On Rapid Estimation of Impedance-Matrix Ranks via Grid-Based Techniques

The performance of three sampling-grid-based techniques for estimating the rank of impedance matrix blocks are evaluated: Method I constructs a volumetric grid-to-grid propagation matrix between regular but coarsely sampled grids enclosing the source/observer domains and evaluates this matrix's rank using the truncated-SVD. While effective in the quasi-static regime, the method rapidly becomes impractical for electrically large domains. Method II evaluates the rank of the same grid-to-grid propagation matrix using the ACA. Method III uses a set of reduced/belt proxy grids designed for multilevel compression and interpolation of phase- and amplitude-compensated fields. For quasi-planar configurations of electrically large domains, Method III is found to be asymptotically superior while Method II is found to be effective until ~10
⁶
degrees of freedom.