A data structure for finite element method

Nonzero elements compressed storage is a key technique for dealing with super-large sparse matrices in finite element(FE) analysis, and a proper data structure helps to improve the computation efficiency significantly. A new algorithm for nonzero elements storage is presented based on the fact that the sides of the FE elements are one-to-one corresponding to the nonzero elements of the global FE matrix, consequently, the side information can be used for indexing the nonzero elements in the compressed vector. Since the position of each element in the compressed vector is predefined in the meshing procedure, the assembly and the compression storage of the global matrix, along with the application of the boundary conditions, can be directly done in the element analysis progress, with no need of cumbersome addressing operations. The sparse matrix-vector multiplication can also be calculated fast and conveniently. Data structure and algorithm is discussed in detail, and the effectiveness of the method is validated through a FEM analysis of an eddy current testing problem. The presented method, promising a significant reduction of the memory as well as the CPU time requirements, is suitable for FE analysis of high-dimensional problems and of high-order elements. ©, 2015, Chinese Machine Press. All right reserved.