用MATLAB实现波动方程多核并行计算

MATLAB solve wave equation on multi-core computer

波动方程数值模拟在油气勘探中发挥着重要作用,如何提高它的计算效率一直是人们研究的课题.目前多核计算机已非常普及,而现有程序基本都是采用MPI实现并行计算的.这种进程级粒度的并行计算方式在PC-Cluster之类的分布式计算机上效果很好,可是在单个节点上却受内存限制,往往只能使用少数几个甚至单个计算核心,多核处理器的效能难以得到有效发挥.本文基于MATLAB科学计算平台构建波动方程数值模拟算法,将占主要计算量的波场外推式计算分解为矩阵-向量乘法、向量对应元素相乘或相减运算,通过MEX文件机制,在MATLAB中引入了OpenMP多线程并行计算,解决了MPI进程级并行在内存使用受限的情况下,多核利用效率低的问题.在四核计算机上测试表明,右端项计算平均加速3.37倍,解对角线方程平均加速1.66倍,波场外推式的计算平均加速3.11倍,使正演计算的总体计算速度提高了近3倍,有效提高了计算效率.

Numerical simulation of wave equation played an important role in oil and gas exploration,and engineers always looked forward to seeking out more efficientalgorithms for it.Nowadays,multi-core computers had been very popular,and the most existing procedures were using MPI parallel programming.This process level granularity parallel calculation results in distributed computer such as PC-cluster is very good.However,on a single node,often only few or even a single core could be used by memory constraints. The multi-core processor＇s performance is difficult to effectively play.In this paper,a method of wave equation thread level parallel computation for MATLAB on multi-core computer was presented. According to the predominantcomputation was wavefieldextrapolation formula,and it was composed of matrixvector multiplication,vector-vector subtraction and vectorvector element-by-element multiplication,the wavefieldextrapolation formula was rewrited from MATLAB m-version to OpenMP multithread C mex-version.This resulted higher performance than MPI parallelism with limited memory. Numerical experiment indicated that this parallel algorithm could improve the computational efficiency significantly. On a quad-core computer,the speedup of solutiondiagonal equation was nearly1.66,the speedup of calculation right-hand term was up to 3.37.As a result,the speedup of wavefield extrapolationformula was up to 3.11,and theentire forward modeling accelerated nearly to 3times.