Solution And Application Of Sparse Linear System Based On GPU

Many scientific and engineering computational and numerical calculating problems have been changed into sparse linear equation. Recently, the most common and useful method to solve a large sparse linear system is to use Krylov subspaces which is based on projection processes. However, it will spend a large amount of time in calculating sparse linear equation on CPU, while on GPU, it will speed up the computation.Smoothed Particle Hydrodynamics (SPH), which is a kind of meshfree particle method, can easily handle the problems with great deformation. Incompressible SPH (ISPH) has many advantages such as accuracy and efficiency in calculating the pressure value and thus was applied to imitate free surface wave, multiphase flow, complex3D model etc.. The pressure equation within ISPH is a typical sparse linear equation. Since it relates to global particles’ pressures, solving the equation consumes a large amount of time and it occupies a most of time in ISPH algorithm.It will spend a large amount of time in calculating sparse linear equation on CPU, while on GPU, it will speed up the computation. Also, It adopts sparse linear equation on GPU to calculate pressure equations in ISPH and using the GPU’s strong parallel ability to speed up the calculation in ISPH.The main works of this thesis are listed below:(1) The problems in calculating sparse linear equations are discussed. Storage style of linear matrix is introduced. Realization of vector to add and subtract, inner product and sparse matrix-vector multiplication on CUDA are analyzed. Finally, the detailed scheme in calculating sparse linear equations on the basis of CUDA is given.(2) As the utilizing of GPU’s structural characteristics, the calculating in sparse matrix linear equations are optimized. It mainly rationalizes the distributions of the thread and the program structures between CPU and GPU, enhances the fetch efficiency of sharing storage, speed up the visit of partial data space with texture memory and optimizes register and global memory.(3) With C++design, the Fortran3D model of single screw extruder based on ISPH is realized. At the same time, with the calculating method in sparse matrix linear equations on GPU, the pressure equations of ISPH are calculated. The experimental results show that under the functions of calculating in linear equations on GPU, the system is obviously better than on CPU.