| According to the Calderon relation of electrical field integral operator and magnetic fieldintegral operator, Calderon multiplicative preconditioner which is applicated in the electric fieldintegral equation method is studied. In order to reduce the enormous storage generated by theCalderon multiplicative preconditioner, the hierechical matrix fast algorithm is introduced to reducethe storage and speed up the multiplication of matrix and vector.The thesis firstly introduces the establishment of the electric field integral equation andmagnetic field integral equation. The basic principle of method of moments which contains theselection of basis functions and testing functions is presented to build the linear equations.According to the basic theory of electromagnetic field and the equivalence principle identities,Calderon relation is deduced. RWG basis functions and BC basis functions are used to discretize theCalderon preconditioner operators. The linear relationship between BC basis functions and RWGbasics functions defined on the barycentric mesh is deduced. The BC basis functions are defined onthe barycentric mesh which leads to significantly increased storage. To alleviate this problem, the Hmatrix is introduced. The H matrix is divided into so called near-blocks and far-blocks according toadmissibility condition. The near-blocks which dissatisfy the admissibility condition are directlycalculated with MoM. The far-blocks which satisfy the admissibility condition are obtained byLagrange interpolations. The layers of H matrix, admissibility coefficient and Lagrangeinterpolations are analyzed to control the accuracy. At last the Calderon multiplicativepreconditioner, combined with hierechical matrix fast algorithm is used to deal withelectromagnetic scattering problems of perfect conductor. The numerical results demonstrate thatthe CMP-H fast algorithm calculate accurately, converges rapidly and needs less memory. |
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