Mathematics

Algebraic multilevel preconditioner for second order finite element approximation in rectangular domains. II. Multigrid preconditioner

Yu. R. Hakopian, H. A. Hovhannisyan

Yerevan State University

Abstract: The present paper, consisting of two parts, is devoted to constructing an algebraic multigrid preconditioner for stiffness matrices arising in second-order finite element approximation of elliptic boundary value problems. In the second part of the paper, being based on the two-level preconditioner described in the first part, the multigrid preconditioner is constructed. The multigrid preconditioner is proved to be spectrally equivalent to the initial stiffness matrix and its arithmetic cost is proportional to the dimensionality of the finest-grid algebraic problem.

Keywords: Elliptic boundary value problems, two-level preconditioner.

UDC: 519.6

Received: 28.03.2002
Accepted: 03.06.2003