H-matrix compression of discontinous Galerkin method exact radiating boundary conditions

The discontinuous Galerkin method (DGM) is a flexible high-order forward solver for time-harmonic scattering problems in electromagnetics that results in a typically sparse system of linear equations. However, when exact radiating boundary conditions (ERBCs) are used to truncate the computational domain, a dense block is introduced into the DGM system that relates elements on a Huygens surface to elements on the boundary of the computational domain. In the context of iterative solution methods, this dense block can dominate the cost of evaluating matrix-vector-products and should be accelerated. Herein, we investigate the application of Hierarchical Matrices (H-matrices) to compress and accelerate the evaluation of the dense ERBC sub-matrix. Results are limited to high-order 2D transverse magnetic problems but demonstrate that effective compression resulting in substantial memory and time savings can be achieved even for relatively small problem sizes.