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.
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APA Style
Hales, J.D., Novascone, S.R., Williamson, R.L., Gaston, D.R., Tonks, M.R. (2012). Solving nonlinear solid mechanics problems with thejacobian-free newton krylov method. Computer Modeling in Engineering & Sciences, 84(2), 123-154. https://doi.org/10.3970/cmes.2012.084.123
Vancouver Style
Hales JD, Novascone SR, Williamson RL, Gaston DR, Tonks MR. Solving nonlinear solid mechanics problems with thejacobian-free newton krylov method. Comput Model Eng Sci. 2012;84(2):123-154 https://doi.org/10.3970/cmes.2012.084.123
IEEE Style
J.D. Hales, S.R. Novascone, R.L. Williamson, D.R. Gaston, and M.R. Tonks "Solving Nonlinear Solid Mechanics Problems with theJacobian-Free Newton Krylov Method," Comput. Model. Eng. Sci., vol. 84, no. 2, pp. 123-154. 2012. https://doi.org/10.3970/cmes.2012.084.123