A Mixed-Order Stabilized Bi-Conjugate Gradient FFT Method for Magnetodielectric Objects

Magnetodielectric materials have many emerging applications, but their scattering problems are challenging for volume integral equation solvers. In this paper, a mixed-order stabilized bi-conjugate gradient FFT (mixed-order BCGS-FFT) method for solving the scattering problem of magnetodielectric objects is presented. This method uses the volumetric roof-top basis functions as testing functions for the coupled field volume integral equation (CFVIE) and basis functions for the electric and magnetic flux densities (D,B). However, unlike the conventional weak form BCGS-FFT methods for dielectric objects, the mixed-order BCGS-FFT method uses the second-order curl conforming basis functions for the electric and magnetic vector potentials (F,A). The curl conforming basis functions preserve the continuity of the tangential components for F and A, while the use of second-order basis functions avoids the zero terms caused by the divergence operations on the vector potentials. Numerical examples show excellent performance of the mixed-order BCGS-FFT method over the currently available BCGS-FFT method as well as high accuracy of the mixed-order BCGS-FFT method on large contrast magnetodielectric scatterers.

[1]  Weng Cho Chew,et al.  A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems , 1995 .

[2]  G. Vecchi,et al.  Synthetic function analysis of large printed structures: the solution space sampling approach , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).

[3]  P. M. Berg,et al.  The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems , 1992 .

[4]  M. Cátedra.  The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics , 1995 .

[5]  Matthys M. Botha,et al.  Solving the volume integral equations of electromagnetic scattering , 2006, J. Comput. Phys..

[6]  Qing Huo Liu,et al.  A volume adaptive integral method (VAIM) for 3-D inhomogeneous objects , 2002 .

[7]  Steven A. Cummer,et al.  A microwave metamaterial with integrated power harvesting functionality , 2013 .

[8]  J. D. Shea,et al.  Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms , 2010, Inverse problems.

[9]  Er-Ping Li,et al.  AIM Analysis of Electromagnetic Scattering by Arbitrarily Shaped Magnetodielectric Object , 2007, IEEE Transactions on Antennas and Propagation.

[10]  Y. Gan,et al.  A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability , 2006, IEEE Transactions on Antennas and Propagation.

[11]  M. Bleszynski,et al.  AIM: Adaptive integral method for solving large‐scale electromagnetic scattering and radiation problems , 1996 .

[12]  Qing Huo Liu,et al.  RCS computation of large inhomogeneous objects using a fast integral equation solver , 2003 .

[13]  Qing Huo Liu,et al.  The stabilized biconjugate gradient fast Fourier transform method for electromagnetic scattering , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[14]  Caicheng Lu.  A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes , 2003 .

[15]  Jacob K. White,et al.  A precorrected-FFT method for electrostatic analysis of complicated 3-D structures , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Paul M. Meaney,et al.  Enhancing breast tumor detection with near-field imaging , 2002 .

[17]  S. Hagness,et al.  Toward contrast-enhanced microwave-induced thermoacoustic imaging of breast cancer: an experimental study of the effects of microbubbles on simple thermoacoustic targets , 2009, Physics in medicine and biology.

[18]  D. Wilton,et al.  A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies , 1984 .

[19]  Norbert N. Bojarski,et al.  The k-space formulation of the scattering problem in the time domain , 1982 .

[20]  K. Sertel,et al.  Multilevel fast multipole method solution of volume integral equations using parametric geometry modeling , 2001, IEEE Transactions on Antennas and Propagation.

[21]  C.-C. Su,et al.  The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT , 1993 .

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

[23]  Sergey N. Makarov.  MoM antenna simulations, with Matlab: RWG basis functions , 2001 .

[24]  O. P. Gandhi,et al.  Calculation of High-Resolution SAR Distributions in Biological Bodies Using the FFT Algorithm and Conjugate Gradient Method (Short Papers) , 1985 .

[25]  Tat Soon Yeo,et al.  Fast analysis of scattering by arbitrarily shaped three‐dimensional objects using the precorrected‐FFT method , 2002 .

[26]  T. Sarkar,et al.  Comments on "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies" , 1986 .

[27]  Raj Mittra,et al.  The biconjugate gradient method for electromagnetic scattering , 1990 .

[28]  Qing Huo Liu,et al.  Applications of the BCGS-FFT method to 3-D induction well logging problems , 2003, IEEE Trans. Geosci. Remote. Sens..

[29]  MacroBasis Functions and MultiLevel algorithms for printed antennas , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).

[30]  Juan R. Mosig,et al.  A subdomain multilevel approach for the efficient MoM analysis of large planar antennas , 2000 .

[31]  Daniël De Zutter,et al.  Accurate and Conforming Mixed Discretization of the MFIE , 2011, IEEE Antennas and Wireless Propagation Letters.

[32]  Z. Q. Zhang,et al.  Three‐dimensional weak‐form conjugate‐ and biconjugate‐gradient FFT methods for volume integral equations , 2001 .

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

[34]  Norbert N. Bojarski,et al.  K-Space Formulation of the Electromagnetic Scattering Problem , 1972 .

[35]  Y. Geng.  A plane wave scattering from two concentric ferrite anisotropic spherical shells , 2010, Proceedings of the 9th International Symposium on Antennas, Propagation and EM Theory.

[36]  David R. Smith,et al.  Metamaterial Electromagnetic Cloak at Microwave Frequencies , 2006, Science.

[37]  David R. Smith,et al.  Controlling Electromagnetic Fields , 2006, Science.

[38]  Kun-mu Chen,et al.  Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies , 1974 .