The Combination Of Calderon Preconditioner And Hierrchical Basis H-Matrix For Solving Electromagnetic Scattering Problems

Method of moments(MoM)-based electric field integral equation(EFIE) solvers are widely used for electromagnetic scattering problems. However, for large-scale electromagnetic scattering problems, the eigenvalues of the electric field integral operator tend to accumulate at zero and infinity, which leads to the condition numbers of impedance matrices generated by EFIE grow rapidly and low iteration convergence rates. The Calderon preconditioner based on Calderon identity is a good solution to this problem. Calderon preconditoner can improve the spectrum property of electric field integral operator and converge rapidly. This proposed preconditoner is applicable to open and closed structures.In this thesis, the Calderon preconditioner is used to improve the properties of electric field integral operator. The impedance matrices of the Calderon-preconditioned EFIE are well-conditioned which makes the MoM system converging rapidly independent of the electrical sizes of the objects. By using the Buffa Christiansen(BC) basis functions, the Calderon preconditioner is compatible with former MoM codes,but the BC basis functions are defined on the barycentric mesh which could increase a good many of the computational complexity and storage requirements. To solve this problem, the Calderon preconditioner and the H~2-matrix method are combined in this thesis. In H~2-matrix method, the impedance matrix is decomposed into admissible blocks and inadmissible blocks according to the admissibility condition. MoM is used to compute the inadmissible blocks directly, while degenerated kernel function is used for admissible blocks.Much more storage requirements can be reduced by using the transfer matrix in the H~2-matrix method. From numerical examples, we can see that the CP-H~2 algorithm can reduce 66.7 percent of memory requirements compared with Method of Moments. Numerical examples demonstrate the accuracy and efficiency of the proposed method.