Study Of Absorbing Boundary Conkition And Its Applications

Absorbing boundary conditions(ABC) in frequency domain and their applications are studied systematically in this thesis. In chapter two, based on the property of uniform plane wave, field at boundary node is expressed with field in the computation region and expanded as Taylor抯 series. By truncating it at second order, a concise ABC is obtained. This condition involves only three nodes located on the line which is perpendicular to the mesh boundary. So it is suitable for not only rectangular grid but also curvilinear grid system. In addition, it can be applied to both two and three dimensional problems. In chapter three, one way wave equation in frequency domain is obtained from that in FDTD and approximated at second order. After some theoretical derivation, another second order ABC in both Cartesian system and circular cylindrical system is achieved for two dimensional problems. Finally, the results are extended to three dimensional problems. The analysis of this chapter has lay a foundation for higher order ABC. It is shown, all above ABCs have precision of o(h2) for out going plane wave. In chapter four, on truncating the one way wave equation and approximating partial derivatives in it at fourth order, a kind of two dimensional fourth order ABC is derived in Cartesian system and circular cylindrical system respectively. The error of this ABC for out going plane wave is much smaller than fore-mentioned ABCs. Precision of 0(h4) is shown. Measured Equation of Invariance(MEI) is a novel numerical approach in electromagnetic field calculations. This approach can bring the mesh boundary very close to the physical boundary of the object. But some theoretical defects of it have to be concerned. In chapter five, theory of M1EI is analyzed and its defects are demonstrated. Several instructive conclusions are given. From chapter six through eight, ABCs obtained in this thesis are applied to two dimensional scattering problems such as perfectly conducting cylinders, dielectric cylinders and dielectric covered conducting cylinders. Numerous numerical results are obtained. All the results show that the ABCs are correct and applicable. In chapter nine, as new application of MEl, it is used to analyze the static field problem -transmission line with round outer conductor. Good agreement between the results and that available is shown. If the Green's function can be found, the analyzing method in this chapter is suitable for transmission lines with complex shaped outer conductor too.