一种求解二维Helmholtz方程的并行高精度算法

A PARALLEL HIGH-ORDER ACCURACY ALGORITHM FOR SOLVING THE TWO-DIMENSIONAL HELMHOLTZ EQUATION

本文采用混合型紧致有限差分方法建立了一种新的求解二维Helmholtz方程的高精度混合型紧致有限差分格式。针对串行算法在求解大波数Helmholtz方程时效率低下的问题,我们在Linux集群系统上基于MPI环境提出了并行高阶混合型紧致有限差分算法.截断误差分析表明本文构造的格式具有六阶精度.数值实验结果表明,本文提出的方法在处理变波数和大波数Helmholtz方程问题时均能达到理论上的六阶精度.此外,本文设计的并行算法展现出良好的并行加速比,能够有效提高计算效率.

In this paper,a new high-order accuracy hybrid compact finite-difference scheme for solving the two-dimensional Helmholtz equation is developed using a hybrid compact finitedifference methods.To address the inefficiency of serial algorithm in solving the Helmholtz equation with large wave numbers,we propose a parallel high-order hybrid compact finitedifference algorithm based on the MPI environment on Linux cluster systems.Truncation error analysis shows that the proposed scheme has sixth-order accuracy.Numerical experimental results show that the proposed method can achieve the theoretical sixth-order accuracy in solving Helmholtz equation problems with variable wave numbers and large wave numbers.In addition,the parallel algorithm designed in this paper exhibits good parallel speedup,which can effectively improve computational efficiency.