Solver Performance of Accelerated MoM for Connected Arrays

TL;DR

This paper introduces two novel accelerated solvers leveraging the multilevel Toeplitz structure in large array simulations, significantly reducing computational time and storage compared to traditional methods.

Contribution

It develops and compares an iterative multilevel FFT-based solver and a fast direct Toeplitz solver, both utilizing a new mesh-partitioning algorithm for large array analysis.

Findings

Both methods outperform conventional solvers in speed and storage.

The direct solver achieves near machine epsilon accuracy.

Performance depends on residual thresholds, geometry, and frequency.

Abstract

Simulating and developing large rectangularly shaped arrays with equidistant interspacing is challenging as the computational complexity grows quickly with array size. However, the geometrical shape of the array, appropriately meshed, leads to a multilevel Toeplitz structure in the RWG-based Method of Moment impedance matrix representation that can be used to mitigate the increased complexity. This paper develops, presents and compares two different accelerated solvers that both utilize the matrix structure to determine antenna properties. Both methods use a novel mesh-partitioning algorithm and its associated data representation, reducing storage and computational costs. The first solver is an iterative method based on multilevel fast Fourier transform to accelerate matrix multiplications. The second solver approach is based on an extension of a fast direct Toeplitz solver, adapted to a block-matrix structure. This fast direct solver is demonstrated to have close to machine epsilon accuracy. Both accelerated methods are evaluated on two different array element types, for arrays with up to 900 elements. The results are compared with conventional direct and iterative matrix solvers. Improvements are seen in both the time and required storage to solve the problem. The choice of the most efficient method depends on the residual thresholds in the iterative method, geometry of the element and frequency. Two different preconditioners for the iterative method are investigated to evaluate their performance. The two accelerated methods vastly outperform regular matrix inversion methods.