BLOCK ILU PRECONDITIONED ITERATIVE
METHODS FOR REDUCED LINEAR SYSTEMS

N. GUESSOUS AND O. SOUHAR

Abstract. This paper deals with the iterative solution of a large sparse matrix when this matrix is in block-partitioned form arising from discrete elliptic Partial Differential Equations (PDEs). We introduce a block red-black coloring technique to reorder the unknowns, which is based on the standard red-black coloring. We propose some preconditioning techniques which combine the block incomplete LU factorization and the Schur complement technique, where the reduced system is preconditioned using different preconditioners. Some theoretical results to control the residual norm are presented.