Hierarchical conjugate gradient method applied to MoM analysis of electrically large structures

Arbitrary metallic and dielectric/magnetic structures can be analyzed by applying the method of moments (MoM) to the surface integral equations (SIEs). Such a structure is usually modeled by triangular or quadrilateral patches. Hierarchical higher order basis functions defined on those patches allow very efficient analysis. However, even for such sophisticated current expansions, the number of unknowns for electrically large structures can be so high that the analysis based on the direct solution of the matrix equation (e.g., LU decomposition) becomes inefficient. The paper presents the hierarchical conjugate gradient method (HCGM), a simple but effective modification of the standard CGM for higher order systems. In addition, we investigate the influence of the orthogonality of basis functions and the normalization of the basis functions in respect to their Euclidean norms on the behavior of iterative solvers. Significant reduction in analysis time for higher order problems is achieved. Conclusions based on the numerical results are given.