Ming-Da Zhu

An Adaptive Marching-on-in-Order Method With FFT-Based Blocking Scheme

An adaptive marching-on-in-order (MOO) method with FFT-based blocking scheme is proposed to solve the time-domain electric field integral equation (TD-EFIE) for conductive objects, with the temporal basis of Laguerre polynomials (LP) employed. In contrast to most MOO approaches that utilize a priori fixed order of weighted LP for the temporal variation, we choose suitable polynomial order by computing the relative error of the weighted LP expansions. Thus, the accuracy of the MOO scheme is guaranteed. A general principle for choosing the optimal scaling factor of LP is presented, which is crucial for efficiently predicting scattering information of objects. The fast Fourier transform (FFT)-based blocking scheme is also implemented to reduce the computational complexity to O(NS2 No log2 (No))Numerical results that demonstrate the accuracy and efficiency of this methodology are presented.

Efficient Evaluation of Double Surface Integrals in Time-Domain Integral Equation Formulations

A new integration approach is presented for accurately calculating time-domain EFIE, MFIE, and CFIE matrix elements over triangular domains. It mainly consists of a radial integration scheme for handling weakly singular and near-hypersingular inner integrals and some new smoothing techniques for treating outer two-dimensional (2-D) integrals. The proposed approach has sufficient generality and efficiency for solving time-domain integral equations (TDIE) with arbitrary types of temporal basis functions and temporal discretization schemes, such as marching-on-in-time (MOT), marching-on-in-degree (MOD), and finite difference delay modeling/convolution quadrature (FDDM/CQ), etc. The numerical results for calculating some typical integrals are given to demonstrate its capability, with high accuracy and rapid convergence rate achieved.

HYBRID TDIE-TDPO METHOD FOR STUDYING ON TRANSIENT RESPONSES OF SOME WIRE AND SURFACE STRUCTURES ILLUMINATED BY AN ELECTROMAGNETIC PULSE

An e-cient hybrid method, based on time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is proposed for studying on transient electromagnetic responses of some wire and surface structures illuminated by an electromagnetic pulse (EMP), respectively. Two groups of triangular-type basis functions are used to expand the currents on both of them. The derived

Investigation on Time- and Frequency-Domain Responses of Some Complex Composite Structures in the Presence of High-Power Electromagnetic Pulses

Investigation on time- and frequency-domain responses of some complex composite structures in the presence of high-power electromagnetic pulses (EMP) is carried out in this paper. An efficient hybrid numerical method is proposed and implemented for studying an EMP penetrating through arbitrary apertures on a perfectly conducting (PEC) screen, coupled with conical spiral wire and even with Yagi-Uda antennas. This method effectively combines the time-domain integral equation (TDIE) with time-domain physical optics (TDPO), where hybrid TDIE-TDPO equations are solved by marching-on-in-time scheme (MOT). In its implementation, the antennas, wire-surface junctions, and the small part of the solid platform in the vicinity of the junctions are assigned to the TDIE region; nevertheless, a small part of the PEC screen in the vicinity of the apertures is set to be the TDIE region, while the remainder of the solid platform and the PEC screen is in the TDPO one. Our developed numerical algorithm is sufficiently verified in both time and frequency domains for predicting input admittance, S11 and S21 parameters, directivities, excited transient current responses as well as backward scattered fields of different antennas mounted on a PEC platform. These results are useful for further evaluating electromagnetic environments of some complex communication.

Radial Integration Scheme for Handling Weakly Singular and Near-Singular Potential Integrals

An efficient integration scheme is proposed for calculating weakly singular and near-singular potential integrals over planar triangles, with an essential improvement over the original polar integration. The reason for the problem of slow convergence of polar integration is revealed according to some careful investigations. A new technique of smoothing integrand based on variable transformation is presented to guarantee the smoothness of the integral kernel, which results in much faster convergence than that of the polar integration. Some numerical results are given to demonstrate the capability of our proposed scheme for achieving high accuracy as well as rapid convergence rate in several numerical experiments.

Investigation on electromagnetic responses of double objects illuminated by a high-power EMP using hybrid TDIE-TDPO method

An efficient and stable hybrid method, based on time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is proposed for investigating electromagnetic responses of double 3-D objects illuminated by a high-power EMP. The planar triangular patches are used to model the conductive surface with RWG basis functions implemented, while the temporal basis functions of weighted Laguerre polynomials are also employed. A set of hybrid TDIE-TDPO equations are solved by marching-on-in-order scheme (MOO) for the sake of stability. Under such circumstances, compared with the full TDIE solver, the computational complexity of our developed hybrid TDIE-TDPO method is reduced greatly. Several examples are presented to demonstrate its validity and efficiency. In particular, transient electromagnetic responses of different double 3-D conductive objects, illuminated by a HPEMP, are captured and compared for different pulse waveforms and pulse parameters.

Investigation on electromagnetic responses of some complex wire-surface composite objects using hybrid TDIE-TDPO based MOT method

An efficient hybrid method, based on time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is proposed for investigating on electromagnetic responses of some complex wire-surface composite objects illuminated by an electromagnetic pulse (EMP), respectively. Three triangular-type basis functions are used to represent the currents on the bodies, wires, and wire/surface junctions, respectively. A set of hybrid TDIE-TDPO equations are solved by marching-on-in-time scheme (MOT). In comparison with the full TDIE-based MOT method, computational complexity is reduced drastically using our developed hybrid TDIE-TDPO method, and with the accuracy maintained successfully. Numerical results of EMP responses of some composite objects are given to demonstrate its versatility, accuracy and efficiency.

TDEFIE-PMCHW Method Combined With an Adaptive Marching-On-in-Order Procedure for Studying on Time- and Frequency-Domain Responses of Some Composite Structures

One effective method, based on time-domain PMCHW (Poggio, Miller, Chang, Harrington, and Wu) integral equation, is presented for studying on time- and frequency-domain electromagnetic responses of some composite structures. A set of derived equations is solved by an adaptive marching-on-in-order (MOO) procedure. During its implementation, dielectric parts of the composite structure are described by the PMCHW equations, and its metallic parts are governed by the time-domain electric field integral equations, where temporal basis of the Laguerre polynomials are employed for both of them. As an example of composite microstrip patch structure, its dielectric- metallic junction is handled using an appropriate combination of the full RWG basis functions so as to obtain high computational accuracy, and one MOO acceleration scheme is employed for accelerating the temporal convolution effectively. Numerical results are given to demonstrate efficiency as well as accuracy of our proposed method used for capturing electromagnetic responses of some typical composite structures, with their transient current responses, far-field distributions, radar cross sections, and directivities predicted successfully.

Hybrid TDIE-TDPO Method Using Weighted Laguerre Polynomials for Solving Transient Electromagnetic Problems

An e-cient and stable hybrid method, based on the time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is developed for investigating transient radiation and scattering from perfectly electrical conducting (PEC) objects. It at flrst requires partitioning the PEC object surface into TDIE and TDPO regions, respectively. Then, a set of hybrid TDIE-TDPO equations is derived and solved using an adaptive marching-on-in- degree (MOD) method. The fast Fourier transforms (FFT)-based blocking scheme is further implemented into the proposed algorithm so as to reduce N 2 O dependence of the traditional MOD method to NO log 2 (NO), where NO is the highest order of the weighted Laguerre polynomials used for computation. Under such circumstances, its computational cost, in comparison with the full TDIE-MOD solver, is reduced signiflcantly. Several numerical examples are presented to demonstrate its accuracy and e-ciency in solving some typical transient electromagnetic problems.

Solution of time-domain MFIE and CFIE using adaptive MOO Method for transient scattering in the presence of an EMP

The adaptive marching-on-in-order method (MOO) to solve time-domain magnetic and combined field integral equations is proposed for capturing transient responses of some 3-D PEC objects illuminated by an EMP. We directly employ an exact temporal Galerkin testing with no central approximation used, and using surface current density of the object as the unknown without employing the Hertz vector. The fast Fourier transform (FFT)-based blocking scheme is further implemented. This method is similar to the improvement over the earlier MOO for solving time-domain eclectic field integral equation. Transient electromagnetic responses of some typical conductive objects are obtained and compared for validating both computational accuracy and applicability of our proposed three TDIE-MOO algorithm.