A Weak-Form Combined Source Integral Equation With Explicit Inversion of the Combined-Source Condition

The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest order Rao–Wilton–Glisson basis and testing functions if the combined-source (CS) condition is enforced in a weak form. We introduce a technique to accelerate the iterative solution for this kind of CSIE. It is demonstrated that the iterative solution of the equation system can be performed very efficiently by explicitly inverting the weak-form CS condition in any evaluation of the forward operator. This reduces the number of unknowns and results in improved convergence behavior at negligible linear cost. Numerical results demonstrate that the new CSIE outperforms the classical combined field integral equation for high-accuracy simulations.

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

[2]  Marion Darbas,et al.  Generalized combined field integral equations for the iterative solution of the three-dimensional Maxwell equations , 2006, Appl. Math. Lett..

[3]  Levent Gurel,et al.  Validation through comparison: Measurement and calculation of the bistatic radar cross section of a stealth target , 2003 .

[4]  P. Yla-Oijala,et al.  Stable Discretization of Combined Source Integral Equation for Scattering by Dielectric Objects , 2012, IEEE Transactions on Antennas and Propagation.

[5]  Olaf Steinbach,et al.  Modified Combined Field Integral Equations for Electromagnetic Scattering , 2009, SIAM J. Numer. Anal..

[6]  L. Gurel,et al.  Investigation of the inaccuracy of the MFIE discretized with the RWG basis functions , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[7]  X. Antoine,et al.  GENERALIZED COMBINED FIELD INTEGRAL EQUATIONS FOR THE ITERATIVE SOLUTION OF THE THREE-DIMENSIONAL HELMHOLTZ EQUATION , 2007 .

[8]  V. Okhmatovski,et al.  Novel Single-Source Surface Integral Equation for Scattering Problems by 3-D Dielectric Objects , 2018, IEEE Transactions on Antennas and Propagation.

[9]  D. R. Wilton,et al.  E-Field, H-Field, and Combined Field Solution for Arbitrarily Shaped Three-Dimensional Dielectric Bodies , 1990 .

[10]  T. Eibert,et al.  A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals , 2005, IEEE Transactions on Antennas and Propagation.

[11]  Yan Shi,et al.  An Efficient Single-Source Integral Equation Solution to EM Scattering From a Coated Conductor , 2015, IEEE Antennas and Wireless Propagation Letters.

[12]  Allen W. Glisson,et al.  An integral equation for electromagnetic scattering from homogeneous dielectric bodies , 1984 .

[13]  Egon Marx,et al.  Single integral equation for wave scattering , 1982 .

[14]  Peter Werner,et al.  Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung , 1965 .

[15]  Jens Markus Melenk,et al.  Mapping Properties of Combined Field Helmholtz Boundary Integral Operators , 2012, SIAM J. Math. Anal..

[16]  Utkarsh R. Patel,et al.  A Novel Single-Source Surface Integral Method to Compute Scattering From Dielectric Objects , 2016, IEEE Antennas and Wireless Propagation Letters.

[17]  Roger F. Harrington,et al.  A combined-source solution for radiation and scattering from a perfectly conducting body , 1979 .

[18]  Michael S. Yeung,et al.  Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects , 1999 .

[19]  R. Harrington.  Boundary integral formulations for homogeneous material bodies , 1989 .

[20]  Ralf Hiptmair,et al.  Regularized Combined Field Integral Equations , 2005, Numerische Mathematik.

[21]  Thomas F. Eibert,et al.  A Combined Source Integral Equation With Weak Form Combined Source Condition , 2018, IEEE Transactions on Antennas and Propagation.

[22]  T.F. Eibert,et al.  Surface Integral Equation Solutions by Hierarchical Vector Basis Functions and Spherical Harmonics Based Multilevel Fast Multipole Method , 2009, IEEE Transactions on Antennas and Propagation.

[23]  V. Okhmatovski,et al.  New Single-Source Surface Integral Equations for Scattering on Penetrable Cylinders and Current Flow Modeling in 2-D Conductors , 2013, IEEE Transactions on Microwave Theory and Techniques.