Application of an IE-Based Domain Decomposition Method for Analysis of Planar Microstrip Array Structures: Meshless Approach
Keywords:
Array, domain decomposition, EFIE, meshfree, microstrip, MPIEAbstract
In this paper, application of an integral equation based domain decomposition method (DDM), developed for numerical solution of one-dimensional Fredholm integral equations of the second kind, is extended to electric field and mixed potential integral equations in two dimensions. Even though the original DDM was developed based on the Nyström method, results of the present work shows that meshfree approach can also be utilized. The extended DDM is employed for efficient meshfree analysis of planar microstrip array structures in the sense of reduced-size shape function and stiffness matrices. Results are validated by method of moments.
Downloads
References
H. A. Schwarz, “Uber einige abbildungsaufgaben,” Ges. Math. Abh., vol. 70, pp. 105-120, 1869.
Domain Decomposition Methods in Science and Engineering, 1-12, Proc. Int. Conf., SIAM, AMS, John Wiley & Son, DD Press, 1987-1999.
C. Carstensen, M. Kuhn, and U. Langer, “Fast parallel solvers for symmetric boundary element domain decomposition methods,” Numer. Math., vol. 79, pp. 321-347, 1998.
R. Schaback, “Error estimates and condition numbers for radial basis function interpolation,” Adv. Comput. Math., vol. 3, pp. 251-264, 1995.
T. Kaufmann, “The meshless radial point interpolation method for electromagnetics,” Doctoral and Habilitation Theses, ETH, 2011.
Z. Peng, X. C. Wang, and J. F. Lee, “Integral equation based domain decomposition method for solving electromagnetic wave scattering from nonpenetrable objects,” IEEE Trans. Antennas Propag., vol. 59, no. 9, pp. 3328-3338, 2011.
J. Hu, W. Hong, H. X. Zhou, W. D. Li, and Z. Song, “An overlapped domain decomposition method for solving electromagnetic surface integral equations,” IEEE Int. Conf. Comput. ProblemSolving (ICCP), pp. 1-4, 2010.
E. P. Stephan and T. Tran, “Domain decomposition algorithms for indefinite hypersingular integral equations: the h and p versions,” SIAM J. Sci. Comput., vol. 19, no. 4, pp. 1139-1153, 1998.
W. D. Li, W. Hong, and H. X. Zhou, “Integral equation-based overlapped domain decomposition method for the analysis of electromagnetic scattering of 3D conducting objects,” Microwave Opt. Tech. Lett., vol. 49, no. 2, pp. 265-274, 2007.
P. Ylä-Oijala, V. Lancellotti, B. P. de Hon, and S. Järvenpää, “Domain decomposition methods combining surface equivalence principle and macro basis functions,” ACES J., vol. 25, no. 12, pp. 1017-1025, 2010.
M. Campos and C. E. Perez, “A domain decomposition scheme for Fredholm integral equations using Nyström discretization,” Technical Report 98-21, Departamento de Ingenieria Matematica, Universidad de Concepcion, 1998.
J. R. Mosig, “Arbitrarily shaped microstrip structures and their analysis with a mixed potential integral equation,” IEEE Trans. Microwave Theory Tech., vol. MTT-36, pp. 314-323, 1988.
B. Honarbakhsh and A. Tavakoli, “Analysis of thick microstrip antennas by meshfree collocation method,” ACES J., vol. 28, no. 2, pp. 99-109, 2013.
P. S. Hall, “Review of techniques for dual and circularly polarized microstrip antennas,” in Microstrip Antennas, the Analysis and Design of Microstrip antennas and Arrays, D. M. Pozar and D. H. Schaubert, IEEE Press, pp. 107-116, 1995.
