Research On Parallel Solving Of Large Scale Sparse Linear Systems

Currently,the solution of large-scale sparse linear systems is an important part of many scientific computing and engineering techniques.In some sparse linear system solving tasks based on direct method,the calculation of linear trigonometric system is the core link for solving large-scale sparse linear systems.Therefore,the rapid solution of the sparse linear triangulation system becomes the key to solving the scientific calculation problem.In recent years,as the scale and complexity of scientific computing problems have increased,the size and complexity of sparse linear triangulation systems are also growing,resulting in a sudden increase in the amount of data that needs to be processed.However,the existing methods are limited by the traditional view of linear trigonometric system solving,that is,the solution of a certain variable must wait until all its precursor variables have been solved.This approach not only limits the degree of parallelism that can be achieved when solving,and does not take advantage of the rich parallel hardware resources of many-core processors.Moreover,frequent data transfer between threads makes synchronization overhead larger,even offsets the advantages brought by parallel computing technology.In order to solve the problems in the existing methods,this thesis proposes a parallel algorithm based on partial value addition.The method first calculates the partial values of the variables in parallel,and then adds all the partial values of the variables to get the final values.Since the variables are calculated without waiting for all the predecessor variables to complete the calculation,the parallelism and calculation speed are greatly improved.In the work,the parallel solving algorithm is implemented based on the CUDA computing platform.The algorithm decomposes the association graph representing the order of the variables into multiple subgraphs.Each thread calculates a layer of subgraphs,making full use of the GPU's rich parallel computing resources.Second,in order to reduce the impact of memory access on the performance of the algorithm,make full use of the large global memory capacity and low shared memory latency,the parallel algorithm proposed in this thesis is optimized.The experimental results show that compared with the calculation time of the cuSPARES library and the non-synchronous parallel algorithm,the calculation speed of the parallel algorithm is increased by 80% on average,the maximum increase is 99%.Under the premise of ensuring the calculation accuracy,the solution speed of the sparse linear triangulation system is greatly improved.