Accurate and Efficient Evaluation of Characteristic Modes

A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method-of-moment (MoM) solution of the electric-field integral equation to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated, illustrating the improved accuracy and performance of the new method.

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

[2]  Juan R. Mosig,et al.  Complete semi-analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method , 2010 .

[3]  Gerhard Kristensson,et al.  Scattering of Electromagnetic Waves by Obstacles , 2016 .

[4]  Weng Cho Chew,et al.  A memory saving fast A-EFIE solver for modeling low-frequency large-scale problems , 2012 .

[5]  A. Polimeridis,et al.  On the Direct Evaluation of Weakly Singular Integrals in Galerkin Mixed Potential Integral Equation Formulations , 2008, IEEE Transactions on Antennas and Propagation.

[6]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[7]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[8]  S. Nordebo,et al.  Characterization of MIMO Antennas Using Spherical Vector Waves , 2006, IEEE Transactions on Antennas and Propagation.

[9]  Chao-Fu Wang,et al.  Electrically Small UAV Antenna Design Using Characteristic Modes , 2014, IEEE Transactions on Antennas and Propagation.

[10]  James Demmel,et al.  IEEE Standard for Floating-Point Arithmetic , 2008 .

[11]  R. Harrington,et al.  Computation of characteristic modes for conducting bodies , 1971 .

[12]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[13]  Jacob J. Adams,et al.  Systematic Shape Optimization of Symmetric MIMO Antennas Using Characteristic Modes , 2016, IEEE Transactions on Antennas and Propagation.

[14]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

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

[16]  Lukas Jelinek,et al.  Optimal Composition of Modal Currents for Minimal Quality Factor $Q$ , 2016, IEEE Transactions on Antennas and Propagation.

[17]  S. Nordebo,et al.  Optimal Antenna Currents for Q, Superdirectivity, and Radiation Patterns Using Convex Optimization , 2013, IEEE Transactions on Antennas and Propagation.

[18]  Kristopher L. Kuhlman,et al.  mpmath: a Python library for arbitrary-precision floating-point arithmetic , 2017 .

[19]  Weng Cho Chew,et al.  Integral Equation Methods for Electromagnetic and Elastic Waves , 2007, Synthesis Lectures on Computational Electromagnetics.

[20]  P. Hazdra,et al.  A Method for the Evaluation of Radiation Q Based on Modal Approach , 2012, IEEE Transactions on Antennas and Propagation.

[21]  Lukas Jelinek,et al.  Optimal Currents on Arbitrarily Shaped Surfaces , 2016, IEEE Transactions on Antennas and Propagation.

[22]  R. Harrington,et al.  Theory of characteristic modes for conducting bodies , 1971 .

[23]  P. Waterman.  Matrix formulation of electromagnetic scattering , 1965 .

[24]  L. Dagum,et al.  OpenMP: an industry standard API for shared-memory programming , 1998 .

[25]  Walton C. Gibson,et al.  The Method of Moments in Electromagnetics , 2007 .

[26]  F. Venneri,et al.  Use of the Simultaneous Diagonalization Technique in the Ax̄ = λBx̄ Eigenproblem Applied to the Computation of the Characteristic Modes , 2003 .

[27]  Weng Cho Chew,et al.  Error analysis for the truncation of multipole expansion of vector Green's functions [EM scattering] , 2001, IEEE Microwave and Wireless Components Letters.

[28]  Clive Parini,et al.  Spherical near-field antenna measurements , 2014, Theory and Practice of Modern Antenna Range Measurements, 2nd Expanded Edition, Volume 2.

[29]  R. Harrington.  Time-Harmonic Electromagnetic Fields , 1961 .

[30]  Mats Gustafsson,et al.  Antenna Current Optimization using MATLAB and CVX , 2016 .

[31]  Thomas F. Eibert,et al.  On the calculation of potential integrals for linear source distributions on triangular domains , 1995 .

[32]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[33]  C. J. Reddy,et al.  Characteristic Mode Analysis: Putting Physics back into Simulation , 2015, IEEE Antennas and Propagation Magazine.

[34]  Jennifer T. Bernhard,et al.  Radiation and Energy Storage Current Modes on Conducting Structures , 2015, IEEE Transactions on Antennas and Propagation.

[35]  P. Waterman,et al.  SYMMETRY, UNITARITY, AND GEOMETRY IN ELECTROMAGNETIC SCATTERING. , 1971 .

[36]  Mats Gustafsson,et al.  Minimization of Antenna Quality Factor , 2017, IEEE Transactions on Antennas and Propagation.

[37]  Mats Gustafsson,et al.  Validating the Characteristic Modes Solvers , 2017, IEEE Transactions on Antennas and Propagation.

[38]  J. R. Mosig,et al.  On the Direct Evaluation of Surface Integral Equation Impedance Matrix Elements Involving Point Singularities , 2011, IEEE Antennas and Wireless Propagation Letters.

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

[40]  Timothy Gallwey.  Numerical Techniques in Electromagnetics with MATLAB, 3rd Edition - Solutions Manual , 2009 .