Calderón Multiplicative Preconditioned EFIE With Perturbation Method

In this paper, we address the low-frequency breakdown and inaccuracy problems in the Calderón multiplicative preconditioned electric field integral equation (CMP-EFIE) operator, and propose the perturbation method as a remedy for three-dimensional perfect electric conductor (PEC) scatterers. The electric currents at different frequency orders as a power series can be obtained accurately in a recursive manner by solving the same matrix system with updated right hand side vectors. This method does not either require a search for the loops in the loop-tree/-star based method or include charge as additional unknown in the augmented EFIE method. Numerical examples show the far-field pattern can be accurately computed at extremely low frequencies by the proposed perturbation method.

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

[2]  R.J. Adams,et al.  Physical and analytical properties of a stabilized electric field integral equation , 2004, IEEE Transactions on Antennas and Propagation.

[3]  Weng Cho Chew,et al.  Magnetic field integral equation at very low frequencies , 2003 .

[4]  B. Dembart,et al.  Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering , 2002 .

[5]  Giuseppe Vecchi,et al.  Loop-star decomposition of basis functions in the discretization of the EFIE , 1999 .

[6]  G. Vecchi,et al.  Spectral Properties of the EFIE-MoM Matrix for Dense Meshes With Different Types of Bases , 2007, IEEE Transactions on Antennas and Propagation.

[7]  R. Kleinman,et al.  Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics , 1997 .

[8]  Jian-Ming Jin,et al.  EFIE Analysis of Low-Frequency Problems With Loop-Star Decomposition and Calderón Multiplicative Preconditioner , 2010, IEEE Transactions on Antennas and Propagation.

[9]  Weng Cho Chew,et al.  An augmented electric field integral equation for high‐speed interconnect analysis , 2008 .

[10]  D. De Zutter,et al.  Low frequency scaling of the mixed MFIE for scatterers with a non-simply connected surface , 2011, 2011 International Conference on Electromagnetics in Advanced Applications.

[11]  Weng Cho Chew,et al.  Fast Full-Wave Surface Integral Equation Solver for Multiscale Structure Modeling , 2009, IEEE Transactions on Antennas and Propagation.

[12]  N. Champagne,et al.  A numerical implementation of a modified form of the electric field Integral equation , 2004, IEEE Transactions on Antennas and Propagation.

[13]  S. Orszag,et al.  Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory. , 1999 .

[14]  Weng Cho Chew,et al.  On the Dual Basis for Solving Electromagnetic Surface Integral Equations , 2009, IEEE Transactions on Antennas and Propagation.

[15]  J. Fostier,et al.  Combining Calderón preconditioning with Fast Multipole Methods , 2010, 2010 IEEE Antennas and Propagation Society International Symposium.

[16]  Roger F. Harrington,et al.  An E-Field solution for a conducting surface small or comparable to the wavelength , 1984 .

[17]  Weng Cho Chew,et al.  An augmented electric field integral equation for low frequency electromagnetic analysis , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[18]  E. Michielssen,et al.  Nullspaces of MFIE and CalderÓn Preconditioned EFIE Operators Applied to Toroidal Surfaces , 2009, IEEE Transactions on Antennas and Propagation.

[19]  Jin-Fa Lee,et al.  Loop star basis functions and a robust preconditioner for EFIE scattering problems , 2003 .

[20]  E. Michielssen,et al.  A Calderón-Preconditioned Single Source Combined Field Integral Equation for Analyzing Scattering From Homogeneous Penetrable Objects , 2011, IEEE Transactions on Antennas and Propagation.

[21]  Jin-Fa Lee,et al.  Preconditioned Electric Field Integral Equation Using Calderon Identities and Dual Loop/Star Basis Functions , 2009, IEEE Transactions on Antennas and Propagation.

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

[23]  E. Michielssen,et al.  A CalderÓn Multiplicative Preconditioner for the Combined Field Integral Equation , 2009, IEEE Transactions on Antennas and Propagation.

[24]  D. Wilton,et al.  Electromagnetic scattering by three-dimensional arbitrary complex material/conducting bodies , 1990, International Symposium on Antennas and Propagation Society, Merging Technologies for the 90's.

[25]  Paola Pirinoli,et al.  Application of numerical regularization options to the integral-equation analysis of printed antennas , 1997 .

[26]  E. Michielssen,et al.  A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation , 2008, IEEE Transactions on Antennas and Propagation.

[27]  T. Eibert.  Iterative-solver convergence for loop-star and loop-tree decompositions in method-of-moments solutions of the electric-field integral equation , 2004 .

[28]  W. Chew,et al.  Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies , 2000 .

[29]  D. Levadoux,et al.  A new well-conditioned Integral formulation for Maxwell equations in three dimensions , 2005, IEEE Transactions on Antennas and Propagation.

[30]  Weng Cho Chew,et al.  Enhanced A-EFIE With Perturbation Method , 2010, IEEE Transactions on Antennas and Propagation.