ МНОГОСЕТОЧНЫЙ МЕТОД РЕШЕНИЯ СЛАУ ДЛЯ ЗАДАЧ ГИДРОДИНАМИКИ // Научное обозрение. Физико-математические науки . 2020. № 1. С. 52-53;
URL: https://physics-mathematics.ru/en/article/view?id=72 (дата обращения: 24.06.2026).