Sensitivity analysis of 3-D composite structures through linear embedding via green's operators

We propose a methodology | based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) | for solving electromagnetic problems involving large 3-D structures comprised of ND ? 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body difier from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the \ideal" structure, we follow a deterministic approach, i.e., we allow for a flnite number of difierent realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND i 1 \flxed" bodies. Since the latter has to be computed only once, the overall procedure is indeed e-cient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the ofiset of one element in the array.

[1]  I. Lindell.  Huygens' principle in electromagnetics , 1996 .

[2]  Computational analysis of complicated metamaterial structures using MLFMA and nested preconditioners , 2007 .

[3]  Anton G. Tijhuis,et al.  Transient scattering by a lossy dielectric cylinder: marching-on-in-frequency approach , 1993 .

[4]  G. Vecchi,et al.  Analysis of Large Complex Structures With the Synthetic-Functions Approach , 2007, IEEE Transactions on Antennas and Propagation.

[5]  D.J. Bekers,et al.  An Eigencurrent Approach for the Analysis of Finite Antenna Arrays , 2009, IEEE Transactions on Antennas and Propagation.

[6]  Gaobiao Xiao,et al.  A Generalized Surface Integral Equation Formulation for Analysis of Complex Electromagnetic Systems , 2009, IEEE Transactions on Antennas and Propagation.

[7]  Jiming Song,et al.  Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects , 1997 .

[8]  W. Chew,et al.  Wave-Field Interaction With Complex Structures Using Equivalence Principle Algorithm , 2007, IEEE Transactions on Antennas and Propagation.

[9]  V. Lancellotti,et al.  An Eigencurrent Approach to the Analysis of Electrically Large 3-D Structures Using Linear Embedding via Green's Operators , 2009, IEEE Transactions on Antennas and Propagation.

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  Raj Mittra,et al.  CHARACTERISTIC BASIS FUNCTION METHOD FOR ITERATION-FREE SOLUTION OF LARGE METHOD OF MOMENTS PROBLEMS , 2008 .

[12]  van Mc Martijn Beurden,et al.  Iterative Solution of Field Problems with a Varying Physical Parameter , 2002 .

[13]  Raj Mittra,et al.  Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM) , 2003 .

[14]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[15]  V. Rokhlin,et al.  The fast multipole method (FMM) for electromagnetic scattering problems , 1992 .

[16]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[17]  R. Mittra,et al.  Solution of Electrically Large Problems With Multilevel Characteristic Basis Functions , 2009, IEEE Transactions on Antennas and Propagation.

[18]  B. P. de Hon,et al.  On the Convergence of the Eigencurrent Expansion Method Applied to Linear Embedding via Green's Operators (LEGO) , 2010, IEEE Transactions on Antennas and Propagation.

[19]  Ying Guan,et al.  Scattering Analysis of the Large Array Antennas Using the Synthetic Basis Function Method , 2009 .

[20]  M. Taskinen,et al.  Electromagnetic scattering by large and complex structures with surface equivalence principle algorithm , 2009 .

[21]  C. Balanis.  Advanced Engineering Electromagnetics , 1989 .

[22]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[23]  V. Lancellotti,et al.  Linear embedding via Green's operators , 2012, 2012 42nd European Microwave Conference.

[24]  V. Lancellotti,et al.  Analysis of antennas in the presence of large composite 3-D structures with linear embedding via Green's operators (LEGO) and a modified EFIE , 2010, Proceedings of the Fourth European Conference on Antennas and Propagation.

[25]  V. Lancellotti,et al.  A total inverse scattering operator formulation for solving large structures with LEGO , 2009, 2009 International Conference on Electromagnetics in Advanced Applications.

[26]  Accurate Analysis of Metamaterials Involving Finite Arrays of Split-ring Resonators and Thin Wires , 2007 .