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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)
NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for(More)
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)
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)
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 truncated-Newton 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)
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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)