A new mixed preconditioning method based on the clustered element-by-element preconditioners

Abstract

We describe a new mixed preconditioning method for finite element computations. In the clustered element-by-element (CEBE) preconditioning, the elements are merged into clusters, and the preconditioners are defined as series products of cluster level matrices. The (cluster companion) CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associatedC C preconditioner. Because these two preconditioners complement each other, when they are mixed, they give better performance. Our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, show that the mixed CEBE/CC preconditioning results in convergence rates which are significantly better than those obtained with the best of the CEBE and CC methods.