Study On High And Low Frequency Algorithm For Target Electromagnetic Scattering Based On Surfaces Modeling

The study of target electromagnetic scattering is of great significance in both military and civil fields.Radar cross section is a direct reflection of the target's electromagnetic scattering ability,and it is a key physical quantity to measure scattering characteristics of target,the main methods to obtain the radar cross section are experimental measurement and theoretical simulation.Because the experimental measurement requires a lot of manpower and material resources,and the influence of human factors and system errors on the measurement results must be taken into account,the researchers more often use the electromagnetic simulation results to replace the measurement results,so as to save the cost of electromagnetic experiments and shorten the cycle of product design.In this thesis,the high frequency method and numerical method are applied to simulate the electromagnetic scattering from objects.The physical optics method and diffraction theory method based on NURBS modeling,and the higher order method of moments based on interpolation surface modeling and its fast algorithm are studied in this paper.Also a series of optimization methods are proposed to improve the efficiency of electromagnetic simulation.The main work of the thesis includes:To solve the numerical instability problem of traditional NURBS modeling method,a new NURBS surface modeling method based on parametric domain decomposition technique and local support property of B-spline basis is proposed.It doesn't only eliminate the recursive form of B-Spline basis,simplifiy the calculation process of the geometric parameters of the target,but also completely solves the disadvantages of the traditional NURBS modeling method that can not be directly used in electromagnetic calculation because of the numerical instability.Based on the double quadratic B-spline interpolation technique,a new interpolation surface modeling method is proposed,which simplifies the calculation process of the interpolation surface method,makes the modeling method better combined with the electromagnetic simulation algorithm,and improves the modeling efficiency of electromagnetic simulation.The NURBS surface modeling method and the interpolation surface modeling method are unified by B-spline interpolation technique.In order to solve the problem that the calculation time of physical optics method increases rapidly with the frequency of incident wave,a fast calculation method of stationary phase points is proposed based on B-spline surface modeling method.At the same time,the frequency independent characteristic of the physical optics method is realized by the stationary phase method,and the physical optics integral of any high-frequency band can be calculated quickly.Aiming at the problem that the traditional delaminating quadrature method can not consider the shadowing of surface elements,a fast shadowing algorithm based on integral domain decomposition and key point shadowing is proposed.Numerical simulation shows that the proposed algorithm can not only obtain good shadowing results,but also the shadowing time is independent of the incident incident wave frequency.Based on the NURBS modeling method,the terahertz scattering characteristics of the simple electrically large targets are analyzed by using the physical diffraction theory and the stationary phase method(PTD-SPM).Because the simulation time of PTD-SPM algorithm is independent of the frequency of incident wave,it can quickly realize the electromagnetic scattering simulation of simple target with arbitrary electric size,which provides an effective method to estimate the radar cross section from electrically large target.Based on the NURBS modeling method,a numerical algorithm is proposed to trace reflected rays and diffraction rays of UTD.The tracing algorithm can degenerate the two-dimensional ray tracing problem into the solution of one-dimensional nonlinear equation,and simplify the problem of one-dimensional diffraction ray tracing to analytic calculation,which greatly improves the efficiency of ray tracing,and the computation time of ray tracing is independent of the incident wave frequency.In order to solve the singularity problem of impedance element integral,a fast method is proposed to calculate the singular integrals by using Duffy transformation.This method can not only calculate the singular integral accurately,but also have the same computational complexity as the nonsingular integral.Based on the far region approximation method of Green function,the four-fold far region impedance integral is simplified to the calculation of double integral,which doesn't only ensures the calculation accuracy,but also improves the filling efficiency of impedance matrix.In order to solve the problem that the traditional Krylov subspace iteration method is difficult to converge,the condition number of the matrix equation is reduced by using the near region preconditioning technique,and the caculation process of the GMRES is accelerated by the sparse matrix LU decomposition method,which greatly improves the iterative convergence efficiency.A fast method based on the multilevel far region approximation(MLFRA)algorithm is proposed to calculate the matrix vector product.The MLFRA algorithm uses multi-layer aggregation,transfer,and configuration to calculate matrix vector product of far region grid,while the matrix vector product of near region grid can be transferred to the last layer of grid and caculated by traditional method.MLFRA algorithm can not only guarantee the calculation accuracy,but also improve the efficiency of iterative solution by 40%.The method of layer by layer transfer can maximize the advantage of MLFRA,but the condition of far region group of MLFRA is more strict than that of FMM,which makes the proportion of the near zone group of MLFRA method is larger than that of the FMM,so we can use FMM to further accelerate the matrix vector product of near zone group in MLFRA.Numerical results show that the acceleration efficiency of FMM to MLFRA is lower than that of MLFRA to HOMoM,but it can still improve the efficiency of iterative method.