A Global Interpolator With Low Sample Rate for Multilevel Fast Multipole Algorithm

• Published in: IEEE transactions on antennas and propagation Vol. 61; no. 3; pp. 1291 - 1300
• Main Authors: Jarvenpaa, S., Yla-Oijala, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Agglomeration; Algorithms; Antennas; Anterpolation; Applied classical electromagnetism; Applied sciences; Circuit properties; Electric, optical and optoelectronic circuits; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Electronics; Exact sciences and technology; fast Fourier transform (FFT); Fundamental areas of phenomenology (including applications); Interpolation; Mathematical models; Matrix converters; method of moments; Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits; Multilevel; multilevel fast multipole algorithm; Multipoles; Nickel; Octrees; Phases; Physics; Polynomials; Vectors; Anterpolation; Fourier transformation; Electromagnetism; Microwave radiation; Moments method; multilevel fast multipole algorithm; Trigonometric polynomial; fast Fourier transform (FFT); Aggregation; Multipole field; interpolation; Fast Fourier transforms; Octrees; Modelling; method of moments; Fast algorithm; High frequency
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2012.2231927

A new, improved version of a global interpolator utilizing trigonometric polynomials is presented for the high-frequency multilevel fast multipole algorithm. The number of required points to sample the outgoing and incoming field patterns is low, almost half in some levels, compared with the earlier published versions. Compared with local interpolators based on Lagrange interpolating polynomials, the proposed technique performs even more favorably and reduces the number of sample points by a factor of eight. The numerical examples demonstrate that the interpolator allows full numerical accuracy control during the aggregation and disaggregation phases, regardless of the number of the levels in the octree.