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ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n × 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… (More)

With the rise in popularity of compatible finite element, finite difference and finite volume discretizations for the time domain eddy current equations, there has been a corresponding need for fast solvers of the resulting linear algebraic systems. However, the traits that make compatible discretizations a preferred choice for the Maxwell's equations also… (More)

- P B Bochev, C M Siefert, R S Tuminaro, J Xu, Y Zhu
- 2007

We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique for the reformulated problem. The reformulation uses discrete Hodge… (More)

—Trilinos is an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific problems. While the original version of Trilinos was designed for highly scalable solutions for large problems, the need for increasingly higher fidelity simulations has pushed the problem sizes beyond what could have been… (More)

The design and analysis of computer experiments (DACE) usually envisions performing a single experiment , then replacing the expensive simulation with an approximation. When the simulation is a nonlin-ear function to be optimized, DACE may be inefficient , and sequential strategies that synthesize ideas from DACE and numerical optimization may be warranted.… (More)

A template-based generic programming approach was presented in a previous paper [19] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic… (More)

Trilinos is an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific problems. While Trilinos was originally designed for scalable solutions of large problems, the fidelity needed by many simulations is significantly greater than what one could have envisioned two decades ago. When problem sizes… (More)

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that… (More)