Research On Fast Hybrid Algorithm For Composite Electromagnetic Scattering From Rough Surface And Target Based On FEM

Study on the composite electromagnetic scattering from target and rough surface has developed into an important issue because of its extensive application in remote sensing,target recognition and radar monitoring.The finite element method(FEM)is a numerical technique for obtaining approximate solutions to boundary-value problems.The basic idea of FEM is to discretize the entire continuous region into finite number of subdomains and represent the unknowns in each subdomain with interpolation functions.Then the solution to the boundary-value problem can be obtained by solving the matrix equation obtained by the Ritz method or Galerkin method.FEM is a powerful tool for dealing with the inhomogeneous medium problems.To study the composite scattering between target and rough surface,the fast hybrid methods based on the FEM are investigated in detail in this thesis.Main works of this thesis can be summarized as follows.The two-dimensional(2-D)scalar FE-BI-FMM is introduced into the study of electromagnetic scattering from one-dimensional(1-D)dielectric rough surface and 2-D coated target.The composite electromagnetic scattering from coated targets on or above a single or layered rough surface under the incident of different polarization waves are mainly considered.To obtain the scattering information of the model efficiently,a hybrid solver combining parallel LU decomposition with the generalized minimum residual method(GMRES)is adopted to solve the FEM-BIM matrix equation.And the fast multipole method is used to speed up the matrix-vector multiplication in GMRES,which can further improve the computational efficiency and reduce the memory requirements.To investigate the composite scattering characteristics of coated targets and rough surface,three-dimensional(3-D)vector FE-BI-FMM based on Tetrahedral edge basis function is developed for the electromagnetic scattering from single or multiple coated targets above/under 2-D conductor/dielectric rough surface.The FE-BI-FMM formulas for different scattering conditioins are derived.The validity of our method is verified by comparing the results with that of method of moment(MoM)and conventional FEM-BIM.The numerical results also show that FE-BI-FMM is superior to the traditional FEM-BIM in terms of computational efficiency and memory requirement,and is an efficient algorithm for dealing with the composite electromagnetic scattering from rough surface and coated target.A multi-hybrid method combining vector FEM-BIM and analytic Kirchhoff approximation(KA)is developed to investigate the composite electromagnetic scattering characteristics of 3-D electrically large coated target above/below 2-D conductor/dielectric rough surface.The FEM-BIM is applied to model the scattering from the coated target while the scattering from the rough surface is studied by KA.The multiple interactions between the coated target and rough surface are taken into account by updating the electric and magnetic current densities on them.The FMM and OpenMP parallel acceleration technology are used to accelerate the iterative solution process of the hybrid method,which can greatly improve the efficiency of the algorithm.Finally,using the coated missile,NASA almond and torpedo-type targets as examples,the radar cross section(RCS)and difference field radar cross section(d-RCS)of the composite model under the incident of TE and TM polarization waves are numerically calculated.The validity and efficiency of our algorithm are verified by comparing the results with that of the FE-BI-FMM and the image Green's function method.The time domain finite element method(TDFEM)is introduced into the study of the composite scattering from the rough surface and target.The perfectly matched layer(PML)is chosen as the truncation boundary of the FEM region to absorb the outgoing wave scattered by the composite model with no reflection.A total field boundary which splits the whole region into total and scattered field region is built around the composite model.In the total field region which contains the scatterers,the total filed formula is used.Meanwhile,in the scattered field region which contains the PML,the scattered field formula is used.The bistatic scattering coefficient and transient far-field response of a target above a 1-D conductor rough surface under the incident of the time-harmonic source and the pulsed wave source are calculated,respectively.The validity of our method is verified by comparing the results with that of MoM and time domain integral equation(TDIE)method.Because of the flexibility of FEM,TDFEM-PML has certain advantages in dealing with the scattering from multiple targets and rough surface.However,since the PML needs to be set at a certain distance from the composite model and the whole computational domain need to be meshed,the computational resource consumption is serious.