An optimized three-sub-step composite time integration method with controllable numerical dissipation

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.