Time Domain Integral Equations And Its Hybrid Solutions For Investigating On Electromagnetic Pulse Effects

With the miniaturization of electronic and electrical devices, systems are increasingly sensitive and susceptible to electromagnetic interference (EMI). Similarly, many antennas are mounted on electrically large platforms, which will suffer much more EMI problems than before. In modern electronic countermeasures, especially, after the emergence of some new-style weapons such as the high-power wideband EMP launcher and EM bomb, countries around the world initiate a new round competition in the research of electromagnetic interference (EMI) and protection techniques. This dissertation is focused on the development of time-domain integral equations and its hybrid methods with high accuracy and efficiency to study electromagnetic pulse effects and interaction mechanism in some typical systems illuminated by a high-power electromagnetic pulse (EMP).Firstly, time-domain integral equations with explicit and implicit marching-on-in-time (MOT) schemes are presented. An efficient hybrid method, TDIE-TDPO-MOT, is proposed for studying electromagnetic responses of several groups of wire and surface structures illuminated by an electromagnetic pulse (EMP), respectively. In comparison with the full TDIE-MOT method, computational complexity can be reduced drastically using our developed TDIE-TDPO-MOT method, and computational accuracy is still maintained.Secondly, a time-domain magnetic (TD-MFIE) and combined field integral equations (TD-CFIE) for analyzing scattering from3-D PEC objects are presented. The surface current density is directly used as the unknown, and an exact temporal Galerkin testing procedure is performed with no central approximation used. An adaptive marching-on-in-degree method with FFT-based blocking scheme is proposed, with the approach to determine the optimal scaling factor also given. It is indicated that the proposed scheme can guarantee the accuracy of MOD scheme without increasing the computational cost. Our numerical results also show that the O(NO2NS2) dependence of the MOD method can be reduced to O(NS2NOlog2(NO)) now.Thirdly, a radial integration scheme is proposed for handling weakly singular and near-singular potential integrals, which is an essentialimprovement over the previous polar integration method. We at first carryout some careful investigations on the problem of slow convergence. Then,a new technique of smoothing integrand based on polynomialtransformation is presented, which results in much faster convergencerate than that of the polar integration. Finally, some numerical resultsare given to demonstrate both accuracy and convergence rate of ourproposed scheme.Fourthly, a new integration approach is proposed for accurate andefficient calculation of time-domain EFIE, MFIE, and CFIE matrixelements over triangular domains. It mainly consists of a radialintegration scheme for handling weakly singular and near-hypersingularinner integrals as well as some new smoothing techniques for treatingthe outer surface integrals. As the proposed method preserves theflexibility for handling different integral kernels, they are applicablefor both time-domain and frequency-domain integral equations.Fifthly, an efficient hybrid TDIE-TDPO method with high stability,based on the weighted Laguerre polynomials and MOD scheme, is proposedfor investigating transient electromagnetic responses of3-D compositePEC objects, while the TDPO approximation is applicable to the large PECobjects with smooth surface. These objects are partitioned into tworegions: TDIE and TDPO ones. In the TDIE region, currents are updatedby solving a set of time-domain electric field integral equation (TD-EFIE)using the MOD. In the TDPO region, PO currents are obtained accordingto the incident fields as well as the ones radiated by all currents inthe TDIE one. The hybrid TDIE-TDPO method has advantages over TDPOapproximation alone, as it can control the approximation errors bychanging the percentage of TDIE regions. On the other hand, the proposedmethod does not require any specific acceleration algorithm such as PWTD,and its saving of both memory and CPU time is obtained by TDPOapproximation. Therefore, the hybrid formula can be directly applied forMOT scheme as well as finite difference delay modeling method with nodifficulty.Finally, the TDPO-TDPO projection part of the system matrix is madeto be an identity block matrix by a projection procedure for theRao–Wilton–Glisson (RWG) basis functions. Thus, the reduction of dimension of system matrix can be obtained by this projection procedure. In other words, the reduced dimension of system matrix is equal to NIES and irrespective of NPOS, where NIES and NPOS is the number of spatial unknowns in TDIE and TDPO regions, respectively. Since the TDIE region is not electrically large for most hybrid problems, we can solve the linear equations by direct solver without convergence problem introduced by iterative methods. The method for adaptively determining the number of temporal basis functions and the fast Fourier transform (FFT)-based blocking scheme for accelerating the temporal convolutions, is also employed.