结构动力响应精细时程法的一种并行算法

A parallel algorithm of high precision direct integration method for structural dynamic response

结构动力响应精细时程法的并行算法分为两类:基于特解的并行算法和基于直接积分法的并行算法;后者因为不需知道荷载的具体形式而更具应用价值。精细时程法的时程积分由齐次方程的通解和非齐次项的积分构成,基于直接积分法的并行算法很好地并行了非齐次项的积分,而对通解项采用串行计算。设计了一种不均衡步数的负载分配策略,能够减少处理器等待自身初值的时间,相对均衡步数的分配策略,能够获得更高的加速比,给出了相应的证明和算例验证。

The parallel algorithms of high precision direct integration methods for structural dynamic responses could be divided into two classes. They were the parallel algorithm based on the particular solution of equations and the direct integration method. The latter could be applied widely because it didn＇t need the analytic expression of the force vector. The solution consisted of the general solution of homogeneous equations and the integration of the nonhomogeneous term. The integration of the nonhomogeneous term was effectively paralleled by the parallel algorithm based on the direct integration method. But the general solution was calculated in series. A new load distributed strategy was designed and the unbalanced distribution of time steps was implemented. The strategy can decrease the waiting time of the initial value and obtains better speedups than the strategy based on the balanced distribution of time steps. The corresponding proof and a numerical example were given.