A Geometric Cross Approximation Method
Free (open access)
537 - 546
Jianming Zhang & Xingshuai Zheng
The matrices resulting from the discretisation of non-local operators occurring in the boundary element method (BEM) are fully populated and require special compression techniques for efficient treatment. Among the several standard techniques, the H-matrix representation is used to approximate the dense stiffness matrix in admissible blocks which can be approximated by low-rank matrices. This paper presents a geometric cross approximation (GCA) algorithm to assemble the low-rank matrices. Compared with the adaptive cross approximation (ACA), the GCA determines the skeleton points from the two interacting groups of nodes corresponding to an admissible block by their topological spatial relations directly and, thus, has a remarkable non-iterative nature and requires the spatial geometric information of the nodes, only. Numerical examples are presented to further demonstrate the feasibility and effectivity. Keywords: H-matrix, dense matrix, low-rank matrices, adaptive cross approximation, skeleton points, topological spatial relations.
H-matrix, dense matrix, low-rank matrices, adaptive cross approximation, skeleton points, topological spatial relations