Large-scale sparse symmetric linear equation set parallel processing method based on elimination tree

Abstract

The invention discloses a large-scale sparse symmetric linear equation set parallel processing method based on an elimination tree. The method comprises the following steps: step 1, conducting LU decomposition on an A matrix; step 2, carrying out forward and backward substitution, calculating Ly = b, solving y, then Ux = y, and solving x; adopting a double-task division method based on the elimination tree to carry out forward and backward substitution; step 3: carrying out X array recombination, which comprises: recombining an X array to enable data required by single thread calculation to belocated in a continuous space in a memory; and step 4, performing circular combination, and performing circular combination of division operation, X array recombination and the like into a forward and backward substitution process to reduce circular iteration overhead and OpenMP thread creation overhead. According to the method, parallel computing is carried out through the double task division method based on the elimination tree, multi-core computing resources are fully utilized, and the forward and backward substitution speed of the large-scale sparse matrix is remarkably increased.

Description

technical field [0001] The invention relates to the field of data processing using computing equipment, in particular to a large-scale sparse symmetric linear equation group parallel processing method based on elimination trees. Background technique [0002] The algorithm for solving large sparse matrices is a relatively complex algorithm with relatively high requirements for computing resources, both for computing time and memory space. Due to the rapid development of the computer industry, the amount of data has increased rapidly, and the process of matrix solving often involves huge data arrays and large-scale data operations, which puts forward higher requirements for the efficiency of large sparse matrix algorithms. Ordinary computers can no longer bear the amount of single-time data processing calculations, and general-purpose serial processing can no longer meet the increasing data volume and the requirements for fast real-time processing and operation of data. [00...

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Problems solved by technology

[0008] 2. Large-scale sparse linear equations of general types cannot be parallelized, and the scope of application is limited

[0009] Existing technical solutions can only parallelize some special large sparse matrices, such as Yang Jianlin (2011) deriving the block diagonal plus edge form (BBDF), and Xiaofang Wang mentioned in Parallel Direct Solution of LinearEquations on FPGA-Based Machines Specially for the parallelism of large sparse linear equations whose coefficient matrix is ​​BDB matrix, it is all parallelism for special coefficient matrices, but it is powerless for general coefficient matrices

[0010] 3. It does not consider that if there are constant items that change, but the matrix is ​​almost constant

However, the existing algorithm does not perform parallel optimization of the algorithm when the constant term is variable and the matrix remains unchanged.

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