Algebraic Partition Construction Method for Hierarchical Matrices

A hierarchical matrix (H-matrix) is an approximated form of a dense matrix, which is derived from an integral equation with a degenerate kernel. An H-matrix is constructed by determining an appropriate permutation and partition for the matrix, such that most of the submatrices attain a numerically low rank. In this article, an algebraic method for the H-matrix construction is proposed. The proposed method requires only the values of the original dense matrix, unlike the conventional method which requires geometrical information. We confirm through numerical experiments on electrostatic-field analyses that the proposed algebraic method achieves high compressibility close to that of the conventional method using auxiliary geometrical information.