Publications

Journal of Computational Physics

Elman, Howard; Howle, Victoria E.; Shadid, John N.; Shuttleworth, Robert R.; Tuminaro, Raymond S.

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier-Stokes system first presented in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier-Stokes equations, Computational Methods in Applied Mechanical Engineering 188 (2000) 505-526]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code. © 2007 Elsevier Inc. All rights reserved.

Gray, Genetha A.; Williams, Pamela J.; Hough, Patricia D.; Howle, Victoria E.

Abstract not provided.

Gray, Genetha A.; Hough, Patricia D.; Howle, Victoria E.; Williams, Pamela J.

Abstract not provided.

Howle, Victoria E.; Shuttleworth, Robert R.; Tuminaro, Raymond S.

Abstract not provided.

Proposed for publication in the SIAM Journal on Scientific Computing.

Howle, Victoria E.; Shadid, John N.; Tuminaro, Raymond S.

Abstract not provided.

Howle, Victoria E.

Abstract not provided.

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.