Preconditioned Localized-Solution Iterative Solver With Nested Cross Approximation for Large Arrays

A localized solution-based iterative solver for method of moments (MoM) analysis of large antenna arrays with disjoint, nonidentical elements is presented. The formulation introduces computational cost reducing extensions for the direct coupling technique (DCT), which is a domain decomposition method (DDM) whereby element-associated overlapping local problems are iteratively solved. A residual-driven formulation improves convergence and enables matrix sparsification. Macro basis functions (MBFs) are incorporated, with convergence to user-specified error tolerance maintained. Through near-interaction preconditioning, local domain extensions are rendered implicit, removing the need for overlapping local solutions. A single-level, hybrid nested cross-approximation (NCA) acceleration scheme is employed. Rapid, controllable convergence is demonstrated for very large arrays. Faster runtimes than with the multilevel fast multipole method (MLFMM) in the commercial FEKO software suite, are demonstrated. Convergence rate is practically independent of excitation, including scattering analysis. The capability of preconditioner and local matrices being independent of excitation and iteration, enables efficient solution of multiple right-hand sides, e.g., for embedded element pattern (EEP) computations. The solver is well suited to parallelization.