一种针对大波数Helmholtz方程的高性能并行预条件迭代求解算法

针对传统串行迭代法求解大波数Helmholtz方程存在效率低下且受限于单机内存的问题,提出了一种基于消息传递接口(Message Passing Interface,MPI) 的并行预条件迭代法。该算法利用复移位拉普拉斯算子对Helmholtz方程进行预条件处理,联合稳定双共轭梯度法和基于矩阵的多重网格法来求解预条件方程离散后的大规模线性系统,在Linux集群系统上基于 MPI环境实现了求解算法的并行计算,重点解决了多重网格的并行划分、信息传递和多重网格组件的构建问题。数值实验表明,对于大波数问题,提出的算法具有良好的并行加速比,相较于串行算法极大地提高了计算效率。

High-performance Parallel Preconditioned Iterative Solver for Helmholtz Equation with Large Wavenumbers

For solving the Helmholtz equation with a large wavenumber,the traditional sequential iterative solver is inefficient and limited to the memory of a single computer.To deal with these problems,a parallel preconditioned iterative solver was proposed based on the message passing interface(MPI).The complex shifted-Laplacian is used to precondition the Helmholtz equation,and the Krylov subspace method Bi-CGSTAB combined with the matrix-based multigrid method is employed to solve the large linear system resulted from discretization of the preconditioned equation.Paral-lelization of the preconditioned solver is achieved under the environment of MPI on the Linux cluster system,and the problems of parallel partition of the multigrid,information transfer and construction of the multigrid components are mainly tackled.Finally,numerical experiments were given.The results show that the proposed method contributes to an excellent parallel speedup,and improves the computing efficiency considerably compared with the sequential iterative solver.