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The error control of local interpolation for a 2D MLFMA will be discussed. The way to select proper parameters is proposed in terms of both numerical accuracy and computational cost. Satisfying the conditions derived in this paper, error can be controlled at the same level as global interpolation, and the computational cost becomes less expensive than the global one. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 8–12, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10655 [ABSTRACT FROM AUTHOR]

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 109–114, 2001. [ABSTRACT FROM AUTHOR]

This study presents the application of fast spherical transforms developed by Driscoll and Healy (Adv Appl Math 15 (1994), 202–250) to the full-wave multilevel fast multipole method. An accurate uniform-grid based quadrature rule is presented, along with fast algorithms for interpolation and anterpolation. Error behavior and algorithmic complexities are discussed. Finally an efficient method for the generation of translation operators is presented. The overall method results in efficient and error-controllable schemes for quadrature and interpolation. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1961–1964, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21825 [ABSTRACT FROM AUTHOR]