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Analysis of periodic structures in time domain is an increasingly important tool in the design of a wide range of novel structures. Time Domain Integral Equation based methods provide an accurate means of solving transient periodic problems, but require costly convolutions that scale as O(Nt2Ns2), where Nt and Ns are the temporal and spatial degrees of freedom. This work proposes a fast method for effecting convolutions with the periodic Greens function that scales as O(Ns Nt log2 Nt). The method relies on a temporal Floquet expansion of the periodic Greens function that is accelerated in space using the O(Ns) method of Accelerated Cartesian Expansions and in time using an O(Nt log2 Nt) blocked FFT scheme.
Date of Conference: 2-7 Sept. 2012