On the proving of convergence of multigrid methods

S. I. Martynenko

Central Institute of Aviation Motors, State Scientific Center of Russian Federation, Moscow

Abstract: The paper deals with some problems concerning the proving of convergence of multigrid methods. Special attention is paid to the robust multigrid technique as a variant of geometric multigrid methods with problem-independent transfer operators. The matrix of multigrid iterations is obtained; its norm is estimated. A mesh-independent convergence rate is proved, and a comparison with the classical multigrid methods is performed.

Keywords: geometric multigrid method, robust multigrid technique, convergence.

UDC: 519.632.4

Received: 01.10.2012