Truncated Newton-Raphson Methods for Quasicontinuum Simulations

Abstract

The quasicontinuum method provides an efficient way to simulate the mechanical response of relatively large crystalline materials at zero temperature by combining continuum and atomistic approaches. Unconstrained optimization constitutes the key computational kernel of this method. The efficiency of the techniques for minimization depends on both the time needed to evaluate the energy expression and the number of iterations needed to converge to the minimum. In this research, we report the effectiveness of the truncated Newton-Raphson method and quasi-Newton method with low-rank Hessian update strategy that are evaluated against the full Newton-Raphson and preconditioned nonlinear conjugate gradient implementation. Results of illustrative examples mainly focus on the number of minimization iterations to converge and CPU time for the two-dimensional nanoindentation and shearing grain boundary problems.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2006
Accession Number
ADA451394

Entities

People

  • Peter W. Chung
  • Ramdev Kanapady
  • Yu Liang

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Atoms
  • Boundaries
  • Computational Complexity
  • Crystal Structure
  • Crystals
  • Equations
  • Grain Boundaries
  • High Performance Computing
  • Iterations
  • Materials
  • Military Research
  • Optimization
  • Potential Energy
  • Simulations
  • Three Dimensional
  • Two Dimensional

Readers

  • Computational Modeling and Simulation
  • Materials Science and Engineering.
  • Operations Research