Abstract: Generalized minimal residual method (GMRES) is the most commonly used method for solving asymmetric large-scale linear algebraic equations,and it has fast convergence and stable property.Intel many integrated co-processors (MIC) has strong computing power and it can program easily.In this paper,MPI+OpenMP+offload hybrid programming paradigm was used to port GMRES algorithm to the MIC heterogeneous cluster platform.The perfor-mance of GMRES parallel algorithm was greatly improved by using kinds of optimization methods,such as hiding collective communications using asynchronous execution model,vectorization optimization,data transfer optimization,extensibility of MIC thread optimization,etc.Finally,GMRES parallel algorithm was used to improve the perfomance of solving high dimensional PDEs by the localized radical basis functions (RBFs) collocation methods.Results from tests indicate that the parallel efficiency can be up to 71.74% when using 32 processes in cluster,and the maximum speedup ratio of 4 MICs to 1 CPU can be up to 7.

Key words: GMRES,MIC,MPI,Large-scale linear algebraic equations