Local preconditioners for two-level non-overlapping domain decomposition methods

We consider additive two-level preconditioners, with a local and a global c omponent, for the Schur complement system arising in non-overlapping domain decomposition methods. We propose two new parallelizable local preconditio ners. The first one is a computationally cheap but numerically relevant alt ernative to the classical block Jacobi preconditioner. The second one explo its all the information from the local Schur complement matrices and demons trates an attractive numerical behaviour on heterogeneous and anisotropic p roblems. We also propose two implementations based on approximate Schur com plement matrices that are cheaper alternatives to construct the given preco nditioners but that preserve their good numerical behaviour. Through extens ive computational experiments we study the numerical scalability and the ro bustness of the proposed preconditioners and compare their numerical perfor mance with well-known robust preconditioners such as BPS and the balancing Neumann-Neumann method. Finally, we describe a parallel implementation on d istributed memory computers of some of the proposed techniques and report p arallel performances. Copyright (C) 2001 John Wiley & Sons, Ltd.