Eibert, T. F.; Sertel, K.; Volakis, J. L. Hybrid finite element modelling of conformal antenna and array structures utilizing fast integral methods. (English) Zbl 0960.78011 Int. J. Numer. Model. 13, No. 2-3, 81-101 (2000). Summary: Hybrid finite element methods (FEM) which combine the finite element and boundary integral methods have been found very successful for the analysis of conformal finite and periodic arrays embedded on planar or curved platforms. A key advantage of these hybrid methods is their capability to model inhomogeneous and layered material without a need to introduce complicated Green’s functions. Also, they offer full geometrical adaptability and are thus of interest in general-purpose analysis and design. For the proposed hybrid FEM, the boundary integral is only used on the aperture to enforce the radiation condition by employing the standard free space Green’s function. The boundary integral truncation of the FEM volume domain, although necessary for rigor, is also the cause of substantial increase in CPU complexity. In this paper, we concentrate on fast integral methods for speeding-up the computation of these boundary integrals during the execution of the iterative solver. We consider both the adaptive integral method (AIM) and the fast multipole method (FMM) to reduce the complexity of boundary integral computation down to \(O(N^\alpha)\) with \(\alpha< 1.5.\) CPU and memory estimates are given when the AIM and FMM accelerations are employed as compared to the standard \(O(N^2)\) algorithms. In addition, several examples are included to demonstrate the practicality and application of these fast hybrid methods to planar finite and infinite arrays, frequency selective surfaces, and arrays on curved platforms. Cited in 3 Documents MSC: 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78A50 Antennas, waveguides in optics and electromagnetic theory 65Z05 Applications to the sciences Keywords:hybrid finite element methods; boundary integral truncation; adaptive integral method; fast multipole method PDFBibTeX XMLCite \textit{T. F. Eibert} et al., Int. J. Numer. Model. 13, No. 2--3, 81--101 (2000; Zbl 0960.78011) Full Text: DOI References: [1] Volakis, IEEE Transaction on Antennas and Propagation pp 493– (1997) [2] Gong, Radio Science 31 pp 1837– (1996) [3] Özdemir, IEEE Transactions on Antennas Propagation pp 788– (1997) [4] Graglia, IEEE Transaction Antennas and Propagation 46 pp 442– (1998) · Zbl 0945.78016 [5] Finite Element Methods for Electromagnetics. IEEE Press: Piscataway, NJ, 1998. [6] Lucas, IEEE Transaction on Antennas and Propagation 43 pp 145– (1995) [7] McGrath, Radio Science 31 pp 1173– (1996) [8] Eibert, IEEE Transaction on Antennas and Propagation 47 pp 843– (1999) [9] Rao, IEEE Transaction on Antennas and Propagation 30 pp 409– (1982) [10] Yang, Journal of the Optic Society of America B 14 pp 2513– (1997) [11] The artificial puck frequency selective surface. URSI Radio Science Meeting, Ann Arbor, 1993, p. 266. [12] Aroudaki, IEEE Transaction on Antennas and Propagation 43 pp 1486– (1995) [13] Kempel, IEE Proceedings of Microwave Antennas and Propagation 142 pp 233– (1995) [14] Jordan, Journal of Computational Physics 43 pp 222– (1986) · Zbl 0647.65084 [15] Ewald, Annals of Physics 64 pp 253– (1921) · JFM 48.0566.02 [16] Chew, IEEE Transaction on Antennas and Propagation 45 pp 533– (1997) [17] Bleszynski, Radio Science 31 pp 1225– (1996) [18] Coifman, IEEE Antennas and Propagation Magnetics 35 pp 7– (1993) [19] Bindiganavale, IEEE Antennas and Propagation Magnetics 39 pp 47– (1993) [20] In Application of Iterative Methods to Electromagnetic and Signal Proceedings, (ed.). Elsevier: Amsterdam, 1991; 159-240. [21] Fast memory-saving hybrid algorithms for electromagnetic scattering and radiation. Ph.D. thesis, University of Michigan, 1997. [22] Mittra, Proceedings of the IEEE 76 pp 1593– (1988) [23] Handbook of Mathematical Functions. National Bureau of Standards, 1972. [24] Rao, IEEE Transaction on Antennas and Propagation AP-30 pp 409– (1982) [25] Microstrip antennas on a cylindrical surface. In Handbook of Microstrip antennas, (eds). Pergrinus: London, 1989; 1227-1255. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.