The Research On Late Time Unstability In Time Domain Integral Equation And Its Application

The integral equation attracted extensive attention since it can satisfy the radiation boundary conditions automatically and only the target surface is required to be discretized. With the development of computer, the field of research and application of integral equation is expanded. And the integral equation method has being an important tool to analysis the electromagnetic problems.Firstly, we introduce the theory of moment of methods (MOM) to study the basis functions of frequency domain integral equation. And then the solution for Hallen's equation, and the electrical field integral equation (EFIE), magnetic field integral equation (MFIE) and the combined field equation (CFIE) for two-dimensional are deduced. The inverse discrete Fourier transform in conjugation with MOM for analysis the transient scattering problems is also introduced.Secondly, time domain integral equation (TDIE) method based on marching on in time (MOT) is introduced to analysis the thin straight wire. And the explicit and implicit scheme of the TD-EFIE,TD-MFIE and TD-CFIE is deduced, which is used to scattering analysis of two-dimensional objects illuminated by a Gaussian plane wave pulse. Both the TM and TE mode are discussed. For the later-time oscillation problems, an improved solution scheme based on further study of averaging techniques is proposed.Thirdly, for the transient field analysis of dielectric objects, PMCHW equations of two forms are deduced for the calculation of two-dimensional dielectric objects.Finally, considering analyzing the effect for different kinds of the temporal basis functions is also an important aspect of MOT in time scheme optimization, the relationship between the frequency distributions of temporal basis with the stability of MOT is discussed for two kinds of temporal basis. Based on the discussion, the second order sub-domain time basis is proposed for the solution of PMCHW equation, and numerical results and analysis shows that the proposed method is practicable.