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.