Abstract
Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner.
Highlights
Analysis of a large multilayer structure is an usual task in electrical device designs as reflectarrays antennas [1], frequency selective surfaces [2], leaky-waves antennas [3], phased arrays, etc.These devices are made of resonant planar layouts
We will show results of three analyses of whole printed reflectarray antennas: (1) focused beam reflectarray made of two sets of four parallel dipoles with small rotations, (2) reflectarray made of two orthogonal sets of four parallel dipoles to generate South-American coverage, and (3) dual band circular polarized focused beam reflectarray made of dual concentric split rings
Fast computation of the reduced coefficient matrix that leads the sparse approximate inverse (SAI) preconditioner for iterative version of the MM was proposed using pulse expansion and equivalent periodic problem (EPP) approaches for large multilayer structures
Summary
Analysis of a large multilayer structure is an usual task in electrical device designs as reflectarrays antennas [1], frequency selective surfaces [2], leaky-waves antennas [3], phased arrays, etc. These devices are made of resonant planar layouts. Bézier patches [5,6] After this discretization, in [7] generalized rooftops are defined on these patches as basis functions (BFs) in the approximation of surface current densities. The system of MPIEs can be transformed in a linear system of equations where the weights of BFs are unknown coefficients
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