An H2-matrix-based direct integral-equation solver of linear complexity for solving electrodynamic problems

In this work, an H² matrix was constructed to represent the dense system matrix resulting from integral-equation-based analysis of electrodynamic problems. The H- and H²-matrix framework is a general mathematical framework that enables a highly compact representation and efficient numerical computation of dense matrices. Here, fast multiple based methods, fast low-rank compression methods, and FFT-based methods have been developed that dramatically reduce the memory. The process involves a full-matrix inverse at the leaf level and a number of matrix-matrix multiplications at other levels.