| For almost half a century, CEM (Computational Electromagnetics), as an effective method to solve electromagnetic problem, has gained tremendous development. Now there are two kinds of developing trend in CEM, one is how to solve the emerging new problems; the other is how to accelerate the calculation speed. This thesis, which focuses on the above two trends, can be divided into three parts:In the first part, a new single integral equation for homogeneous dielectric object is proposed. The unknown number is halved compared to double integral equations. Further more, the new equation reduces the singularity of the integral core by avoiding gradient of Green's function. The numerical results of RCS (Radar Cross Section) obtained from several dielectric objects with large permittivity are in agreement with the exact results. The validity of the new single integral equation is also discussed.In the second part, CUDA (Compute Unified Device Architecture) technology is applied to calculate the impedance matrix for electromagnetic scattering from metal object. An optimization based on the unique architecture of CUDA is carried out. Comparing to the codes totally running on CPU, the CUDA codes could apparently lower the occupancy rate of CPU and increases the calculation speed by 11 times. Source codes are available in the appendix.In the third part, a volume integral equation is proposed to solve the inhomogeneous multi-objects problems. The physical interpretation of this equation is that no matter how many objects there are, it can be treated as electromagnetic scattering from a single object. The derivation of impedance matrix is presented in details. The numerical treatment to different singular integral and how to choose the unknown function are also discussed.
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