A Geometric Mapping Cross Approximation method

The matrices of Boundary Element Method (BEM) are fully populated and require special compression techniques for the efficient treatment. In this article, the H-matrix representation is used to approximate the dense stiffness matrix in admissible blocks by low-rank matrices. This paper presents a Geometric Mapping Cross Approximation (GMCA) algorithm to compute the low-rank matrices. Compared with the Adaptive Cross Approximation (ACA), the GMCA determines the skeleton points from the two interacting groups of nodes by their spacing characteristics directly and, thus, has a remarkable non-iterative nature and requires some simple geometric transformations, only. Numerical examples show that the new algorithm is feasible.