Parabolic Equation In Electromagnetic Scattering Analysis

The rigorous techniques like the method of moments (MOM), the finite element method (FEM) or the finite difference time domain (FDTD) method work well for small objects, but become prohibitively expensive in computer resources. Approximate methods based on ray-tracing or physical optics(PO) which are often used for large objects,are only effective for regularly shaped bodies, and the error is big relatively. The parabolic equation (PE) method provides a bridge between these techniques. PE is an approximation of the wave equation which models energy propagation in a cone centered on a preferred direction, which is named the parabolic direction.The article mainly focuses on the basic derivation and application of the parabolic equation method. The main studies are as follows:First, The Parabolic Equation theoretics are deduced, including:two-dimension forward parabolic equation, two-dimension backward parabolic equation, the parabolic equation in the cylindrical coordinates, three-dimension standard parabolic equation and vector parabolic equation.For solving the parabolic equation, we use the difference method because the parabolic equation is differential equation. As for the scatting problem of the two-dimension object, we introduce the Crank-Nicolson formula and the pade-(1,0) formula in the free space. Then we give the theory of perfectly match layer (PML), and deduce the Crank-Nicolson formula and the pade-(1,0) formula in the PML. We also introduce the rotating PE algorithm because the regular PE is exact in the small angle area. We can get the accurate result in the whole area by rotating the incident direction and resetting the boundary conditions on the object.As for the three-dimension object, the pade-(1,0) formulas in the free space and in the PML are deduced. A problem in the three-dimension scatting is the number of the unknowns is very large, which leads the difficulty when solving the matrix equation. In the dissertation, we introduce the method of solving the large sparse matrix. At the end of the chapter, we also give the Double Pass method.At the end of the dissertation, we introduce a method which can transform the data on the triangle gridding to the data on the cube gridding. Using the method, we can solve the problem expediently, because we can get the data which using in the PE method automatically, have no use of handcraft or half- handcraft constructing the model, and we can reduce the workload and construct the universal mode. The PE method is the important theory of the electromagnetic scattering and the design of the radar, which have the magnitude sense in the radar explore and the object identify.