http://www.inf.ufes.br/~luciac/comcie/JFNK-Knoll.pdf

Jacobian-free Newton-Krylov methods: a survey of approaches and applications

hypre is a software library for the solution of large, sparse linear systems on massively parallel computers. Its emphasis is on modern powerful and scalable preconditioners. hypre provides various conceptual interfaces to enable application users to access the library in the way they naturally think about their problems. This paper presents the conceptual interfaces in hypre. An overview of the preconditioners that are available in hypre is given, including some numerical results that show the efficiency of the library.

/pdf/hypre-a-library-of-high-performance-preconditioners-142t82tfp6.pdf

hypre: A Library of High Performance Preconditioners

The numerical simulation of groundwater flow through heterogeneous porous media is discussed. 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 effects of boundary conditions, coarse grid solver strategy, increasing the grid resolution, enlarging the domain, and varying the geostatistical parameters used to define the subsurface realization. Scalability is also examined. The results were obtained using the PARFLOW groundwater flow simulator on the CRAY T3D massively parallel computer.

A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations

Newton–Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems

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 methods such as geometric multigrid which require additional information beyond just the matrix. This chapter discusses the design of the conceptual interfaces in hypre and illustrates their use with various examples. We discuss the data structures and parallel implementation of these interfaces. A brief overview of the solvers and preconditioners available through the interfaces is also given.

/pdf/the-design-and-implementation-of-hypre-a-library-of-parallel-35ol472pjh.pdf

The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners

The purpose of this paper is to present a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two- and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients. The discrete equations are assumed to be defined on a logically rectangular grid, obtained possibly through grid generation for a problem defined on an irregular domain. The basic algorithm is described along with some modifications which are designed to improve its efficiency and robustness for certain types of problem cases. FORTRAN codes that implement the two- and three-dimensional semicoarsening multigrid algorithms are described briefly, and numerical results are presented.

A Semicoarsening Multigrid Method for Elliptic Partial Differential Equations with Highly Discontinuous and Anisotropic Coefficients

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A Semicoarsening Multigrid Method for Elliptic Partial Differential Equations with Highly Discontinuous and Anisotropic Coefficients