CAJ | 학술논문

热传导方程在地下水流动数值模拟、油藏数值模拟等工程计算中有着广泛应用,其并行实现是加速问题求解速度、提高问题求解规模的重要手段,因此热传导方程的并行求解具有重要意义.对Krylov子空间方法中的CG和GMRES算法进行并行分析,并对不同的预处理CG算法作了比较.在Linux集群系统上,以三维热传导模型为例进行了数值实验.实验结果表明,CG算法比GMRES算法更适合建立三维热传导模型的并行求解.此外,CG算法与BJACOBI预条件子的整合在求解该热传导模型时,其并行程序具有良好的加速比和效率.因此,采用BJACOBI预处理技术的CG算法是一种较好的求解三维热传导模型的并行方案.
열전도방정재지하수류동수치모의、유장수치모의등공정계산중유착엄범응용,기병행실현시가속문제구해속도、제고문제구해규모적중요수단,인차열전도방정적병행구해구유중요의의.대Krylov자공간방법중적CG화GMRES산법진행병행분석,병대불동적예처리CG산법작료비교.재Linux집군계통상,이삼유열전도모형위례진행료수치실험.실험결과표명,CG산법비GMRES산법경괄합건립삼유열전도모형적병행구해.차외,CG산법여BJACOBI예조건자적정합재구해해열전도모형시,기병행정서구유량호적가속비화효솔.인차,채용BJACOBI예처리기술적CG산법시일충교호적구해삼유열전도모형적병행방안.
Heat equation has been widely used in engineering, such as numerical simulation of groundwater flow, reservoir simulation and so on. The parallelism of heat equation is an important means of accelerating the simulation process and enhancing the modeling capabilities. This paper analyzed the parallelism of GMRES and CG algorithm included in Krylov subspace method, made a comparison with different preconditioned conjugate gradient methods. Numerical experiments on the three-dimensional heat equation were carried out on Linux clusters. The numerical results demonstrate that CG algorithm is more suitable than the GMRES algorithm for parallelizing the three-dimensional heat equation. The parallel program has a desirable speedup and efficiency when use CG algorithm integrating with BJACOBI preconditioner to solve the three-dimensional heat equation. So a better parallel solution to the three-dimensional heat equation is CG algorithm integrating with BJACOBI preconditioner.