弹性波动方程数值解的有限元并行算法

Finite element parallel algorithm for numerical solution of elastic wave equation

在求解弹性波动方程中,有限元法的高内存量和巨大运算量的需求在基于单CPU串行算法中一直难于满足,制约其优势的发挥。根据有限元法的“化整为零、集零为整”的基本思想与并行处理技术的“分而治之”的原则基本一致,采用基于多CPU的并行算法,从有限元参数矩阵计算和线性方程组求解两个方面入手,把求解区域分到多个CPU上并行计算参数矩阵,对线性方程组采用循环块三对角线方程组进行并行求解。对比了不同大小空间和不同CPU个数下的加速比,证实了多CPU的并行算法能够克服基于单CPU串行算法的物理限制,满足了有限元法的巨大空间量和运算量的需求。此算法具有理论上的正确性和实践上的可行性。

The numerical solution of the elastic wave equation requires too much computer memory and calculation time to achieve by finite dement method based on single CPU（central processing unit）. The basic idea of finite element method is consistent with the basic principle of parallel algorithm. Based on multi-CPU paralld algorithm and carried out from matrix calculation of finite element and ,solution of linear equations, the solution region was located on many CPUs, and system linear equations were paralld solved by using circle block-tridiagonal equations, Through contrasting the speedup-ratios of different size of regions and different CPU numbers, it shows that the paralld algorithm on multi-CPU can overcome the limits of the single CPU on memory and calculation rate, and be .satisfied all requirements of the finite dement method in the calculation of the practical data processing. This algorithm has theoretical correctness and feasibility in practice.