A Geometric Cross Approximation Method
Author(s)
Jianming Zhang & Xingshuai Zheng
Abstract
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.
Keywords
H-matrix, dense matrix, low-rank matrices, adaptive cross
approximation, skeleton points, topological spatial relations
Related Book
Other papers in this volume
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