Memory Reduced Half Hierarchal Matrix (H-Matrix) for Electrodynamic Electric Field Integral Equation

This letter shows 50 percent memory saving for a Hierarchal Matrix (H-matrix) by converting a regular H-matrix to symmetric H-matrix for large and complex electrodynamic problems. Only the upper diagonal near-field and compressed far-field matrix blocks of the H-matrix are stored. Far-field memory saving is achieved by computing and keeping the upper diagonal far-field blocks leading to compressed column block U and row block V at a level. Due to symmetry, the lower diagonal far-field H-matrix compressed column is transpose of V, and the compressed row block is transpose of U. Storage and computation of lower diagonal blocks are not required. Similarly, in the case of near-field, only the upper diagonal near-field blocks are computed and stored. Numerical results show that the proposed memory reduction procedure retains the accuracy and cost of regular H-matrix.