基于边界元法的弹性动力问题并行求解

Parallel Algorithms to Solve Elasto-dynamic Problem Based on Boundary Element Method

为了扩大结构弹性动力分析的规模和提高分析速度,在微机机群环境下给出了两种基于边界元法的瞬态问题并行求解算法,即并行拉普拉斯变换求解算法和并行时域求解算法。并行拉氏变换法通过拉氏变换隐去时间变量,由各结点机独立求解各自负责的变换边界元问题。并行时域法采用与时间有关的基本解,使得边界元系统矩阵可以实现时间域上的并行形成。系数矩阵采用卷帘存储,以保持负载平衡。通过矩阵向量运算的并行化实现时间步进算法的并行化。理论分析和数值试验结果表明:两种算法都具有较好的并行性能,可以用于大型问题的高效求解。

To enlarge the analytical scale and increase the analytical rate of structural elasto-dynamic problem, two parallel algorithms on PC cluster to solve elasto-dynamic transient problem are presented based on Boundary Element Method (BEM), which are parallel Laplace transform algorithm and parallel time domain algorithm. In the parallel transform algorithm, the time variable is eliminated by Laplace transform. The serials of transformed boundary element problems are parallel computed independently on the nodes respectively belonging to. Introducing the time related fundamental solution, the time dependency is released from the formation of time-domain BE equations. The wrap storage of equations is used to balance the computing load. The time stepping method is parallelized by distributed parallelization of the matrix and vector computation. The theoretical analyses and numerical experiments show the good parallel performance for solving large-scale problems.