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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 … more
Date: October 1, 2009
Creator: Lehoucq, Richard B.; Segalman, Daniel Joseph; Hetmaniuk, Ulrich L. & Dohrmann, Clark R.
Partner: UNT Libraries Government Documents Department
open access

Large-Scale Eigenvalue Calculations for Stability Analysis of Steady Flows on Massively Parallel Computers

Description: We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi… more
Date: August 1, 1999
Creator: Lehoucq, Richard B. & Salinger, Andrew G.
Partner: UNT Libraries Government Documents Department
open access

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 f… more
Date: March 1, 2002
Creator: Salinger, Andrew G.; Bou-Rabee, Nawaf M.; Burroughs, Elizabeth A.; Pawlowski, Roger P.; Lehoucq, Richard B.; Romero, Louis A. et al.
Partner: UNT Libraries Government Documents Department
open access

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… more
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
open access

On the Convergence of an Implicitly Restarted Arnoldi Method

Description: We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM… more
Date: July 12, 1999
Creator: Lehoucq, Richard B.
Partner: UNT Libraries Government Documents Department
open access

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… more
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
open access

Peridynamics as a rigorous coarse-graining of atomistics for multiscale materials design.

Description: This report summarizes activities undertaken during FY08-FY10 for the LDRD Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design. The goal of our project was to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. The goal of our project is to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical m… more
Date: September 1, 2010
Creator: Lehoucq, Richard B.; Aidun, John Bahram; Silling, Stewart Andrew; Sears, Mark P.; Kamm, James R. & Parks, Michael L.
Partner: UNT Libraries Government Documents Department
open access

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 include… more
Date: January 1, 2008
Creator: Lehoucq, Richard B.; Silling, Stewart Andrew; Plimpton, Steven James & Parks, Michael L.
Partner: UNT Libraries Government Documents Department
open access

Peridynamics with LAMMPS : a user guide.

Description: Peridynamics is a nonlocal extension of classical continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamics model. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized within LAMMPS. An example problem is also included.
Date: November 1, 2011
Creator: Lehoucq, Richard B.; Silling, Stewart Andrew; Seleson, Pablo (University of Texas at Austin, Austin, TX); Plimpton, Steven James & Parks, Michael L.
Partner: UNT Libraries Government Documents Department
open access

Stability Analysis of Large-Scale Incompressible Flow Calculations on Massively Parallel Computers

Description: A set of linear and nonlinear stability analysis tools have been developed to analyze steady state incompressible flows in 3D geometries. The algorithms have been implemented to be scalable to hundreds of parallel processors. The linear stability of steady state flows are determined by calculating the rightmost eigenvalues of the associated generalize eigenvalue problem. Nonlinear stability is studied by bifurcation analysis techniques. The boundaries between desirable and undesirable operating… more
Date: October 25, 1999
Creator: Lehoucq, Richard B.; Romero, Louis & Salinger, Andrew G.
Partner: UNT Libraries Government Documents Department
open access

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 … more
Date: October 1, 2007
Creator: Silling, Stewart Andrew & Lehoucq, Richard B.
Partner: UNT Libraries Government Documents Department
open access

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 surfac… more
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
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