Method optimizing sparse matrix vector multiplication to improve incompressible pipe flow simulation efficiency

Abstract

The invention discloses a method optimizing sparse matrix vector multiplication to improve incompressible pipe flow simulation efficiency. The method uses a QCST storage structure to combine with the advantages of a quadtree structure and a CSR storage structure to operate recursion decomposition and rearrangement to a sparse matrix to realize the storage of the sparse matrix, so that the sparse matrix vector multiplication operating process has the universality to the matrix form, particularly is suitable for the matrix with the whole being sparse and the local part being provided with a plurality of dense sub-matrixes. The method realizes the sparse matrix vector multiplication based on the QCSR storage structure through four strategies of thread mapping optimization, data storage optimization, data transmission optimization and data reusing optimization in a CPU / GPU (central processing unit / graphics processing unit) heterogeneous parallel system. The method has the advantages that the data locality and the cache hit rate in the sparse matrix vector multiplication value calculating process are improved, and the better calculating acceleration and the whole acceleration effect are obtained, so that the incompressible pipe flow simulation efficiency is improved.

Description

technical field [0001] The invention belongs to numerical simulation of fluid mechanics, in particular to a method for optimizing sparse matrix-vector multiplication to improve the efficiency of incompressible pipe flow simulation. Background technique [0002] The problem of incompressible pipe flow is an important research object of fluid mechanics, and the research results have been widely used in scientific research and industrial technology in related fields such as plasma physics, magnetohydrodynamics and astrophysics. With the development of computer science and technology, the incompressible pipe flow problem that can only be solved through field tests can be solved by computer numerical simulation methods. Simulation of incompressible pipe flow requires solving a large system of linear equations, namely Ax=b form( A as a matrix, x, b is a vector), while solving the matrix of the system of equations A It is often a sparse matrix, where the number of non-zero ele...

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Problems solved by technology

[0004] These methods are greatly affected by the distribution characteristics of the non-zero elements of the matrix and are not general

For matrices that are generally sparse but have many dense sub-matrix characteristics locally, the sparse matrix-vector multiplication operation based on the traditional sparse matrix storage format has poor spatial and temporal locality, and the optimization for this will also introduce additional overhead, which is incompressible The simulation efficiency of pipe flow still needs to be improved

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