Multilevel Non-uniform Grid Algorithm Research Articles

Adaptive Multilevel Nonuniform Grid Algorithm for the Accelerated Analysis of Composite Metallic–Dielectric Radomes

An adaptive multilevel nonuniform grid (MLNG) algorithm is developed for the accelerated computation of fields radiated through composite metallic–dielectric radomes as well as antenna-radome interactions. The MLNG approach is applied to the mixed potential formulation of the coupled surface and volume electric field integral equations. The radome is decomposed into a hierarchy of subdomains (SDs) by an adaptive algorithm that closely follows the radome geometry, allowing significant savings in memory and CPU time. In the MLNG algorithm, only local generalized impedance matrices of the finest level SDs are evaluated. Far-zone potentials and fields are indirectly evaluated through a multilevel aggregation involving phase-and amplitude-compensated interpolation on nonuniform grids (NGs), requiring considerably fewer calculations as compared with the classical method of moments (MoM). The MLNG algorithm is incorporated in a preconditioned iterative solver. Accuracy as well as memory consumption and computation times of the algorithm are studied on realistic examples. The radome effect on the antenna input impedance and electric current density distribution is demonstrated. The method is validated by comparison with a commercial MoM software and shown to exhibit a computational complexity (CC) of O(NlogN), N being the number of unknowns.

Fast Antenna Diagnosis Algorithm Using Oblate Spheroidal Nonuniform Grids

A fast algorithm for the diagnosis of large antennas is developed. The algorithm is based on the Rayleigh-Sommerfeld (RS) backpropagation method, accelerated by a multilevel nonuniform grid algorithm. Comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions. The optimal performance is obtained by using oblate spheroidal grids, which are tailored to both the measurement and antenna surfaces. Further acceleration can be achieved, for particular cases, via optimal sampling on the antenna surface. The algorithm’s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions, and compared to that achieved with spherical grids. The accuracy and error controllability are studied in comparison to the direct RS integral computation.

Multilevel nonuniform grid algorithm for acceleration of integral equation-based solvers for acoustic scattering

A fast algorithm for the evaluation of acoustic fields produced by given source distributions is developed with the aim of accelerating iterative boundary element method (BEM) solvers. The algorithm is based on field smoothing by phase and amplitude compensation, which allows for sampling of the fields radiated by finite-size source distributions over coarse nonuniform (spherical) grids (NGs). Subsequently, the fields at the desired target points can be obtained by an interpolation and phase and amplitude restoration. Combining this approach with the divide-and-conquer strategy, the total field is computed via a hierarchical decomposition of the source domain. In this computational scheme, the phase and amplitude compensated fields produced by neighboring subdomains are gradually aggregated through a multilevel process involving interpolation between increasingly dense NGs and the scatterer surface. This multilevel NG algorithm is used to reduce the computational cost of applying the field evaluation operator and its adjoint, as required in each iteration of the conjugate gradient solver based on the BEM-discretized integral representation of scattering problems. Accuracy and computational efficiency of the NG algorithm are demonstrated on representative examples of elongated, quasi-planar, and full 3-D scatterers.