【摘要】 常规边界元法(boundary element method,BEM)因形成的方程矩阵稠密非对称而难以应用于大规模问题,BEM矩阵的存储限制了BEM的工程应用。该文介绍了递阶矩阵(hierarchical matrix,H-matrix)的基本概念,并引入了一种新颖的H-matrix压缩技术:自适应交叉逼近(adaptive cross approximation,ACA)。通过对普法BEM的节点根据拓扑结构重新分区和编号,可以将方程矩阵分解为若干具有递阶特性的子矩阵,应用自适应交叉逼近技术将这些子矩阵进行低秩分解可大大降低BEM矩阵对内存的消耗。为了对基于ACA技术的BEM内存消耗和有效性进行验证,建立了三维球形电极模型,通过与普通BEM比较,证实了该文方法可显著减小边界元法的内存使用,并验证了该方法的有效性。更多还原

【Abstract】 Since system matrix of classical boundary element method(BEM) is non-symmetrical and dense,classical BEM realizations are applicable only to a rather moderate problem.Fortunately,all BEM system matrices can be decomposed into a hierarchical system of blocks which can be approximated by low rank matrices.This paper introduced basic concept of hierarchical matrix(H-matrix);illustrated adaptive cross approximation(ACA) technique for low rank decomposition of H-matrix.Based on H-matrix and ACA technique a novel ACA-BEM was presented.In ACA-BEM,a cluster tree was constructed by recursively partitioning the collocation points,the system matrix was split into collections of sub-matrices which described remote interactions of far-field clusters.Most of the sub-matrices in ACA-BEM could be compressed by ACA,so disadvantages of large memory requirements in classical BEM were overcome.The efficiency of ACA-BEM was tested on 3D electric field analysis of spherical electrodes.更多还原