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LOCA 1.0 Library of Continuation Algorithms: Theory and Implementation Manual

Description: LOCA, the Library of Continuation Algorithms, is a software library for performing stability analysis of large-scale applications. LOCA enables the tracking of solution branches as a function of a system parameter, the direct tracking of bifurcation points, and, when linked with the ARPACK library, a linear stability analysis capability. It is designed to be easy to implement around codes that already use Newton's method to converge to steady-state solutions. The algorithms are chosen to work for large problems, such as those that arise from discretizations of partial differential equations, and to run on distributed memory parallel machines. This manual presents LOCA's continuation and bifurcation analysis algorithms, and instructions on how to implement LOCA with an application code. The LOCA code is being made publicly available at www.cs.sandia.gov/loca.
Date: March 1, 2002
Creator: SALINGER, ANDREW G.; BOU-RABEE, NAWAF M.; BURROUGHS,ELIZABETH A.; PAWLOWSKI, ROGER P.; LEHOUCQ, RICHARD B.; ROMERO, LOUIS et al.
Partner: UNT Libraries Government Documents Department

Final report LDRD project 105816 : model reduction of large dynamic systems with localized nonlinearities.

Description: Advanced computing hardware and software written to exploit massively parallel architectures greatly facilitate the computation of extremely large problems. On the other hand, these tools, though enabling higher fidelity models, have often resulted in much longer run-times and turn-around-times in providing answers to engineering problems. The impediments include smaller elements and consequently smaller time steps, much larger systems of equations to solve, and the inclusion of nonlinearities that had been ignored in days when lower fidelity models were the norm. The research effort reported focuses on the accelerating the analysis process for structural dynamics though combinations of model reduction and mitigation of some factors that lead to over-meshing.
Date: October 1, 2009
Creator: Lehoucq, Richard B.; Segalman, Daniel Joseph; Hetmaniuk, Ulrich L. (University of Washington, Seattle, WA) & Dohrmann, Clark R.
Partner: UNT Libraries Government Documents Department

Peridynamics with LAMMPS : a user guide.

Description: Peridynamics is a nonlocal formulation of continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamic model. This document details the implementation of a discrete peridynamic model within the LAMMPS molecular dynamic code. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized, and overviews the LAMMPS implementation. A nontrivial example problem is also included.
Date: January 1, 2008
Creator: Lehoucq, Richard B.; Silling, Stewart Andrew; Plimpton, Steven James & Parks, Michael L.
Partner: UNT Libraries Government Documents Department

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Description: This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.
Date: October 1, 2007
Creator: Wagner, Gregory John (Sandia National Laboratories, Livermore, CA); Collis, Samuel Scott; Templeton, Jeremy Alan (Sandia National Laboratories, Livermore, CA); Lehoucq, Richard B.; Parks, Michael L.; Jones, Reese E. (Sandia National Laboratories, Livermore, CA) et al.
Partner: UNT Libraries Government Documents Department

Substructured multibody molecular dynamics.

Description: We have enhanced our parallel molecular dynamics (MD) simulation software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator, lammps.sandia.gov) to include many new features for accelerated simulation including articulated rigid body dynamics via coupling to the Rensselaer Polytechnic Institute code POEMS (Parallelizable Open-source Efficient Multibody Software). We use new features of the LAMMPS software package to investigate rhodopsin photoisomerization, and water model surface tension and capillary waves at the vapor-liquid interface. Finally, we motivate the recipes of MD for practitioners and researchers in numerical analysis and computational mechanics.
Date: November 1, 2006
Creator: Grest, Gary Stephen; Stevens, Mark Jackson; Plimpton, Steven James; Woolf, Thomas B. (Johns Hopkins University, Baltimore, MD); Lehoucq, Richard B.; Crozier, Paul Stewart et al.
Partner: UNT Libraries Government Documents Department

An overview of Trilinos.

Description: 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.
Date: August 1, 2003
Creator: Long, Kevin R.; Tuminaro, Raymond Stephen; Bartlett, Roscoe Ainsworth; Hoekstra, Robert John; Phipps, Eric Todd; Kolda, Tamara Gibson et al.
Partner: UNT Libraries Government Documents Department

Statistical coarse-graining of molecular dynamics into peridynamics.

Description: This paper describes an elegant statistical coarse-graining of molecular dynamics at finite temperature into peridynamics, a continuum theory. Peridynamics is an efficient alternative to molecular dynamics enabling dynamics at larger length and time scales. In direct analogy with molecular dynamics, peridynamics uses a nonlocal model of force and does not employ stress/strain relationships germane to classical continuum mechanics. In contrast with classical continuum mechanics, the peridynamic representation of a system of linear springs and masses is shown to have the same dispersion relation as the original spring-mass system.
Date: October 1, 2007
Creator: Silling, Stewart Andrew & Lehoucq, Richard B.
Partner: UNT Libraries Government Documents Department