Research Of Efficient Algorithm On Solving Surface Integral Equations

The electromagnetic scattering from a target is very important in many fields of engineering, such as modern radar guidance and interception technology, the target stealth technology, radar target recognition, underground target exploration. Integral method is a very important tool in analyzing electromagnetic fields because of its high precision, and has attracted much attention in the application of electromagnetic scattering problems. The accurate modeling and efficient solving of the electromagnetic scattering from the electrically large 3-D targets, complex object composed by the conductor and dielectric, and the perfect electric conductor (PEC) in complex electromagnetic environment, are studied in this thesis, which are based on the theories of electromagnetic surface integral equation method and supported by the theories of higher order basis functions in the frequency domain and the temporal basis functions in the time domain.The first part is some basic theories of this thesis, including the fundamentals and the theoretical deductions of the electromagnetic surface integral equations’ methods. The establishment course and the solving process of the frequency and time domain surface integral equations for the PEC have been studied. Next, the discretization scheme of generalized curvilinear parametric triangles, some type of spatial basis functions which defined on the parametric triangles, and the temporal basis functions are introduced, respectively. Finally, the expression of the impendence matrix elements for frequency and time domain surface integral equations are presented.The second part of this thesis systematically studied the accurate computation of the impedance matrix elements of the time and frequency domain integral equation methods. Based on the singularity cancellation methods for the weak singularities of the electric field integral equation and the near strongly singular integrals of the magnetic field integral equation on the plane triangular element, the concrete implementation process of singularity cancellation technique in time domain and frequency domain integral equation method is discussed in a unified way. The technique of canceling the singularity on the parametric curved triangular modeling has been proposed in this part, further we promote it to the time domain surface integral equation method. The singularity cancellation method breaks the limits of basis functions, elements shapes and curvature both in the frequency and time domain integrals. The numerical results demonstrate the precision and convergence speed of the singularity cancellation method.In the third part, the applications of the higher order hierarchical vector basis functions (HOBFs) that based on the curvilinear triangular elements in the frequency domain surface integral equations are studied, and that given the name of higher order surface integral equation method (HOSIEM). Firstly, by the method of higher order basis functions as the foundation, and according to a new type of curl-conforming HOBFs in the finite element method (FEM), a new set of divergence-conforming HOBFs is derived in this thesis. The proposed divergence-conforming HOBFs are proved to have the good iteration convergence properties by comparing the condition number of impedance matrix with other sets of divergence-conforming higher order hierarchical vector bases. A hybrid modeling technique that based on HOBFs is also studied. And the numerical results show that the computer resource utilization has been improved by using the hybrid modeling technique. In order to analysis the electromagnetic scattering problems efficiently, the constructions of surface integral equations based on the equivalence principle and the boundary conditions, are discussed for the perfect electrical conductor (PEC) targets, the homogeneous dielectric targets, and the combined conductor-dielectric targets in free space, and for PEC targets in planar layered media, respectively. In order to give the selecting principle of the higher order MoM, some calculation parameters, such as the size of discretized elements, the number of gauss integral points, which have great effect on the efficiency and accuracy of the results, have been analyzed. Numerical example showed that through reasonably choosing the order of basis functions, the size of triangular elements, and the number of gauss integral points, the HOSIEM can reducing the total number of unknown, and have high precision and calculation efficiency at the same time. In order to improve the ability of HOSIEM for the electrically large targets, some fast algorithms have been studied in this part. For the electrically large targets in free space, the combination of the multilevel fast multiple algorithm (MLFMA) with the HOSIEM has been studied. For the electrically large PEC targets in planar layered media, the method of the adaptive cross algorithm (ACA) combined with the HOSIEM has been proposed. To improve the efficiency of higher order MLFMA and higher order ACA with large patches, a detailed discussion for grouping and parameters and the referenced principle are given by the numerical examples.In the last part of this thesis, the accurate modeling and efficient solution of the time domain integral equation (TDIE) methods for the transient scattering problems has been studied. Aimed at resolving the time domain simulation by the electrically large PEC objects, and based on the physical properties of the time domain induced surface current and the theory of the frequency domain asymptotic phase basis functions, a kind of space delayed temporal basis functions is proposed in this thesis. The space delayed temporal basis functions combined with the CRWG or higher order spatial basis functions can efficiently approximate the time domain induced surface current using much fewer unknowns. By using the space delayed temporal basis functions, the calculation of the singular integrals of the time domain impedance matrix elements become difficult. In order to calculate the time-domain impedance matrix elements, the usage of singularity cancellation technique based on the curvilinear triangular elements is necessary. Numerical results demonstrated that the new MOT-based TDIE method with the space-delayed temporal basis functions can greatly reduce the number of spatial unknowns when compared with the conventional MOT-based TDIE method for the transient analysis of electromagnetic scattering from the PEC objects with large smoothly surface.