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Solving Nonlinear Solid Mechanics Problems with theJacobian-Free Newton Krylov Method
Computer Modeling in Engineering & Sciences 2012, 84(2), 123-154. https://doi.org/10.3970/cmes.2012.084.123
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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.Keywords
JFNK, multiphysics, solid mechanics, fully implicit, finite element, nonlinear solvers
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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
Copyright © 2012 The Author(s). Published by Tech Science Press.This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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