Implicit-explicit (IMEX) time integration schemes are well suited for nonlinear structural dynamics because of their low computational cost and high accuracy. However, stability of IMEX schemes cannot be guaranteed for general nonlinear problems. In this article, we present a scalar auxiliary variable (SAV) stabilization of high-order IMEX time integration schemes that leads to unconditional stability. The proposed IMEX-BDFk-SAV schemes treat linear terms implicitly using kth-order backward difference formulas (BDFk) and nonlinear terms explicitly. This eliminates the need for iterations in nonlinear problems and leads to low computational cost. Truncation error analysis of the proposed IMEX-BDFk-SAV schemes confirms that up to kth-order accuracy can be achieved and this is verified through a series of convergence tests. Unlike existing SAV schemes for first-order ordinary differential equations (ODEs), we introduce a novel SAV for the proposed schemes that allows direct solution of the second-order ODEs without transforming them to a system of first-order ODEs. Finally, we demonstrate the performance of the proposed schemes by solving several nonlinear problems in structural dynamics and show that the proposed schemes can achieve high accuracy at a low computational cost while maintaining unconditional stability.
Efficient schemes with unconditionally energy stability for the anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented Variable (S-SAV) approach
A class of new linear, efficient and high-order implicit-explicit methods for the coupled free flow-porous media system based on nonlinear Lions interface condition
Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization
The Center for Subsurface Modeling, The Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校计算工程与科学研究所地下建模中心）
Pointwise Monotonicity of the Allen--Cahn Flow and Dynamical Limitations of Energy-Stable Schemes
Hunan Research Center of the Basic Discipline Fundamental Algorithmic Theory and Novel Computational Methods, National Center for Applied Mathematics in Hunan, School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院，湖南省应用数学中心，基础学科基本算法理论与新型计算方法湖南研究中心）
