土体-结构非线性耦合系统动力响应并行计算方法研究

A study on parallel computing methods for dynamic response analysis of soil-structurenonlinear interaction systems

针对土体-结构非线性耦合(Soil-Structure Interaction,SSI)系统动力响应数值模拟带来的大规模计算量问题,提出基于SSI负载均衡及对偶图理论两种区域分解算法的并行计算方法。结合传统的贪婪法及递归坐标对分方法,对这四种方法的并行性能进行研究。SSI采用基于对称罚函数的方法处理,系统方程采用显式中心差分有限元方法求解。对典型的SSI工程问题动力响应进行并行数值模拟,并对这四种方法的可扩展性进行分析。结果表明:基于SSI负载均衡的并行计算方法,充分考虑土体和结构耦合负载的均衡,并行效率最优,基于对偶图理论区域分解的方法和递归坐标对分方法效率次之,贪婪法并行效率最低;随核数增加,并行效率下降,需根据实际模型规模合理选择并行计算核数,获得最优的并行计算效益;基于罚函数的显式有限元方法能够较好的解决SSI动力响应问题。

In order to solve the problem of massive amount of computation brought by the numerical dynamic response simulation of soil-structure nonlinear interaction（ SSI） systems,a parallel computing method using SSI load balanced and dual-graph theory based domain decomposition（ DD） algorithm was proposed. Combined with the traditional greedy and recursive coordinate bisection algorithm,the parallel performance of four algorithms was investigated. The SSI was dealt with the symmetric penalty method. The system equation was solved using the finite element method（ FEM）with an explicit central difference scheme. The dynamic responses of typical engineering problems with SSI were simulated in parallel,and the scalability of the four algorithms was analyzed. The results indicate that the SSI load balanced algorithm which substantially balances the coupling loads of soil and structure shows the best parallel efficiency,followed by the dual-graph theory based algorithm and the recursive coordinate bisection algorithm. The greedy method has the lowest parallel efficiency. The parallel efficiency decreases with the number of cores,and the number of cores should be chosen properly according to the scale of the actual model to achieve the optimal parallel performance. The explicit FEM with the penalty method is a proper approach for SSI dynamic analysis.