A Block-Circulant Preconditioner for Domain Decomposition Algorithm

by

B. Kiss and G. Molnárka

Department of Mathematics, Széchenyi István College, Győr

Summary

A preconditioned conjugate gradient domain decomposition method was given in [1] for the solution of system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction given in [1] can be generalized for higher order finite elements too. We shall show the construction for second order finite elements. The methos of calculation of matrix entries of preconditioner and the results of calculation. The numerical experiments we will present show that this kind of preconditioner works well and the estimations and the numerical results are close.

Reference

[1] B. Kiss and G. Molnárka, A preconditioned Domain Decomposition Algorithm for the Solution of the Elliptic Neumann Problem., In Parallel Algorithm for Differential Equations, ed. by W. Hackbush, Proc. of 6. GAMM - seminar, Kiel, January, (19-21), 1990. pp.119-129.