Analysis of parallel Krylov subspace method for three-dimensional heat equation
三维热传导方程的Krylov子空间方法并行分析

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.