Results 1 
7 of
7
An overview of the trilinos project
 ACM Transactions on Mathematical Software
"... The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundament ..."
Abstract

Cited by 150 (20 self)
 Add to MetaCart
(Show Context)
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a twolevel 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 lookandfeel, including configuration, documentation, licensing, and bugtracking. Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software. Sandia is a multiprogram laboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department of Energy under Contract DEAC0494AL85000. Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and
Globalization Techniques for NewtonKrylov Methods and Applications to the FullyCoupled SOLUTION OF THE NAVIERâSTOKES EQUATIONS
"... A NewtonâKrylov method is an implementation of Newton's method in which a Krylov subspace method is used to solve approximately the linear subproblems that determine Newton steps. To enhance robustness when good initial approximate solutions are not available, these methods are usually glob ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
A NewtonâKrylov method is an implementation of Newton's method in which a Krylov subspace method is used to solve approximately the linear subproblems that determine Newton steps. To enhance robustness when good initial approximate solutions are not available, these methods are usually globalized, i.e., augmented with auxiliary procedures (globalizations) that improve the likelihood of convergence from a starting point that is not near a solution. In recent years, globalized NewtonKrylov methods have been used increasingly for the fully coupled solution of largescale problems. In this paper, we review several representative globalizations, discuss their properties, and report on a numerical study aimed at evaluating their relative merits on largescale two and threedimensional problems involving the steadystate NavierStokes equations.
A MultiParameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid,” submitted to Siam Journal for Applied Dynamical Systems.16
"... Abstract. In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which c ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluidstructure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed.
FixedPolynomial Approximate Spectral Transformations for Preconditioning the Eigenvalue Problem
, 2003
"... ..."
Bifurcation and stability analysis of laminar isothermal counterflowing jets
, 2006
"... this paper is organized as follows: Section 2 describes the computational models used in our analysis. Section 3 describes the numerical algorithms used to solve the steadystate and transient problems. Finally, the results and conclusions are discussed in 4and 5, respectively ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
this paper is organized as follows: Section 2 describes the computational models used in our analysis. Section 3 describes the numerical algorithms used to solve the steadystate and transient problems. Finally, the results and conclusions are discussed in 4and 5, respectively
unknown title
, 2004
"... Approved for public release; further dissemination unlimited. E ..."
(Show Context)