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- Michael A. Heroux, Roscoe A. Bartlett, +13 authors Kendall S. Stanley
- ACM Trans. Math. Softw.
- 2005

The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i)… (More)

- John N. Shadid, Roger P. Pawlowski, Jeffrey W. Banks, Luis Chacón, Paul T. Lin, Ray S. Tuminaro
- J. Comput. Physics
- 2010

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The… (More)

- David E. Keyes, Lois C. McInnes, +42 authors Barbara I. Wohlmuth
- IJHPCA
- 2013

In this talk I will overview a survey paper developed from the DOE-‐sponsored Institute for Computing in Science Workshop on " Multiphysics Simulations: Challenges and Opportunities. " In this paper, we considered multiphysics applications from algorithmic and architectural perspectives where " architectural " included both software and hardware… (More)

- Andrew G. Salinger, E. A. Burroughs, Roger P. Pawlowski, Eric T. Phipps, Louis A. Romero
- I. J. Bifurcation and Chaos
- 2005

We present the set of bifurcation tracking algorithms which have been developed in the LOCA software library to work with large scale application codes that use fully coupled Newton’s method with iterative linear solvers. Turning point (fold), pitchfork, and Hopf bifurcation tracking algorithms based on Newton’s method have been implemented, with particular… (More)

- Michael Heroux, Roscoe Bartlett, +12 authors Alan Williams
- 2003

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 objectoriented software framework for the solution of large-scale, complex multiphysics engineering and scientific applications.… (More)

- Roger P. Pawlowski, Joseph P. Simonis, Homer F. Walker, John N. Shadid
- SIAM J. Numerical Analysis
- 2008

The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg… (More)

Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability analysis are used to study transition from steady to transient flow… (More)

- Roger P. Pawlowski, John N. Shadid, Joseph P. Simonis, Homer F. Walker
- SIAM Review
- 2006

A Newton–Krylov 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)… (More)

- Patrick K. Notz, Roger P. Pawlowski, James C. Sutherland
- ACM Trans. Math. Softw.
- 2012

Multiphysics simulation software is plagued by complexity stemming from nonlinearly coupled systems of Partial Differential Equations (PDEs). Such software typically supports many models, which may require different transport equations, constitutive laws, and equations of state. Strong coupling and a multiplicity of models leads to complex algorithms (i.e.,… (More)

- Eric T. Phipps, Roger P. Pawlowski
- ArXiv
- 2012

Expression templates are a well-known set of techniques for improving the efficiency of operator overloading-based forward mode automatic differentiation schemes in the C++ programming language by translating the differentiation from individual operators to whole expressions. However standard expression template approaches result in a large amount of… (More)