Solving nonlinear solid mechanics problems with the jacobian-free newton krylov method

J. D. Hales, S. R. Novascone, R. L. Williamson, D. R. Gaston, M. R. Tonks

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


The equations governing solid mechanics are often solved via Newton's method. This approach can be problematic if the Jacobian determination, storage, or solution cost is high. These challenges are magnified for multiphysics applications. The Jacobian-free Newton-Krylov (JFNK) method avoids many of these difficulties through a finite difference approximation. A parallel, nonlinear solid mechanics and multiphysics application named BISON has been created that leverages JFNK. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and multiphysics applications using a series of demonstration problems. We show that JFNK has distinct advantages in many cases.

Original languageEnglish (US)
Pages (from-to)123-152
Number of pages30
JournalCMES - Computer Modeling in Engineering and Sciences
Issue number2
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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