Parallel analysis method of structural nonlinear seismic response based on Woodbury + OpenMP

Nonlinear seismic response analysis becomes an important technical means to evaluate aseismic performance of engineering structures. With increase in structure size, large-scale stiffness matrix iterative updating induced by nonlinearity becomes a key factor to restrict efficiency of structural analysis. Woodbury formula-based nonlinear seismic response analysis method for structures, i. e., Woodbury method, is a new type efficient numerical analysis method. Using local nonlinear characteristics of structure under seismic action, this method can not only ensure higher iterative convergence rate and but also effectively avoid real-time change of structural stiffness matrix and the resulting low computational efficiency. However, the current studies are based on serial computing mode and don' t make full use of parallel computing capabilities of computation hardware. Here, OpenMP mode was introduced to accelerate Woodbury method in parallel, a parallel calculation method for efficient nonlinear seismic response analysis of structures was proposed. Firstly, each iteration calculation step was divided into 3 main calculation parts of updating nonlinear correlation coefficient matrix calculation, solving displacement response based on Woodbury formula, and determining element state. Then, a block calculation method of nonlinear correlation coefficient matrix was established, the calculation process of Woodbury formula was decomposed into 6 parallelizable calculation steps, and each element state was determined separately, OpenMP parallel acceleration strategies suitable for these 3 things were established, respectively to realize parallel optimization for the proposed method's whole process. Finally, the correctness and efficiency of the proposed method were verified with seismic response analysis of a high-rise structure. © 2023 Chinese Vibration Engineering Society. All rights reserved.