摘要
系统研究了高阶矢量有限元方法中的稀疏矩阵存储、重排序和快速求解技术。针对有限元(FEM)矩阵稀疏的特点,验证了高阶矢量有限元矩阵具有随机稀疏结构的特点,并采用合适的变带宽存储技术实现了FEM矩阵的高效稀疏存储。针对有限元矩阵非零元素分布不规则的缺点,采用RCM技术对矩阵元素进行重排序,从而压缩了矩阵带宽。研究了基于稀疏矩阵技术的(直接法、迭代法)快速求解和预处理技术。数值结果验证了稀疏技术极好的计算性能。
Sparse matrix storage,reordering schemes and fast solution technology in higher order vector FEM are researched systematically.Based on the fact that FEM matrix is sparse,the higher order vector FEM matrix is validated to have a random sparse structure,which is more efficient in storage in the case of varying bandwidth.Then,the bandwidth of the global matrix is reduced by RCM reordering technology.And some fast（direct,iterative） solution and preconditioned methods based on sparse technology are studied.Numerical results demonstrate the efficiency of the sparse technology.
出处
《微波学报》
CSCD
北大核心
2011年第2期13-18,28,共7页
Journal of Microwaves
关键词
有限元方法
高阶矢量元
稀疏矩阵技术
finite element method（FEM）
higher order vector element
sparse matrix technology
