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14-02 A fast nonlinear conjugate gradient based method for 3 D frictional contact problems

This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, and use azimuth angles as variables, instead of conventional traction variables. A corresponding preconditioner using diagonal scaling is incorporated. The fast Fourier transform (FFT) technique accelerates all matrix-vector products encountered, due to a Toeplitz structure. Numerical tests show that this method is robust and it significantly reduces the computational time, compared to existing solvers.