Improved Discretization of the Full First-Order Magnetic Field Integral Equation

The inaccuracy of the classical magnetic field integral equation (MFIE) is a long-studied problem. We investigate one of the potential approaches to solve the accuracy problem: higher-order discretization schemes. While these are able to offer increased accuracy, we demonstrate that the accuracy problem may still be present. We propose an advanced scheme based on a weak-form discretization of the identity operator which is able to improve the high-frequency MFIE accuracy considerably — without any significant increase in computational effort or complexity.

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

[2]  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..

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

[4]  First Order Triangular Patch Basis Functions for Electromagnetic Scattering Analysis , 2001 .

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

[7]  Thomas F. Eibert,et al.  Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method , 2014 .

[8]  Din-Kow Sun,et al.  Construction of Nearly Orthogonal Nedelec Bases for Rapid Convergence with Multilevel Preconditioned Solvers , 2001, SIAM J. Sci. Comput..

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

[10]  Juan M. Rius,et al.  Accurate, grid-robust and versatile combined-field discretization for the electromagnetic scattering analysis of perfectly conducting targets , 2020, J. Comput. Phys..

[11]  Low-frequency stability of the Razor blade tested MFIE , 2013, 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[12]  Ozgur Ergul,et al.  The use of curl-conforming basis functions for the magnetic-field integral equation , 2006 .

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

[14]  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.

[15]  Thomas F. Eibert,et al.  A Weak-Form Combined Source Integral Equation With Explicit Inversion of the Combined-Source Condition , 2018, IEEE Antennas and Wireless Propagation Letters.

[16]  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.

[17]  Seppo Järvenpää,et al.  Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods , 2005 .

[18]  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 .

[19]  E. Ubeda,et al.  Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects , 2006, IEEE Transactions on Antennas and Propagation.

[20]  Thomas F. Eibert,et al.  An Accurate Low-Order Discretization Scheme for the Identity Operator in the Magnetic Field and Combined Field Integral Equations , 2018, IEEE Transactions on Antennas and Propagation.

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

[22]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

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

[24]  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.

[25]  Özgür Ergül,et al.  Discretization error due to the identity operator in surface integral equations , 2009, Comput. Phys. Commun..

[26]  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.

[27]  Andrew F. Peterson,et al.  Solution of the MFIE using curl-conforming basis functions , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).