Study And Applications Of Volume-surface Integral Equation And Fast Solvers In Complicated Electromagnetic Problems

To analyze complicated electromagnetic objects efficiently and accurately is always one of the challenging problems in computational electromagnetics. Firstly, the volume-surface integral equation (VSIE) is established to solve composite conducting and dielectric problems, then, in order to the solve the VSIE efficiently, numerical methods including the precorrected-fast Fourier transform (P-FFT) method, characteristic basis function method (CBFM), combined CBFM/P-FFT algorithm and P-CBFM/P-FFT algorithm are studied, and applied to solve electromagnetic scattering and radiation problems of complicated bodies.At first, the VSIE formulation is deduced based on equivalence theorem and boundary condition. Besides, by using different boundary condition at the interface of the conductor and dielectric, two approaches of the VSIE including the non-coupled VSIE (NCVSIE) and the coupled VSIE (CVSIE) are discussed and analyzed. Then, from the compared results using the two approaches to analyze scattering, radiation and circuit problems respectively, it can be concluded that, the performance of the CVSIE is much better than that of NCVSIE for radiation and circuit problems, additionally, the offset problem of resonant frequency can be settled appropriately to an acceptable extent using the CVSIE formulation.Then, in order to accelerate the iterative procedure for solution, the P-FFT algorithm is presented, and combined with surface integral equation (SIE), volume integral equation (VIE) and VSIE respectively, to analyze typical scattering and radiation problems, which indicates the accuracy and efficiency of the algorithm.Besides, in order to reduce the number of unknowns availably, CBFM method is introduced to solve the VSIE. Two methods used to retrieve the characteristic basis function (CBF) are discussed and compared. Then, the CBFM is utilized to analyze the scattering and radiation characteristics of conducting, dielectric and mixed conducting-dielectric objects, which shows the accuracy and generality of CBFM.Additionally, the P-FFT process is introduced to combine with the CBFM algorithm, so as to speed up the iterative procedure. Then the combined CBFM/P-FFT is applied to analyze non-periodic objects, and the accuracy of the combined algorithm has been validated by examples. For the scale of problem analyzed is not large enough, it is difficult to demonstrate the efficiency of CBFM/P-FFT, however, from the calculated results, it can be observed that less memory is required for CBFM/P-FFT than P-FFT and CBFM, and less iterative time is needed for CBFM/P-FFT than P-FFT.To calculate finite periodic structures efficiently, a combined CBFM and P-FFT algorithm which is called P-CBFM/P-FFT, is presented to solve VSIE. A near correction model is introduced to consider the mutual coupling between nearby units. Some large-scale examples about scattering of mixed metallic-dielectric periodic arrays, are illustrated to demonstrate the efficiency and accuracy of the algorithm, based on which, a novel efficient algorithm is provided to analyze periodic structures with dielectric connected between units, the accuracy of the algorithm has been demonstrated by some examples.After the studies above, the fast solvers and basis function methods developed in the paper are applied to analyze complicated electromagnetic problems including: mutual coupling between antennas and circuits, radiation of multi-layer microstrip antenna and conformal antenna arrays by P-FFT algorithm, large antenna array with wide bandwidth by P-CBFM/P-FFT algorithm, radiation of microstrip antenna mounted on helicopter by CBFM method, scattering and transmission characteristics of photonic crystals by P-CBFM/P-FFT algorithm. By comparing the calculated results to analytical solution, measurement or results from references, the accuracy, efficiency and universality of the algorithms are demonstrated. It can be concluded that, an efficient and accurate scheme has been provided in the thesis for the solution of complicated electromagnetic problems.