Study On Time Domain Integral Equation Method For Investigating On Interaction Of Electromagnetic Pulses And Complex Metallic Structures

It is well known that there are numerous electronic systems equipped on modern ship platforms, and they bring a lot of very challenging electromagnetic compatibility(EMC) and electromagnetic interference(EMI) problems. On the other hand, computer simulation technique has been successfully adopted and implemented for predicting the electromagnetic phenomena and the mechanism of EMI. This dissertation, based on our developed stable and efficient time domain integral equation(TDIE) method and its hybrid method, is devoted to analyzing the transient characteristics of some large scale platforms in the presence of high-power electromagnetic pulses(HP-EMP).The main contribution of this dissertation is summarized as follows:(1) As the number of unknowns generated by surface mesh increases, the condition number of the impedance matrix Z0 grows rapidly. Moreover, the convergence of the algorithm deteriorates. In this dissertation, the Calderón precondition technique is implemented in the TDIE method. By utilizing this technique, the condition number of the impedance matrix will not change greatly as the variation of the mesh uniformity and mesh density of the target. At the same time, an excellent convergence characteristic is also achieved.(2) In order to handle the late time instability of TDIE solver, we present two improved methods. One is the choice of the temporal basis function. The approximate prolate spheroidal wave functions(APSWFs) have a short temporal support and limited bandwidth. Based on these properties, APSWFs are suitable for the interpolation or extrapolation of a band-limited function with the error decreased exponentially. Thus, this temporal basis function is usually used for representing the induced transient currents on the PEC surface. On the other hand, a new integration approach for calculating the matrix elements is also presented, and it mainly consists of a radial integration scheme for handling weakly singular inner integrals combined with some new smoothing techniques for treating the outer surface integrals. In comparison with the conventional Gaussian quadrature rule, both the accuracy and efficiency of the new integration approach are improved greatly.(3) Time domain adaptive integral method(TDAIM) is proposed to improve the efficiency of the conventional TDIE method. All the primary spatial basis functions are locally projected onto the auxiliary grids. The multiplication of the propagation matrix and current vector on these grids can be calculated by using the fast fourier fransform(FFT) and the inverse fast fourier fransform(IFFT). Finally, the potential value on each primary basis function is obtained by interpolating these intermediate results. The proposed scheme has a computational complexity and memory requirement of 2( log())t s sO N N N and 3/ 2()sO N when applied to quasiplanar structures, and for general 3-D surfaces, they are of 3/ 2 2( log())t s sO N N N and 2()sO N. Here, Ns and Nt denote the number of spatial and temporal degrees of freedom, respectively.(4) In order to improve the computational efficiency of the TDIE method, we also develop the parallel version. The message passing interface(MPI) is implemented in the parallel TDIE, which is one of the most popular parallel programming environments.(5) A generalized mathematical procedure of hybrid TDIE-TDPO method is proposed, and in particular, the technique for handling the junction between the wire antenna and the PEC platform is implemented. Moreover, the out-of-core technique and the method that improves the instability have been integrated into this hybrid TDIE-TDPO method to enhance its capability for handling complex EM problems. In our analysis, the antenna, the wire-surface junction and the small part of the PEC platform in its vicinity are assigned to the TDIE region. The small part of the PEC screen in the vicinity of multiple apertures is also set to be in the TDIE region, and the remainders of the PEC platform and the PEC screen are assigned to the TDPO region.(6) An efficient solver that hybridizes the TDIE-TDPO and TDAIM is presented. In the hybrid scheme, the TDAIM method uses a single grid system that covers both the TDIE and TDPO regions. The interactions within the TDIE region, as well as from the TDIE to the TDPO region, and back, can be obtained by using TDAIM. The hybrid scheme is computationally far more efficient than its standalone constituents.