Study On Parallel Alogrithm Of Large-scale Numerical Calculation In Cloud Computing Environment

Cloud computing is emerging as a novel computing paradigm. Based on virtualization technology, cloud computing provides enormous computation and storage resources for users via the network. Nowadays, high performance computer(HPC) on CPU/GPU heterogeneous systems can solve large-scale engineering problems effectively, but it is quite professional and the computational cost is high. On the contrary, cloud centers, which provide high-quality computing and storage by integrating a large-scale of general machines, cost lower. With new programming models, data structures and friendly programming interfaces, the program can simply run auto-parallelization. As the scale of engineering problems is increasing all the time, the practical value of large-scale numerical calculation is particularly obvious. Its implementation based on cloud computing is a rather important exploration.Firstly, based on Hadoop MapReduce architectural pattern, this paper presented a parallel domain decomposition finite difference time domain(DD-FDTD) algorithm. The algorithm was implemented on a 6-nodes Hadoop+Spark laboratory test cloud computing cluster to compute the electromagnetic fields of lightning occurring in the downtown area in Shanghai city, PR China. The speedup ratios under different numbers of computational subdomains were evaluated. It shows that the speedup ratio increases with the scale of the mesh model and the nodes of the cluster, and the maximum on our cluster is about 2.4.Secondly, based on the MapReduce architectural pattern, this paper proposed parallel algorithms of assembling global stiffness matrix of linear elastic finite element method(FEM) and solving linear equations using conjugate gradient(CG) method. And they were implemented on a Hadoop+Spark cluster. For the spatial truss systems, the numerical results show that it is simple and easy to implement the FEM calculation by the parallel algorithms. At the stage of assembling global stiffness matrix, the efficiency becomes better as the size of the model and the number of cluster's nodes increase. However, the efficiency of solving linear equations is limited and should be improved in the future.Finally, in order to realize iterative algorithm on cloud platform efficiently, this paper proposed a large-scale finite-element parallel algorithm based on the Resilient Distributed Datasets on the Spark platform. The proposed algorithm was then verified using the space truss model on a 6-nodes Hadoop+Spark platform. Comparisons were conducted between the performance of Spark-based and Hadoop-based algorithms of linear elastic FEM.The results indicate that the DOFs of space truss problem can be solved by the Spark-based parallel algorithm are 15000000, which are much more than that solved by the Hadoop-based parallel algorithm. Obviously, the Spark-based parallel algorithm is preferable. Moreover, the proposed algorithm exhibits an enhanced computing-efficiency compared with the Hadoop-based parallel algorithm. Specifically, for asmall-scale space truss model, the speed-up ratios reach up to 200, while for a large-scale space truss model, it is approximately 7 or 8.