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大型结构动力响应问题采用传统的时间步长直接积分方法求解是非常耗时的，因此发展相应的并行计算方法成为必然．传统的直接积分方法是极度串行而不适于并行计算，而精细时程积分方法可以使用大步长单步计算出求解区间任意时间点的响应值，为并行计算提供了极大的可能性．结构动力响应方程通过变量变换可以转化为一阶线性常微分方程，该方程组的解由表示初值影响的齐次方程解和反映荷载作用的积分之和组成．其中第一项用矩阵指数函数计算；第二项在文中采用精细时程积分傅里叶展开方法计算（设计了３种相应的并行算法），并在ＴＲＡＮＳＰＵＴＥＲ并行机上实现．结果表明，３种ＨＰＤ－Ｆ并行算法有很高的加速比和并行效率．
It is very time-consuming to solve the dynamic response problem of large-scale structures using the traditional direct method of time-step integration. Therefore, it is inevitable to develop the corresponding parallel computing method. The traditional direct integration method is extremely serial and not suitable for parallel computing, while the fine time-integration method can use the large stride length step to calculate the response value of arbitrary time point interval, providing a great possibility for parallel computing. The structural dynamic response equation can be transformed into a first-order linear ordinary differential equation by variable transformation. The solution of the system consists of the solution of the homogeneous equation which represents the initial value and the integral which reflects the action of the load. The first one is calculated by the matrix exponential function. The second one is calculated by using the fine time-integrated Fourier expansion method (three corresponding parallel algorithms are designed) and implemented on the TRANSPUTER parallel machine. The results show that the three HPD-F parallel algorithms have high speedup and parallel efficiency.