Time-domain Combined Field Integral Equation Research Articles

A Stabilized Time-Domain Combined Field Integral Equation Using the Quasi-Helmholtz Projectors

A Stabilized Time-Domain Combined Field Integral Equation Using the Quasi-Helmholtz Projectors

An efficient high order plane wave time domain algorithm for transient electromagnetic scattering analysis

An efficient high order plane wave time domain algorithm is presented for analyzing the transient scattering from three dimensional electrically large conducting objects. This method uses a set of hierarchical divergence-conforming vector basis functions to accurately represent the current distribution on the perfect electrically conducting (PEC) surface. The higher order functions can significantly reduce the number of unknowns without compromise on the accuracy. The time domain combined field integral equation (TD-CFIE) is then discretized using the hierarchical divergence-conforming vector basis functions and shifted Lagrange polynomial functions in spatial and time domain, respectively. The final matrix equation can be accelerated using the plane wave time domain (PWTD) algorithm. Finally, a parallel algorithm that can execute on a distributed-memory parallel cluster is developed, which provides an appealing avenue for analyzing the transient scattering from three-dimensional electrically large complex PEC objects. Numerical examples are given to demonstrate the accuracy and efficiency of the method.

An Efficient High-Order Marching-on-in-Degree Solver for Conducting and Dielectric Bodies of Revolution

The transient electromagnetic (EM) scattering from bodies of revolution (BoRs) is analyzed by the time-domain integral equation with the Silvester–Lagrange polynomials. The high-order spatial basis functions are used along the generatrix, while the weighted Laguerre polynomials are served as the temporal basis functions. In this way, the late time stability can be guaranteed by using the marching-on-in-degree scheme. In this communication, the conducting targets are simulated by the time-domain combined field integral equation while the dielectric ones are formulated in terms of the magnetic current combined field integral equation. Moreover, the multilevel adaptive cross approximation algorithm is adopted to accelerate the calculations of the well-separated groups. The numerical results demonstrate that the proposed solver is efficient to analyze the transient EM scattering from BoRs.

Parallel Marching-on-in-Degree Solver of Time-Domain Combined Field Integral Equation for Bodies of Revolution Accelerated by MLACA

Time-domain combined field integral equation (TD-CFIE) for bodies of revolution (BORs) is solved by marching-on-in-degree (MOD) method. A multilevel partitioning is adopted to group the spatial basis functions along the longitudinal dimension. The interactions of the adjacent groups are calculated directly in the traditional manner, while the impedance matrices associated with the well-separated groups at each level are computed by the multilevel adaptive cross approximation (MLACA) algorithm. The hybrid MPI and OpenMP parallel programming technique is utilized to further accelerate the solving process on a shared-memory computer system. Two numerical results demonstrate that the proposed method can greatly reduce the memory requirement and CPU time, thus enhance the capability of MOD method.

Impulse responses and the late time stability properties of time‐domain integral equations

Impulse responses to the time-domain integral equations (TDIEs) using marching-on-in-time (MOT) scheme are discussed in this study. It can be seen clearly that the interior resonance currents are included in the impulse responses of the time-domain electric field integral equation (TDEFIE) and the time-domain magnetic field integral equation (TDMFIE), but not in those of the time-domain combined field integral equation (TDCFIE), while spurious DC solenoidal currents are only included in the TDEFIE. Analysis shows that the MOT-TDMFIE is basically exponentially convergent, and the MOT-TDCFIE usually converges to a small constant value, while the MOT-TDEFIE is basically unstable. The stability properties are justified by the eigenvalues of the corresponding systems. This study also shows that it is possible to solve time-domain integral equations (TDIEs) using their impulse responses truncated according to the maximum physical size of the scatterer.

Acceleration of the Impedance Matrix Filling for Marching-on-in-Degree Method by Equivalent Dipole Moment

In this article, the equivalent dipole moment method is employed to accelerate the marching-on-in-degree method for the time-domain combined field integral equation. Each element can be viewed as a dipole model when the distance between the source and the testing basis functions is beyond a threshold distance. In this way, the impedance matrix elements of each order can be easily computed by a simple procedure, and the computational time is reduced significantly for transient electromagnetic scattering. Numerical results are presented to demonstrate the efficiency of the proposed method for electromagnetic scattering from perfect electric conductor objects.

Discretization of the Time Domain CFIE for Acoustic Scattering Problems Using Convolution Quadrature

We consider the problem of approximating time domain acoustic scattering by a bounded sound-soft obstacle in three dimensional space via a time domain combined field integral equation (CFIE). Convolution quadrature is used for time discretization of the retarded operators, using an underlying A-stable time-stepping method. We prove operator bounds that imply convergence of a semidiscrete approximation of the time domain CFIE in three cases: (1) a standard regularized time domain CFIE, (2) a new regularized CFIE, and (3) the standard unregularized CFIE. To analyze the first case we use a special mixed formulation of the problem, in the second case we use a perturbation argument, while in the third case a Rellich argument gives the necessary estimates. We conclude with fully discrete error estimates in the case of the new regularized CFIE.

A Space-Time Mixed Galerkin Marching-on-in-Time Scheme for the Time-Domain Combined Field Integral Equation

The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required.

Time-domain augmented EFIE and its marching-on-in-degree solution

A time-domain augmented electric field integral equation (TDAEFIE) and its marching-on-in-degree (MOD) solution are presented for analysis of transient electromagentic responses from three-dimensional closed conducting bodies of arbitrary shape.By enforcing a condition on the normal component of the electric flux density, the TDAEFIE eliminates the potential internal resonance problem of the time-domain electric field integral equation (TDEFIE) algorithm. With the use of weighted Laguerre polynomials as entire-domain temporal basis functions, the MOD solution overcomes the late-time instability problem that often occurs in the marching-on-in-time (MOT) approach. Compared with the MOD solution of the time-domain combined field integral equation (TDCFIE), the MOD solution of the TDAEFIE is more efficient because it takes less computational time for calculating the matrix elements and the matrix-vector multiplications related to the excitation at the right-hand side of the matrix equation. Numerical results are presented to illustrate the good performance of the TDAEFIE algorithm. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1439–1444, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26015

The Solution of Time-Domain Combined Field Integral Equation for Transient Scattering by Conducting Surfaces of Arbitrary Shape

The Solution of Time-Domain Combined Field Integral Equation for Transient Scattering by Conducting Surfaces of Arbitrary Shape

Analysis of transient electromagnetic scattering using UV method enhanced time‐domain integral equations with Laguerre polynomials

AbstractIn this article, the multilevel UV algorithm is utilized to reduce both the memory requirement and CPU time in the time‐domain combined field integral equation (TD‐CFIE) method to analyze transient electromagnetic scattering from conducting structures.The UV method is kernel‐independent, and is based on the rank‐deficiency feature of the impedance submatrix which represents far interaction. To obtain an unconditionally stable solution, finite orders of weighted Laguerre polynomials are used as temporal basis functions and the unknown expansion coefficients of the time variable are solved recursively order by order, as the so‐called matching‐on‐in‐order (MOO) procedure. RWG basis function is used as the spatial basis function for its flexibility in modeling arbitrary geometries. The spatial and temporal testing procedures are separate, and both of them are carried on with the Galerkin's method. Numerical results are given to verify the proposed method. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:158–163, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25646

도체 구조물의 과도 산란 해석을 위한 결합 적분방정식의 안정된 MOT 기법

In this paper, a stable marching-on in time(MOT) method with a time domain combined field integral equation(CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional conducting bodies. This formulation is based on a linear combination of the time domain electric field integral equation(EFIE) with the magnetic field integral equation(MFIE). The time derivatives in the EFIE and MFIE are approximated using a central finite difference scheme and other terms are averaged over time. This time domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. Numerical results with the proposed MOT scheme are presented and compared with those obtained from the conventional method and the inverse discrete Fourier transform(IDFT) of the frequency domain CFIE solution.

Time-domain combined field integral equation using Laguerre polynomials as temporal basis functions

In this paper, we propose a novel formulation to solve the time-domain combined field integral equation (TD-CFIE) for analysing the transient electromagnetic response from three-dimensional (3D) cl...

Time‐domain combined field integral equation using Laguerre polynomials as temporal basis functions

AbstractIn this paper, we propose a novel formulation to solve the time‐domain combined field integral equation (TD‐CFIE) for analysing the transient electromagnetic response from three‐dimensional (3D) closed conducting bodies. Instead of the conventional marching‐on in time (MOT) technique, the solution methods in this paper are based on the Galerkin's method that involves separate spatial and temporal testing procedure. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3D closed structures. The time‐domain unknown coefficient is approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. With the representation of the derivative of the transient coefficient in an analytic form, the time derivative terms in the integral equations can be handled analytically. We also propose an alternative formulation to solve the TD‐CFIE. Two methods are presented that results in very accurate and stable transient responses from conducting objects. Numerical results are presented and compared with the inverse discrete Fourier transform (IDFT) of frequency‐domain combined field integral equation (FD‐CFIE) solutions. Copyright © 2004 John Wiley & Sons, Ltd.

Analysis of transient electromagnetic scattering from dielectric objects using a combined‐field integral equation

AbstractIn this paper, we analyze the transient electromagnetic response from three‐dimensional (3D) dielectric bodies using a time‐domain combined‐field integral equation. The solution method in this paper is based on the method of moments (MoM), which involves separate spatial and temporal testing procedures. Triangular‐patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3D dielectric structures. The time‐domain unknown coefficients of the equivalent electric and magnetic currents are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials and exponential functions. These functions are also used as temporal testing. In addition to use of the Laguerre polynomials as expansion functions for the transient portion of the response, two new source vectors related to the equivalent currents enables one to handle the time derivative terms of the vector potential in the integral equation in an analytic fashion. Numerical results computed by the proposed method are presented and compared. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 476–481, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20009

Transmitting and receiving wide‐band signals using reciprocity

AbstractIn this paper, we present a method based on reciprocity which can transmit and receive a baseband wide‐bandwidth signal without distortion. The time‐domain combined field integral equation (TD‐CFIE) is used to get the simulation results. Numerical results are presented, which show the validity of the presented methodology. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 359–362, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11060

Time-Domain EFIE, MFIE, And CFIE Formulations Using Laguerre Polynomials as Temporal Basis Functions for the Analysis of Transient Scattering from Arbitrary Shaped Conducting Structures — Abstract

In this paper, we present time-domain integral equation (TDIE) formulations for analyzing transient electromagnetic responses from three-dimensional (3-D) arbitrary shaped closed conducting bodies using the time-domain electric field integral equation (TDEFIE), the time-domain magnetic field integral equation (TD-MFIE), and the time-domain combined field integral equation (TD-CFIE). Instead of the conventional marching-on in time (MOT) technique, the solution methods in this paper are based on the Galerkin's method that involves separate spatial and temporal testing procedure. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D structures. The timedomain unknown coefficient is approximated by using an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as temporal testing. Using these Laguerre functions it is possible to evaluate the time derivatives in an analytic fashion. We also propose a second alternative formulation to solve the TDIE. The methods to be described result in very accurate and stable transient responses from conducting objects. Detailed mathematical steps are included and representative numerical results are presented and compared.

Time‐domain CFIE for the analysis of transient scattering from arbitrarily shaped 3D conducting objects

AbstractA time‐domain combined field integral equation (CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three‐dimensional (3D) conducting bodies. This formulation is based on a linear combination of the time‐domain electric field integral equation (EFIE) with the magnetic field integral equation (MFIE). The time derivative of the magnetic vector potential in EFIE is approximated with the use of a central finite‐difference approximation for the derivative, and the scalar potential is averaged over time. The time‐domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. The incident spectrum of the field may contain frequency components, which may correspond to the internal resonance of the structure. For the numerical solution, both the explicit and implicit schemes are considered and two different kinds of Gaussian pulses are used, which may or may not contain frequencies corresponding to the internal resonance. Numerical results for the EFIE, MFIE, and CFIE are presented and compared with those obtained from the inverse discrete Fourier transform (IDFT) of the frequency‐domain CFIE solution. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 289–296, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10440

Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation

In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes.