Solving Nonlinear Solid Mechanics Problems with the
Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston;  and M. R. Tonks

doi:10.3970/cmes.2012.084.123
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 84, No. 2, pp. 123-154, 2012
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Keywords JFNK, multiphysics, solid mechanics, fully implicit, finite element, nonlinear solvers
Abstract 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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