基于区域分解和MPI的线性带状方程组归并迭代解法器

线性带状方程组并行解法器往往基于两层迭代的区域分解方法,采用M P I(m essage pass ing in terface)实现,因此导致的总迭代次数太多或者进程通信开销太大都会使解法器效率低下。该文通过研究减少迭代次数和降低进程通信开销的方法,设计了一种适合区域分解和M P I系统的高效的归并迭代并行解法器。这种解法器通过引入全局加速收敛算法,把两层迭代归并为一层迭代,有效减少了迭代求解的总次数,并且采用分块并行技术降低M P I系统上加速收敛算法的进程通信开销。实验证明归并迭代并行解法器能够保证和串行解法器大致相当的总迭代次数,分块并行加速收敛技术能够降低接近1/2的全局进程通信时间。

Iteration-merged solver for linear banded matrices based on domain decomposition and MPI

Parallel solvers for linear banded systems are often based on domain decomposition methods with two levels of iterations implemented with a message passing interface(MPI).However,excessive iterations,as well as excessive process communications, result in low parallel efficiency.This paper presents an efficient iterationmerged solver suitable for domain decomposition and MPI systems that minimizes the iterations and the process communications.A global acceleration algorithm merged two levels of iterations into one level to reduce the total number of iterations with a block-parallel technique to minimize the process communications on MPI systems caused by the global acceleration.Tests demonstrate that the parallel solver have the same number of iterations with the block-parallel technique reducing the process communication time for the global acceleration by half.