An optimized three-sub-step composite time integration method with controllable numerical dissipation. (15th April 2020) - Ji, Yi; Xing, Yufeng
Highlights: An optimized three-sub-step composite method with controllable dissipation is proposed. The proposed method has second-order accuracy and unconditional stability. The amount of dissipation can be controlled smoothly and accurately by ρ ∞ . The proposed method is more accurate than other composite methods with controllable dissipation. Abstract: This paper proposes an optimized three-sub-step composite time integration methods with controllable numerical dissipation, called the ρ ∞ -Optimal-Trapezoidal-Trapezoidal-Backward-Interpolation-Formula ( ρ ∞ -OTTBIF) method. In this method, a novel Newmark-like method or four-point backward interpolation formula is employed in the third sub-step, instead of the four-point Euler backward difference method as in the Optimal-Trapezoidal-Trapezoidal-Backward-Difference-Formula (OTTBDF) method which was proposed by the present authors and co-workers. The proposed method has second-order accuracy, unconditional stability and controllable numerical dissipation, and the spectral radius ρ ∞ serves as a parameter controlling the degree of numerical dissipation. In addition, the properties of the ρ ∞ -OTTBIF method can reduce to those of the OTTBDF method when ρ ∞ =0. Since the low-frequency accuracy is maximized in construction, the proposed method has higher low-frequency accuracy than other methods with controllable numerical dissipation. Linear and nonlinear numerical simulations are conducted to check the advantages of the proposed method over other similar time integration methods.