Abstract

MLD2P4 (MULTI-LEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON PSBLAS) is a package of parallel algebraic multi-level preconditioners. The first release of MLD2P4 made available multi-level additive and hybrid Schwarz preconditioners, as well as one-level additive Schwarz preconditioners. The package has been extended to include further multi-level cycles and smoothers widely used in multigrid methods. In the multi-level case, a purely algebraic approach is applied to generate coarse-level corrections, so that no geometric background is needed concerning the matrix to be preconditioned. The matrix is assumed to be square, real or complex.

MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) computational framework and can be used in conjuction with the Krylov solvers available in this framework. MLD2P4 enables the user to easily specify different features of an algebraic multi-level preconditioner, thus allowing to search for the ``best'' preconditioner for the problem at hand.

The package employs object-oriented design techniques in Fortran 2003, with interfaces to additional third party libraries such as MUMPS, UMFPACK, SuperLU, and SuperLU_Dist, which can be exploited in building multi-level preconditioners. The parallel implementation is based on a Single Program Multiple Data (SPMD) paradigm; the inter-process communication is based on MPI and is managed mainly through PSBLAS.

This guide provides a brief description of the functionalities and the user interface of MLD2P4.