An orientation-aware grid-based method to remedy hazards of low-rank approximation methods for electromagnetics
Creators: name: Yao, Tian
Publisher: name: The University of Texas at Austin
Year: 2020
Subjects: Electromagnetic scattering
Method of moments
Low rank approximation
Adaptive cross approximation
Hybrid cross approximation

description: The method of moments is commonly accelerated by the low-rank approximation (LRA) of impedance matrix subblocks, either through direct compression or indirectly via sampling grids. While LRA methods can reduce computation times and memory requirements, they suffer from high compression errors when applied to problems containing cross-polarized interactions. A cross-polarized interaction occurs when the polarization of the field due to a source is highly orthogonal to the surface of an observer; a co-polarized interaction occurs when the field polarization is roughly tangential to the surface. In the direct compression of impedance matrix subblocks, e.g., with the adaptive cross approximation (ACA) algorithm, cross-polarized interactions are approximated poorly when compressed together with co-polarized interactions. In the grid-based scalar hybrid cross approximation (HCA) method, where the ACA algorithm is used to compress the grid-to-grid propagation matrix, cross-polarized interactions cannot be accurately approximated even when no co-polarized interactions are present. Such hazards are attributed to the inability of LRA methods to compress both strong and weak interactions in a single matrix, either it be the impedance matrix or grid propagation matrix, when these interactions are represented by different vector subspaces. A remedy based on the dyadic formulation of the HCA method, where vector sources/observers instead of scalar ones are used at grid points, is presented to allow for accurate LRA of cross-polarized interactions with or without the presence of co-polarized interactions. These accurate approximations are achieved by isolating cross-polarized interactions to a single block of the dyadic grid propagation matrix and compressing them separately from other blocks that may contain stronger co-polarized interactions. However, it is shown that the amount of isolation, and thereby the dyadic HCA method’s performance, depends on the directions of the grid sampling-vectors. In the proposed orientation aware dyadic HCA (OAD-HCA) method, the grid sampling-vectors are set using a novel orientation-search algorithm that rapidly reveals the appropriate directions. The algorithm bins the testing (basis) function vector directions into “function-orientation” bins and the polarizations of the fields radiated onto representative points on the observer (source) subdomain into “field-orientation” bins; it evaluates the orthogonality of the most-populated field- and function-orientation bins; and it uses the most-orthogonal pairs to set the directions of the observer (source) grid sampling-vectors. The accuracy of the OAD-HCA method is compared to those of the ACA and scalar grid HCA methods for various problem configurations with significant cross-polarized interactions. Their computation time and memory requirements are also compared through parallelized implementations of the various methods