Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method

Journal Article · Fri Jun 01 04:00:00 EDT 2012 · CMES: Computer Modeling in Engineering & Sciences

OSTI ID:1045497

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

The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: DOE - NE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1045497
• Report Number(s): INL/JOU-11-22230
• Journal Information: CMES: Computer Modeling in Engineering & Sciences, Journal Name: CMES: Computer Modeling in Engineering & Sciences Journal Issue: 2 Vol. 84
• Country of Publication: United States
• Language: English

Related Subjects

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS
97 MATHEMATICS AND COMPUTING
COMPUTERS
FINITE ELEMENT METHOD
JFNK
STORAGE
finite element
fully implicit
multiphysics
nonlinear solvers
solid mechanics