Method of Moments for 2D Scattering Problems

Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conferences papers.Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers.Gildas Kubické is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction Générale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.

• Preface ixIntroduction xiChapter 1 Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces 11.1 Introduction 11.2 Integral equations 21.2.1 TE and TM polarizations and boundary conditions 21.2.2 Electric and magnetic currents for a 2D problem 31.2.3 Huygens’ principle and extinction theorem 41.2.4 Radar cross-section (RCS) 81.2.5 Normalized radar cross-section (NRCS) 101.3 Method of moments with point-matching method 121.4 Application to a surface 141.4.1 The Dirichlet boundary conditions 141.4.2 The Neumann boundary conditions 161.4.3 General case 171.4.4 Impedance boundary condition 181.5 Forward–Backward (FB) method 191.6 Random rough surface generation 211.6.1 Statistical parameters 211.6.2 Generation of a random profile 231.6.3 Simulations 261.6.4 Conclusion 30Chapter 2 Validation of the Method of Moments For a Single Scatterer 312.1 Introduction 312.2 Solutions of a scattering problem 312.3 Comparison with the exact solution of a circular cylinder in free space 342.3.1 Solution of the Helmholtz equation 352.3.2 Dirichlet boundary conditions 372.3.3 Neumann boundary conditions 392.3.4 Dielectric cylinder 422.3.5 MoM for an elliptical cylinder 452.3.6 Numerical comparisons for a circular cylinder 472.3.7 Conclusion 542.4 PO approximation 552.4.1 Formulation 552.4.2 Applications 562.4.3 Sea-like surface 662.5 FB method 692.6 Conclusion 71Chapter 3. Scattering From Two Illuminated Scatterers 733.1 Introduction 733.2 Integral equations and method of moments 753.2.1 Integral equations for two scatterers 753.2.2 Method of moments for two scatterers 773.2.3 Method of moments for P scatterers 843.3 Efficient inversion of the impedance matrix: E-PILE method for two scatterers 863.3.1 Mathematical formulation 863.3.2 Numerical results 893.4 E-PILE method combined with PO and FB 943.4.1 E-PILE hybridized with FB 943.4.2 E-PILE hybridized with PO 963.5 Conclusion 107Chapter 4. Scattering from two scatterers where only one is illuminated 1094.1 Introduction 1094.2 Integral equations and method of moments 1104.2.1 Integral equations 1104.2.2 Method of moments 1134.2.3 Case for which scatterer 2 is perfectly conducting 1164.2.4 Numerical results 1174.3 Efficient inversion of the impedance matrix: PILE method 1224.3.1 Mathematical formulation 1224.3.2 Numerical results 1234.4 PILE method combined with FB or PO 1284.4.1 PILE hybridized with FB 1284.4.2 PILE hybridized with PO 1304.5 Conclusion 138Appendix MATLAB Codes 139Bibliography 141Index 147