COMPARATIVE ANALYSIS OF THE ITERATIVE ALGORITHMS FOR NONLINEAR METHOD BASED ON THE WOODBURY FORMULA

The elements of the stiffness matrix are often partially changed in the solution of local nonlinear problems, in which the tangent stiffness matrix can be written as the sum of the initial stiffness matrix and its low rank perturbation matrix so that the displacement response in each incremental step can be efficiently solved by the Woodbury formula that is used to calculate the inverse matrix in mathematics. However, the iterative calculation is often unavoidable in the structural nonlinear analysis, and the performance of the nonlinear iterative algorithm also has a great impact on the efficiency of the structural nonlinear analysis. This paper studies the iterative solution of the nonlinear method based on the Woodbury formula. The Newton-Raphson (N-R) method, the modified Newton method, the two-point method with three convergence order, the two-point method with four convergence order, and the three-point method, are chosen to solve the equilibrium equations of the nonlinear method based on the Woodbury formula, and the performance of these five iterative algorithms is compared. The time complexity analysis models of the five iterative algorithms solving the equilibrium equations of the nonlinear method based on the Woodbury formula are obtained, and the efficiency of the five algorithms is quantitatively compared. The calculation performance of the five iterative algorithms is compared through two cases from the perspective of convergence rate, time complexity and error; then the applicable nonlinear problems of the five algorithms are analyzed. Finally, the comprehensive performance index of the five iterative algorithms solving the equilibrium equations of the nonlinear method based on the Woodbury formula is calculated.