An Aggregation Multilevel Method Using Smooth Error Vectors

Edmond Chow

Abstract: Many algebraic multilevel methods for solving linear systems assume that the slowly converging, 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 stiffness matrices are available.