Tayloring Multigrid Components for a Diffusion Model Problem

Abstract

The main difficulty to construct efficient algorithms for application problems consists in the careful selection of those components a multigrid algorithm is composed of. The components have to be tuned carefully, because the proper choice decides on the efficiency of the multigrid solver. For realistic applications this problem is complemented by particular technical questions, which sometimes prohibit the use of standard components. A serious and often heard advice, not to say theorem, of the multigrid philosophy is: treat local problems locally. Having this in mind, the presented approach for the model problem of this chapter will differ by several details from other singlegrid and multigrid approaches [89,90,88,99,124].