Application Of Parabolic Equation To Electromagnetic Scattering

Recently, the electromagnetic scattering analysis is a discipline that is becomingincreasingly important in electrical engineering. The development of fast andefficiency algorithms for scattering analysis of complex objects is important in boththeory and practice.Rigorous techniques like the method of moments (MOM) or the finite difference timedomain (FDTD) method work well for small objects, but become prohibitivelyexpensive in computer resources for large objects. Approximate methods based onray-tracing or physical optics (PO), which are often used for large objects, are onlyeffective for regularly shaped bodies. The parabolic equation (PE) method provides abridge between these techniques. PE is an approximation of the wave equation whichmodels energy propagation in a cone centered on a preferred direction, which isnamed the paraxial direction. By the absorbing boundary conditions (ABC) placed onthe top and the bottom of the computational area, the solution is marched in thatdirection from one transverse plane to the next, thus reducing the fullthree-dimensional problem to a sequence of two-dimensional calculations, whichenhance the efficiency of computing greatly. Using PE method can avoid theproblems of the limitation of computation time and memory of computer by theserigorous methods. It can also reduce the error caused by the high-frequencyapproximation.The dissertation mainly focuses on various type of PE algorithms used in computingelectromagnetic, and the main work in this paper can be described as follows:●The Parabolic Equation algorithms are deduced carefully and different kinds ofPE algorithms are introduced, including two-dimension standard parabolicequation, two-dimension backward standard parabolic equation, three-dimensionstandard parabolic equation and vector parabolic equation.●Two kinds of absorbing boundary conditions are introduced and analyzed indetail: Perfectly Matched Layer (PML) based on "stretched coordinate" and Non-localBoundary Condition(NLBC). Numerical results show that theycan work with different parabolic equation algorithms to handle notonly unbounded space electromagnetic wave propagation problems withdifferent incidence angle but compute scattering problems, and theadvantages and weaknesses of the two kinds of absorbing boundaryconditions are also compared.●The linear least square approximation method is proposed to improvethe accuracy of the Taylor series for the radical expression of thepseudo-differential operators in the standard parabolic equation.●The wide-angle claerbout parabolic equation in free space and PML isdeduced from wave equation, so that the effective computational anglebecomes 0～40°, which is expanded to near 50°by the improvement ofthe two order Taylor series. It is the foundation for the solutionof the scattering problem for electrically large objects in actualengineering.●The PE algorithms combined with two kinds of absorbing boundaryconditions are applied in computing the radar cross sections (RCS)of some regular shaped objects.The PE algorithms are proved inaccuracy by comparing the results obtained with that of other methodslike theory results or MOM, and the limitations and some improvementsof the PE algorithms are also clarified.The research into PE method offers an important theory foundation for thescattering analysis of object and the radar designation. It is of greatimportance in many respects, such as enhancing the identify ability ofthe radar, strengthening the viability of object and researching on thestealth and anti-stealth technique, radar detecting and radar targetrecognition.