【摘要】 稀疏矩阵非零元素压缩存储技术是处理大型有限元方程的必要手段,采用合适的数据结构是提高计算效率的关键。本文提出一种基于单元边索引的非零元素压缩存储方案,这种方案利用了单元边与总体矩阵中非零元素之间的一一对应关系,概念清晰。由于每个元素在压缩向量中的位置在网格划分阶段就确定了,因此在单元分析过程中就可以直接完成总体系数阵的压缩存储和边界条件处理,无需繁冗的寻址计算,矩阵的求解运算也非常便捷,最大限度地减少了有限元分析的内存需求,提高了计算效率。文中对相应的数据结构和算法描述做了详细的讨论,并通过一个涡流检测问题的有限元算例验证了本文方法的有效性。该方案可以方便地推广用于三维有限元问题和高阶单元。更多还原

【Abstract】 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.更多还原