Research And Implementation Of Krylov Subspace Algorithm Based On CPU And GPU

In field of scientific computation and engineering, by discretization computation problemoften changed to large-scale sparse linear equations. The solution of linear equation usuallyoccupies a large part time of the entire calculation, in field of petroleum reservoir simulation,the ratio is close to eighty percent. So to solve large-scale sparse linear equations quickly andefficiently becomes the key to the solution of the problem. Krylov subspace algorithm is aclassical iterative algorithm, with the advantages of a small amount of storage andeasy-to-parallel, etc. So it has always been used as an important method to solve sparse linearequations.Orthodir(m) algorithm is one of Krylov subspace algorithms. Every step of the iterativecalculation of the algorithm requires two vector inner product computations and they are datacorrelated. On distributed memory parallel computer, the calculation of vector inner productneeds overall communication and overhead of the communication is tremendous. This paperrefers to the design method in literature[forty-five] and proposed an improved algorithm(IOrthodir(m) algorithm). Under the condition of correctness, by changing the iterative steporder of Orthodir(m) algorithm, IOrthodir(m) algorithm changed two separated vector innerproducts into several continuous vector inner products, global synchronization point reducedfrom two to one and global communication overhead significantly reduced. Theory analysisshows that IOrthodir(m) algorithm’s scalability is better than Orthodir(m) algorithm’s. Whenthe number of processors meets certain requirement, IOrthodir(m) is faster than Orthodir(m).Numerical experiments on sixteen sets of Dawning Cluster show that IOrthodir (m) algorithmis better than Orthodir (m) algorithm. Based on MPI and OpenMP mixed programming model,the two algorithms are realized and the experimental data show that IOrthodir (m) algorithm isalso superior to Orthodir (m) algorithm in different multi-core platform.According to the calculation time of the improved algorithm produced by matrix-vectormultiplication and vector inner product, proposed a CPU-GPU collaborative computingstrategy and allocated computational task. Experiment of collaborative solving on platform ofCPU-GPU indicates that with respect to CPU, GPU-CPU heterogeneous model can betterimprove the computational efficiency.