Increasing the Butterfly-Compressibility of Moment Matrix Blocks: A Quantitative Study

The butterfly (BF)-compressibility of moment matrix blocks is studied quantitatively for various geometrical configurations and compression algorithm parameters. To enable investigation of electrically large geometries, the methodology employs simplified expressions for the compressed memory and fast low-rank (LR)-approximation techniques. The study indicates that a block's optimal BF-compression is obtained for a nontrivial choice of the BF's depth, determined by the underlying geometrical configuration and compression threshold. It is also shown that reduced-dimensionality interactions are more BF-compressible. In particular, the optimal compressibility for the recently introduced generalized equivalence and generalized source integral equations is shown to be dependent on their effective dimensionality, which is dictated by the compression threshold. At high thresholds, these formulations are more BF-compressible than their conventional counterparts. The implications for the design of BF-compression-based solvers, in a geometrically adaptive manner, are discussed.