Abstract
In this Communication, we provide an efficient algorithm for the evaluation of the semi-infinite array Green's function (SAGF) for a semi-infinite planar periodic phased array of dipoles in free space. For observation points not too far from the array plane, the algorithm uses a hybrid spectral-spatial representation of the Green's function accelerated with the Levin T method, that we show to be faster than the Shanks method. For observation points sufficiently far away from the array plane, we show that the SAGF is efficiently evaluated by using asymptotic field expressions. Asymptotics is also used to explain the loss of accuracy of the Levin T accelerator in certain regions, and a correction procedure is proposed to overcome this problem
Highlights
In this Communication, to further accelerate the algorithm presented in [1], we use the Levin T accelerator [9] instead of the Shanks method. We show that it provides accurate results for points not too far from the array, but that a direct application of the Levin method can result in large errors for some conditions of phasing and observation height. We show that these large errors are avoided when we apply the “flip” procedure, i.e., when the semi-infinite array Green’s function (SAGF) is evaluated by subtracting the GF of the complementary problem from the infinite-array GF
We have shown that the line-by-line approach presented in [1] for the semi-infinite array Green’s function (SAGF) and here combined with the use of the Levin T accelerator leads to exponential convergence rates
The exponential convergence makes the line-by-line approach combined with the Levin T accelerator faster than the Shanks method for an accurate evaluation of the SAGF not too far from the array plane
Summary
We have shown that the line-by-line approach presented in [1] for the semi-infinite array Green’s function (SAGF) and here combined with the use of the Levin T accelerator leads to exponential convergence rates. We have shown that the origin of the radiated Floquet waves must be included in the region that is used by the Levin T accelerator to extrapolate the total potential radiated by the semi-infinite array and the decomposition (8) is applied for this purpose. H. Schaubert, “An efficient computation scheme for the free-space Green’s function of a twodimensional semi-infinite phased array,” IEEE Trans. B. Felsen, “Frequency-domain Green’s function for a planar periodic semi-infinite phased array—part I: truncated Floquet wave formulation,” IEEE Trans. “On the use of Levin’s T-transform in accelerating the summation of series representing the free-space periodic Green’s function,” IEEE Trans. Amer., vol 95, no. 2, pp. 638–649, Feb. 1994
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