Discretization of Volume Integral Equation Formulations for Extremely Anisotropic Materials

A stable volume integral equation formulation and its discretization for extremely anisotropic materials is presented. The volume integral equations are written in terms of the volume equivalent currents. The equivalent currents are expanded with piecewise constant basis functions, and the Galerkin's scheme is applied for testing the equations. Numerical results show that the behavior of the formulation is more stable than the behaviors of the more conventional volume integral equation formulations based on fluxes or fields, when the scatterer is extremely anisotropic. Finally, the developed method is applied to analyze a highly anisotropic material interface which approximates the ideal DB boundary.

[1]  Gaps in present discretization schemes for domain integral equations , 2007, 2007 International Conference on Electromagnetics in Advanced Applications.

[2]  Weng Cho Chew,et al.  A novel formulation of the volume integral equation for electromagnetic scattering , 2009 .

[3]  J. P. Webb.  Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements , 1999 .

[4]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[5]  Kin‐Lu Wong,et al.  Electromagnetic scattering by a uniaxially anisotropic sphere , 1992 .

[6]  Caicheng Lu,et al.  Analysis of Volume Integral Equation Formulations for Scattering by High-Contrast Penetrable Objects , 2012, IEEE Transactions on Antennas and Propagation.

[7]  E. Martini,et al.  DB boundary conditions at the inner surface of an arbitrarily shaped cloak , 2011, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP).

[8]  K. Sertel,et al.  On volume integral equations , 2006, IEEE Transactions on Antennas and Propagation.

[9]  A. Sihvola,et al.  Electromagnetic boundary and its realization with anisotropic metamaterial. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  P. Uslenghi,et al.  Electromagnetic scattering from anisotropic materials, part II: Computer code and numerical results in two dimensions , 1987 .

[11]  P. Kildal.  Definition of artificially soft and hard surfaces for electromagnetic waves , 1988 .

[12]  A. Sihvola,et al.  Electromagnetic Boundary Conditions Defined in Terms of Normal Field Components , 2009, IEEE Transactions on Antennas and Propagation.

[13]  Lewei Li,et al.  Scattering by rotationally symmetric anisotropic spheres: potential formulation and parametric studies. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Realization of spherical D′B′ boundary by a layer of wave-guiding medium , 2011, 1104.3495.

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

[16]  A. Sihvola,et al.  Realization of Impedance Boundary , 2006, IEEE Transactions on Antennas and Propagation.

[17]  A. Sihvola,et al.  Computation of Scattering by DB Objects With Surface Integral Equation Method , 2011, IEEE Transactions on Antennas and Propagation.

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

[19]  B. Shanker,et al.  Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies , 2004, IEEE Transactions on Antennas and Propagation.

[20]  Exact Solution to Electromagnetic Scattering by an Impedance Sphere Coated With a Uniaxial Anisotropic Layer , 2009 .

[21]  S. Hrabar,et al.  DB Boundary Based on Resonant Metamaterial Inclusions , 2011 .

[22]  van Stef Stef Eijndhoven,et al.  Well-posedness of domain integral equations for a dielectric object in homogeneous background , 2008 .

[23]  S. Maci,et al.  Alternative derivation of electromagnetic cloaks and concentrators , 2007, 0710.2933.

[24]  Ari Sihvola,et al.  Surface Integral Equation Method for Scattering by DB Objects with Sharp Wedges , 2011 .

[25]  R. Zich,et al.  Moment method with isoparametric elements for three-dimensional anisotropic scatterers , 1989, Proc. IEEE.

[26]  Weng Cho Chew,et al.  Nyström Method Solution of Volume Integral Equations for Electromagnetic Scattering by 3D Penetrable Objects , 2010, IEEE Transactions on Antennas and Propagation.

[27]  Jin-Fa Lee,et al.  A Nonconformal Volume Integral Equation for Electromagnetic Scattering From Penetrable Objects , 2007, IEEE Transactions on Magnetics.

[28]  Tapan K. Sarkar,et al.  Electromagnetic scattering from dielectric bodies , 1989 .

[29]  Zero Backscattering From Self-Dual Objects of Finite Size , 2009, IEEE Transactions on Antennas and Propagation.

[30]  P. Uslenghi,et al.  Electromagnetic scattering from anisotropic materials, part I: General theory , 1984 .