AN AGGREGATION MULTILEVEL METHOD USING SMOOTH ERROR VECTORS

Abstract. Many algebraic multilevel methods for solving linear systems assume that the slow-to-converge, or algebraically smooth error is locally constant. This assumption is often not true and can lead to poor performance of the method. Other multilevel methods require a description of the algebraically smooth error via knowledge of the near-nullspace of the operator, but this information may not always be available. This paper presents an aggregation multilevel method for problems where the near-nullspace of the operator is not known. The method uses samples of low-energy error vectors to construct its interpolation operator. The basis vectors for an aggregate are computed via a singular value decomposition of the sample vectors locally over that aggregate. Compared to many other methods that automatically adjust to the near-nullspace, this method does not require that the element stiness matrices are available. Key words. preconditioning, multilevel and multigrid methods, smoothed aggregation AMS subject classications. 65F10, 65F35, 65F50 1. Introduction. Algebrai