Publications

Siefert, Christopher S.; Bochev, Pavel B.; Hu, Jonathan J.; Tuminaro, Raymond S.

Abstract not provided.

Siefert, Christopher S.; Hu, Jonathan J.; Tuminaro, Raymond S.

Abstract not provided.

Siefert, Christopher S.; Bochev, Pavel B.; Tuminaro, Raymond S.; Hu, Jonathan J.

Abstract not provided.

Robinson, Allen C.; Mosso, Stewart J.; Siefert, Christopher S.; Hu, Jonathan J.

Abstract not provided.

Journal of Computational Physics

Tuminaro, Raymond S.; Hu, Jonathan J.

Abstract not provided.

Proposed for publication in SIAM Journal on Scientific Computing.

Bochev, Pavel B.; Tuminaro, Raymond S.; Hu, Jonathan J.

Abstract not provided.

Domino, Stefan P.; Tuminaro, Raymond S.; Robinson, Allen C.; Hu, Jonathan J.

Abstract not provided.

Siefert, Christopher S.; Bochev, Pavel B.; Hu, Jonathan J.; Tuminaro, Raymond S.

Abstract not provided.

Siefert, Christopher S.; Tuminaro, Raymond S.; Hu, Jonathan J.

Abstract not provided.

Tuminaro, Raymond S.; Bochev, Pavel B.; Hu, Jonathan J.

Abstract not provided.

Tuminaro, Raymond S.; Hu, Jonathan J.; Siefert, Christopher S.

Abstract not provided.

Sala, Marzio S.; Tuminaro, Raymond S.; Hu, Jonathan J.

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package or to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.

Sala, Marzio S.; Hu, Jonathan J.; Tuminaro, Raymond S.

ML development was started in 1997 by Ray Tuminaro and Charles Tong. Currently, there are several full- and part-time developers. The kernel of ML is written in ANSI C, and there is a rich C++ interface for Trilinos users and developers. ML can be customized to run geometric and algebraic multigrid; it can solve a scalar or a vector equation (with constant number of equations per grid node), and it can solve a form of Maxwell's equations. For a general introduction to ML and its applications, we refer to the Users Guide [SHT04], and to the ML web site, http://software.sandia.gov/ml.

Sala, Marzio S.; Hu, Jonathan J.; Tuminaro, Raymond S.

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package or to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.

Heroux, Michael A.; Kolda, Tamara G.; Long, Kevin R.; Hoekstra, Robert J.; Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; Williams, Alan B.; Heroux, Michael A.; Hu, Jonathan J.; Lehoucq, Richard B.; Thornquist, Heidi K.; Tuminaro, Raymond S.; Willenbring, James M.; Bartlett, Roscoe B.; Howle, Victoria E.

The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. In particular, our goal is to develop parallel solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific applications. Our emphasis is on developing robust, scalable algorithms in a software framework, using abstract interfaces for flexible interoperability of components while providing a full-featured set of concrete classes that implement all abstract interfaces. Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking. Trilinos packages are primarily written in C++, but provide some C and Fortran user interface support. We provide an open architecture that allows easy integration with other solver packages and we deliver our software to the outside community via the Gnu Lesser General Public License (LGPL). This report provides an overview of Trilinos, discussing the objectives, history, current development and future plans of the project.