Macro Basis Function Methods with Multilevel DCA Acceleration for Antenna Array Analysis

Efficient method of moments (MoM) analysis of very large antenna arrays of disjoint elements, using macro basis function (MBF) schemes, is considered. Directional cross approximation (DCA), which is a nested, multilevel, algebraic, low-rank factorization scheme suitable for electrically large structures, is used for fast reduced MBF matrix set up and matrix-vector products. A DCA far-field sampling strategy suitable for planar arrays is employed. Optimal log-linear DCA memory scaling is demonstrated. The performance of static MBF formulations is investigated, namely the characteristic basis function method (CBFM), and windowed MBF (WMBF) schemes, which establish MBFs once as a preprocessing step. Static MBF approximation errors are difficult to control. Dynamic MBFs are iteratively refined to obtain a solution within user-specified error tolerance. Residual-driven (RD) CBFM, RD WMBFs, RD Krylov subspace MBFs, and block-Jacobi MBFs (both original and RD) are considered. Effective solution accuracy control is demonstrated. Runtime of all schemes is studied. Given optimal DCA acceleration, the results give a realistic view on relative efficiencies. Static MBFs are much less efficient than dynamic ones. Among dynamic schemes, RD static MBFs are less efficient. Krylov MBFs can perform better than the original block-Jacobi scheme, but the latter requires no parameter choice. RD block-Jacobi and a hybrid Krylov-Jacobi scheme sometimes outperform all others.