Application of a Robust Multigrid Technique for the Parallel Solution of Initial-Boundary Value Problems

• Published in: Mathematical models and computer simulations Vol. 14; no. 6; pp. 1002 - 1010
• Main Authors: Martynenko, S. I., Gökalp, I., Bakhtin, V. A., Karaca, M., Toktaliev, P. D., Semenev, P. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Boundary value problems; Linear algebra; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Robustness (mathematics); Simulation and Modeling; Thermodynamics; multigrid methods; initial-boundary value problems; parallel computing
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048222060096

This article is devoted to the construction of a parallel multigrid algorithm for the numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on a robust multigrid technique (RMT). A distinctive feature of the proposed algorithm is the possibility of the parallel solution of initial-boundary value problems and initial-boundary value problems in a unified manner involving 3 m independent computers (threads, if the OpenMP parallelization technology is used), m  = 1, 2, 3, …. Coarse grids are built only in space, the number of grid levels depends on the conditionality of the coefficient matrix of the resulting system of linear algebraic equations (SLAEs). The Seidel method with the point ordering of the unknowns is used as a smoothing procedure for solving the initial-boundary value problem for a heat equation with constant coefficients. A description of the algorithm and the results of the computational experiments performed using the OpenMP technology are given.