Rapid RWG Moment Method Solution of EFIE for Multiscale Problems via Hierarchical Center of Radiation Approximation in Barnes–Hut Algorithm

The Barnes–Hut algorithm utilizing hierarchical center-of-radiation approximation is applied for acceleration of quasi-static interactions in RWG Moment Method discretization of the electric field integral equation. As the method uses imbalanced oct-tree in hierarchical partitioning of the model, it maintains efficiency in memory and CPU usage when geometry of about a wavelength in size presents multiscale features. Because the center-of-radiation position in each box of hierarchically partitioned space is dependent on the direction to the observation point, the field evaluation in the Barnes–Hut algorithm is done via an interpolation scheme. Augmentation of the Barnes–Hut algorithm with local interpolation schemes is demonstrated. Impact on the error control mechanisms via angular interpolation and source clustering distance on the efficiency of the algorithm is studied.