Robert D. Falgout

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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, AMGe is based on the use of two local measures, which are derived from global measures that appear in existing multigrid theory. These new(More)
This paper discusses the numerical simulation of groundwater ow through heterogeneous porous media The focus is on the performance of a parallel multigrid preconditioner for accelerating convergence of conjugate gradients which is used to compute the pressure head The numerical investigation considers the e ects of boundary conditions coarse grid solver(More)
We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and su cient conditions for constructing the components of e cient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is(More)
The hypre software library provides high performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers. One of its attractive features is the provision of conceptual interfaces. These interfaces give application users a more natural means for describing their linear systems, and provide access to(More)
Substantial effort has been focused over the last two decades on developing multilevel iterative methods capable of solving the large linear systems encountered in engineering practice. These systems often arise from discretizing partial differential equations over unstructured meshes, and the particular parameters or geometry of the physical problem being(More)
We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their use as(More)
Abstract. We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their(More)