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An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao–Wilton–Glisson basis functions for spatial discretization and a \\PE(CE)^m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. [ABSTRACT FROM PUBLISHER]

A method for constructing explicit marching-on-in-time (MOT) schemes to solve the time-domain magnetic field volume integral equation (TD-MFVIE) on inhomogeneous dielectric scatterers is proposed. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using curl conforming spatial basis functions. Inserting this expansion into the TD-MFVIE and spatially testing the resulting equation yield an ODE system with a Gram matrix. This system is integrated in time for the unknown time-dependent expansion coefficients using a linear multistep method. The Gram matrix is sparse and well conditioned for Galerkin testing and consists of only four diagonal blocks for point testing. The resulting explicit MOT schemes, which call for the solution of this matrix system at every time step, are more efficient than their implicit counterparts, which call for inversion of a fuller matrix system at lower frequencies. Numerical results compare the efficiency, accuracy, and stability of the explicit MOT schemes and their implicit counterparts for low-frequency excitations. The results show that the explicit MOT scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy. [ABSTRACT FROM AUTHOR]

A wavelet-enhanced plane-wave time-domain (PWTD) algorithm for efficiently and accurately solving time-domain surface integral equations (TD-SIEs) on electrically large conducting objects is presented. The proposed scheme reduces the memory requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD-accelerated TD-SIE solver, when applied to the analysis of transient scattering from smooth quasi-planar objects with near-normal incident pulses, scale nearly as O(Ns \log Ns) and O(Ns^{1.5}) , respectively. Here, Ns denotes the number of spatial unknowns. The efficiency and accuracy of the proposed scheme are demonstrated through its applications to the analysis of transient scattering from a 185-wavelength long NASA almond and a 123-wavelength long Airbus A-320 model. [ABSTRACT FROM PUBLISHER]

A discontinuous Galerkin time-domain (DGTD) method analyzing signal/power integrity on multilayered power-ground parallel plate pairs is proposed. The excitation is realized by introducing wave ports on the antipads where electric/magnetic current sources are represented in terms of the eigenmodes of the antipads. Since closed-forms solutions do not exist for the eigenmodes of the arbitrarily shaped antipads, they have to be calculated using numerical schemes. Spatial orthogonality of the eigenmodes permits determination of each mode's temporal expansion coefficient by integrating the product of the electric field and the mode over the wave port. The temporal mode coefficients are then Fourier transformed to accurately calculate the S-parameters corresponding to different modes. Additionally, to generalize the DGTD to manipulate dispersive media, the auxiliary differential equation method is employed. This is done by introducing a time-dependent polarization volume current as an auxiliary unknown and the constitutive relation between this current and the electric field as an auxiliary equation. Consequently, computationally expensive temporal convolution is avoided. Various numerical examples, which demonstrate the applicability, robustness, and accuracy of the proposed method, are presented. [ABSTRACT FROM PUBLISHER]

A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time-domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite-difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor–corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as O(N_s\,\log \,N_s) and O(N_sN_t), respectively. Here, N_s is the number of spatial basis functions and N_t is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed-memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements. [ABSTRACT FROM PUBLISHER]

A scalable parallel plane-wave time-domain (PWTD) algorithm for efficient and accurate analysis of transient scattering from electrically large objects is presented. The algorithm produces scalable communication patterns on very large numbers of processors by leveraging two mechanisms: 1) a hierarchical parallelization strategy to evenly distribute the computation and memory loads at all levels of the PWTD tree among processors and 2) a novel asynchronous communication scheme to reduce the cost and memory requirement of the communications between the processors. The efficiency and accuracy of the algorithm are demonstrated through its applications to the analysis of transient scattering from a perfect electrically conducting (PEC) sphere with a diameter of 70 wavelengths and a PEC square plate with a dimension of 160 wavelengths. Furthermore, the proposed algorithm is used to analyze transient fields scattered from realistic airplane and helicopter models under high frequency excitation. [ABSTRACT FROM PUBLISHER]

A time-domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert–Wilton–Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations cannot be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time-domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers. [ABSTRACT FROM PUBLISHER]

A hybrid electromagnetics (EM)-circuit simulator exploiting the discontinuous Galerkin time domain (DGTD) method and the modified nodal analysis (MNA) algorithm is developed for analyzing hybrid distributive and nonlinear multiport lumped circuit systems. The computational domain is split into two subsystems. One is the EM subsystem that is analyzed by DGTD, while the other is the circuit subsystem that is solved by the MNA method. The coupling between the EM and circuit subsystems is enforced at the lumped port where related field and circuit unknowns are coupled via the use of numerical flux, port voltages, and current sources. Since the spatial operations of DGTD are localized, thanks to the use of numerical flux, coupling matrices between EM and circuit subsystems are small and are directly inverted. To handle nonlinear devices within the circuit subsystem, the standard Newton-Raphson method is applied to the nonlinear coupling matrix system. In addition, a local time-stepping scheme is applied to improve the efficiency of the hybrid solver. Numerical examples including single and multiport linear/nonlinear circuit networks are presented to validate the proposed solver. [ABSTRACT FROM PUBLISHER]