H~2-matrix-based Method For Fast Solving The Wire-surface-volume Integral Equation

The electromagnetic field numerical calculation method is widely used to solve practical electromagnetic problems now. Usually objects to be solved are regarded as perfect electric conductors or homogeneous dielectrics. The surface integral equation(SIE) is used to solve perfect electric conductors and homogeneous dielectric scattering problems. However, SIE can not be used to solve the electromagnetic problem of inhomogeneous media. So it is necessary that the establishment of effective integral equations to solve scattering problems of conductor and inhomogeneous dielectrics.On the basis of the method of moments(MoM), this thesis establishes an effective electric field integral equation of wire/surface/volume configuration to solve electromagnetic problems of conductor and inhomogeneous dielectrics. The electric field integral equation is solved by the method of moments directly, which needs O(N2) storages and O(N3) computation complexities respectively. Impedance matrix is divided into near-field region and far-field region based on admissible condition. To improve the efficiency of computing, the far field matrix blocks are obtained by using degenerate kernel function which adopts Lagrange interpolation polynomials. So that the computational complexity and storage can be reduced. Then, this thesis develops the H2-matrix method to solve electric field integral equation of wire/surface/volume configuration. The correctness and effectiveness of the algorithm were validated.Finally, the radar cross section and radiation pattern of different models are calculated by our program. Numerical results show that H matrix algorithm can improve both the computational complexity and storage to O(NlogN).