| The Finite Element Method (FEM) is widely applied in the field of computational electromagnetics (CEM) since its certain superiority in modeling and mesh. Especially for open domain and radiation problems, the FE-BI method that formed by combining FEM with boundary integral method (BI) presents high precision and is also been widely recognized in CEM. However, with the continuous development of the electromagnetics and its engineering application, the electrical size of objects is increasing, and difficulties in analysis of scattering problems with incident source over a broad frequency band or a wide angle range are still existed It means that there is still space for improvement. Based on compressed sensing (CS) theory, some issues such as building an underdetermined equation model for solving FE-BI, rapid scattering analysis of objects illuminated by incident wave over wide angle range or wide frequency band, are discussed. The main work can be summarized as following:Firstly, the basic theory frameworks of compressed sensing are discussed, three basic steps of it are briefly introduced, and the validity of the CS theory is demonstrated through numerical examples.Secondly, a new incident source suitable for calculation by FE-BI is formed, in which rich spatial information is included. The new incident source is used for rapid analysis of the electromagnetic scattering problems over a wide angle. The effectiveness of the new incident source is demonstrated by numerical analysis of perfectly electrical conductor (PEC) objects and a PEC objects covered with homogenous medium.Thirdly, the asymptotic waveform evaluation(AWE) technique is introduced to solve scattering problems under the new incident source, and s new efficient algorithm based on FE-BI for solving electromagnetic scattering characteristics in both spatial and frequency domain. Numerical experiments are carried out to support the theory.Finally, a new computational model for solving an undetermined equation extracted from FE-BI equations is proposed based on CS theory. In this model, the sparse coefficients matrix in FE-BI is treated as the measurement matrix in CS, and the excitation vector is considered as the observations. With the help of sparse transform techniques and the recovery algorithms, fast solution of the undetermined equations can be achieved. Numerical results showed that the new method can reduce the computation scale with high accuracy, thus can save computer memory and improve computational efficiency. |
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