We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the element stiffness matrices, we have that AMGe is based on the use of two local measures, which are derived from global measures that appear in existing multigrid theory. These new measures are used to determine local representations of algebraically "smooth" error components that provide the basis for constructing effective interpolation and, hence, the coarsening process for AMG. Here, we focus on the interpolation process; choice of the coarse "grids" based on these measures is the subject of current research. We develop a theoretical foundation for AMGe and present numerical results that demonstrate the efficacy of the method.

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Abstract.The need to solve linear systems arising from problems posed on extremely large, unstructured glids has sparked great interest in paall&zing algebraic multigrid (AMG) To date, howeva, no parallel AMG algorithms exist We introduce a paallel algorithm fol the selection of coals-glid points, a aucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuistics designed to insme the quality of the cease glids A prototype serial version of the algorithm is implemented, and tests are conducted to d&amine its effect on multigrid convergence, and AMG complexity

Abstract. We continue the comparison of parallel algorithms for solving diagonally dominant and general narrow-banded linear systems of equations that we started in 2 . The solvers compared are the banded system solvers of ScaLAPACK 6 and those investigated by Arbenz and Hegland 1, 5 . We present the numerical experiments that we conducted on the IBM SP 2.

This paper outlines the content and performance of ScaLAPACK, a collection of mathematical software for linear algebra computations on distributed memory computers. The importance of developing standards for computational and message passing interfaces is discussed. We present the different components and building blocks of ScaLAPACK, and indicate the difficulties inherent in producing correct codes for networks of heterogeneous processors. Finally, this paper briefly describes future directions for the ScaLAPACK library and concludes by suggesting alternative approaches to mathematical libraries, explaining how ScaLAPACK could be integrated into efficient and user-friendly distributed systems.