Research On Sparse Problem Storage And Scheduling Of High Performance Computers

Many modern scientific computing problems can be described as a set of partial differential equations.Using the discretization technique to transform solving the partial differential equations into solving the sparse linear equations is the most common method to solve these problems currently.As the high-performance computer plays an increasingly important role in many scientific fields,low computational resource utilization and the high communication overhead of parallel programs become fatal to the overall performance.Therefore,finding the solutions to the problems of parallel communication overhead and processor efficiency would be crucial to improving the performance of these parallel programs running on high performance computer,in order to develop exascale supercomputer with multi-core processors,complex topologies and storage hierarchies.In this paper,we improve the scientific applications performance mainly by utilizing the vectorization optimization of sparse matrix vector multiplication and modifying the resource scheduling strategies of exascale supercomputer.Sparse matrix vector multiplication(Sp MV)is a kernel function which is indispensable for solving problems in many applications.However,the performance of Sp MV is severely limited by its frequent memory access operations.Modern processors implement data-level parallel to improve performance by using single instruction multiple data(SIMD).In order to make full use of SIMD acceleration technology,we propose a new storage format called vectorized variable-dimensional block sparse matrix storage format(VBSF)to change the irregular memory access of traditional matrix storage format.This format combines adjacent non-zero elements into variable-sized blocks using two criteria to ensure that Sp MV can be calculated making use of SIMD vector units.We compare VBSF-based Sp MV with traditional storage formats and use 15 matrices as benchmark matrices on three computing platforms(FT2000,Intel Xeon E5 and Intel Silver)with different SIMD-unit lengths.For the matrices in the benchmark set,VBSF achieved good performance improvements on three platforms and it has better storage efficiency than others.Nowadays,accelerators are generally used for better performance,heterogeneous computing system provides some new opportunities for improving the scientific computing performance.We tentatively proposed a sparse matrix storage format selection model by using machine learning in order to reach the potential of heterogeneous system.While with the rapid increase in application size and the complexity of supercomputer architectures,the importance of topology mapping algorithm optimization is increasing.High communication overhead has become a major limit factor of hindering the performance improvement of applications running on supercomputers.In order to avoid that the improper mapping strategy may lead to poor communication performance,we propose an optimized heuristic topology-aware mapping algorithm OHTMA.This algorithm minimizes the hop-byte metric used to measure the topology mapping results.OHTMA combines a heuristic approach with a pair-exchange based optimization method to reduce the number of remote and large-scale communications to effectively enhance communication locality.The experimental results of the Tianhe-3 Exascale Prototype show that the OHTMA algorithm can relieve the communication bottleneck efficiently.