Accuracy Improvement of the Second-Kind Integral Equations for Generally Shaped Objects

In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.

[1]  Alexander Yarovoy,et al.  Capacitevely loaded bowtie antenna for ultrawideband impulse radio , 2006 .

[2]  M. G. Duffy,et al.  Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex , 1982 .

[3]  Claus Müller,et al.  Foundations of the mathematical theory of electromagnetic waves , 1969 .

[4]  Juan M. Rius,et al.  Accurate computation of the impedance elements of the magnetic‐field integral equation with RWG basis functions through field‐domain and source‐domain integral swapping , 2007 .

[5]  L. Gurel,et al.  Solid-angle factor in the magnetic-field integral equation , 2005 .

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

[7]  L. Gurel,et al.  Improving the accuracy of the MFIE with the choice of basis functions , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[8]  P. Yla-Oijala,et al.  Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects , 2005, IEEE Transactions on Antennas and Propagation.

[9]  L. Gurel,et al.  Linear-Linear Basis Functions for MLFMA Solutions of Magnetic-Field and Combined-Field Integral Equations , 2007, IEEE Transactions on Antennas and Propagation.

[10]  Snorre H. Christiansen,et al.  A dual finite element complex on the barycentric refinement , 2005, Math. Comput..

[11]  R. Harrington,et al.  A surface formulation for characteristic modes of material bodies , 1977 .

[12]  Davis,et al.  High-order convergence with a low-order discretization of the 2-D MFIE , 2004, IEEE Antennas and Wireless Propagation Letters.

[13]  P. Yla-Oijala,et al.  Calculation of CFIE impedance matrix elements with RWG and n/spl times/RWG functions , 2003 .

[14]  Jianming Jin,et al.  Improving the Accuracy of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions , 2011, IEEE Transactions on Antennas and Propagation.

[15]  Z. Nie,et al.  On the Rayleigh-Ritz scheme of 3D MFIE and its normal solution , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[16]  Te-kao Wu,et al.  Scattering from arbitrarily‐shaped lossy dielectric bodies of revolution , 1977 .

[17]  Seppo Järvenpää,et al.  Analysis of surface integral equations in electromagnetic scattering and radiation problems , 2008 .

[19]  L. Gurel,et al.  Singularity of the magnetic-field Integral equation and its extraction , 2005, IEEE Antennas and Wireless Propagation Letters.

[20]  Jianming Jin,et al.  Calderón Preconditioner: From EFIE and MFIE to N-Müller Equations , 2010, IEEE Transactions on Antennas and Propagation.

[21]  Juan M. Rius,et al.  MFIE MoM‐formulation with curl‐conforming basis functions and accurate kernel integration in the analysis of perfectly conducting sharp‐edged objects , 2005 .

[22]  Andrew J. Poggio,et al.  CHAPTER 4 – Integral Equation Solutions of Three-dimensional Scattering Problems , 1973 .

[23]  A. Peterson,et al.  3D MFIE accuracy improvement using regularization , 2007, 2007 IEEE Antennas and Propagation Society International Symposium.

[24]  D. V. Jonesco.  Sur une classe d'équations fonctionnelles , 1927 .

[25]  L. Gurel,et al.  Improved testing of the magnetic-Field integral equation , 2005, IEEE Microwave and Wireless Components Letters.

[26]  Juan M. Rius,et al.  On the testing of the magnetic field integral equation with RWG basis functions in method of moments , 2001 .

[27]  Francesco P. Andriulli,et al.  Improving the MFIE's accuracy by using a mixed discretization , 2009, 2009 IEEE Antennas and Propagation Society International Symposium.

[28]  Jianming Jin.  Theory and Computation of Electromagnetic Fields , 2010 .

[29]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[30]  Ozgur Ergul,et al.  Improving the accuracy of the magnetic field integral equation with the linear‐linear basis functions , 2006 .

[31]  Roberto D. Graglia,et al.  Higher order interpolatory vector bases for computational electromagnetics," Special Issue on "Advanced Numerical Techniques in Electromagnetics , 1997 .

[32]  Jian-Ming Jin,et al.  A Comparative Study of Calderón Preconditioners for PMCHWT Equations , 2010, IEEE Transactions on Antennas and Propagation.