CIRCLE-FIT SUMMATION ACCELERATION OF PERIODIC GREEN’S FUNCTIONS
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CIRCLE-FIT SUMMATION ACCELERATION OF PERIODIC GREEN’S FUNCTIONSAbstract
The circle-fit algorithm is shown to be an attractive alternative to the spectral domain form of the two-dimensional periodic Green’s function when the radiated fields are evaluated in the plane of the array. As the name implies, the circle-fit algorithm predicts the summation limit by fitting circles to the converging spiral of spatial domain partial sums in the complex plane. Several numerical examples comparing the raw spatial, spectral, and circle-fit accelerated spatial sums demonstrate the algorithm's computational savings. While other series extrapolation methods are shown to be more efficient, the circle-fit algorithm has the advantage of providing insight into how the Green’s function converges.
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