Edge-based Matrix Storage Technology In Finite Element Method And Its Application To High-performance Computation Of Geotechnical Engineering Problems

The solution of large linear equations is one of the core techniques for finite element calculation of geotechnical engineering.When using iterative techniques to solve linear equations,the part with the largest computational time overhead is matrix vector multiplication,so how to improve the computational efficiency of matrix vector multiplication is crucial to improve the solution of large linear equations.In this paper,two main aspects of matrix vector multiplication,matrix storage format and computing platform,are studied,and the effects of storage format and parallelization on solving efficiency are compared through numerical experiments.The main research contents and conclusions of this paper are as follows:(1)Anew method for generating edge stiffness matrix is proposed,which is called direct edge matrix generation method(DEMG).By testing different grid types,it is found that this method can improve the performance of triangular and tetrahedral elements by about 20%compared with the existing method.(2)According to the basic principle of edge-based data structure(EDS),assemble the repeated edges by introducing the idea of quick sort,realize the storage of edge-based finite element stiffness matrix and the solution of linear equations.(3)The effects of element types and storage formats on the computational efficiency of finite element programs in single-threaded,multi-threaded parallel and GPU-CPU hybrid architectures were tested.The test results show that EDS storage format has obvious advantages in terms of memory occupation,but its solution efficiency fails to reach the theoretical optimal state due to many indirect addressing operations.In terms of element type selection,the performance of the EDS storage format is strongly dependent on the element type.It is recommended to use the EDS storage format in combination with the tetrahedral mesh to obtain the best computing performance.By studying the EDS storage technology,comparing it with the existing element-by-element(EBE)storage technology and the compressed sparse row/column(CSR/CSC)storage technology on different platforms,this paper gives corresponding suggestions on how to select the storage format in different computing frameworks and different element types,so as to provide references for the subsequent research.