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A fast multipole method for layered media based on the application of perfectly matched layers - the 2-D case

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4 Author(s)
Vande Ginste, D. ; Inf. Technol. Dept., Ghent Univ., Belgium ; Rogier, H. ; Olyslager, F. ; De Zutter, D.

An efficient fast multipole method (FMM) formalism to model scattering from two-dimensional (2-D) microstrip structures is presented. The technique relies on a mixed potential integral equation (MPIE) formulation and a series expression for the Green functions, based on the use of perfectly matched layers (PML). In this way, a new FMM algorithm is developed to evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. Novel iteration schemes have been implemented and a computational complexity of order O(N) is achieved. The theory is validated by means of several illustrative, numerical examples. This paper aims at elucidating the PML-FMM-MPIE concept and can be seen as a first step toward a PML based multilevel fast multipole algorithm (MLFMA) for 3-D microstrip structures embedded in layered media.

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Antennas and Propagation, IEEE Transactions on  (Volume:52 ,  Issue: 10 )