H2-matrix-based fast volume integral equation solver for electrodynamic analysis

An H₂-matrix-based mathematical framework is introduced and further developed to reduce the computational complexity of the volume integral equation (VIE)-based analysis of electrodynamic problems. Numerical experiments have demonstrated a significant reduction in CPU time and memory consumption. A linear scaling with respect to matrix size in both CPU time and memory is achieved for small and medium-sized electrodynamic problems with an interpolation-based H₂-representation of the VIE operator in conjunction with a rank function for accuracy control. The proposed solver is applicable to arbitrarily shaped three-dimensional structures immersed in inhomogeneous materials.