Title: Formalisation of the multigrid computations

Authors: Sergey Martynenko

Addresses: Department of Chemistry of Engine Combustive-Lubricating Materials and Special Engines, Federal State Unitary Enterprise 'Central Institute of Aviation Motors n.a. Baranov', 2, Aviamotornaya St., Moscow, 111116, Russia

Abstract: The paper represents a robust multigrid algorithm for solving a large class of applied problems (from Poisson equation to Navier-Stokes equations) on the structured grids. The algorithm consists of the robust multigrid technique (variant of the geometric multigrid methods with the problem-independent transfer operators) and the smoothing procedure based on Gauss-Seidel iterations with block unknown ordering. Theoretical analysis and numerical experiments show that close-to-optimal convergence rate for many (non)linear problems is obtained with the same multigrid components. Proposed approach can be used in black box software.

Keywords: multigrid computations; robustness; Poisson equation; Navier-Stokes equations; structured grids; robust multigrid; smoothing procedures; Gauss-Seidel iterations; block unknown ordering; black box software.

DOI: 10.1504/IJCSM.2013.058058

International Journal of Computing Science and Mathematics, 2013 Vol.4 No.4, pp.309 - 320

Received: 06 Feb 2013
Accepted: 01 Jul 2013
Published online: 10 May 2014 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article