A global secant relaxation (GSR) method-based predictor-corrector procedure for the iterative solution of finite element systems

In this paper, an iterative procedure based on improving the diagonal stiffness prediction is used to solve general finite element systems. The procedure consists of a predictor and a corrector, for each iteration step, iteratively obtaining the converged solution. The diagonal stiffness prediction works to predict an incremental response vector for the discrete algebraic system, while the global secant relaxation (GSR) technique works as a corrector, in which a scaling factor is used to adjust the incremental response vector. Drastic reduction of the computer memory requirement can be expected by adopting the diagonal stiffness prediction, and the numerical stability and convergence rate can be improved significantly through the introduction of GSR correction. An efficient and reliable scaling factor is used with which a higher order convergence rate can be expected for the iterative computation.