Young Seek Chung

An unconditionally stable scheme for the finite-difference time-domain method

In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwells equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.

Solution of time domain electric field Integral equation using the Laguerre polynomials

In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.

Transient electromagnetic scattering from dielectric objects using the electric field Integral equation with Laguerre polynomials as temporal basis functions

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkins method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared.

Solution of time domain PMCHW formulation for transient electromagnetic scattering from arbitrarily shaped 3-D dielectric objects

In this paper, we analyze the transient electromagnetic response from three-dimensional (3-D) dielectric bodies using a time domain PMCHW (Poggio, Miller, Chang, Harrington, Wu) integral equation. The solution method in this paper is based on the Galerkins method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time domain unknown coefficients of the equivalent electric and magnetic currents are approximated by a set of orthonormal basis functions that are derived from the Laguerre functions. These basis functions are also used as the temporal testing. Use of the Laguerre polynomials as expansion functions characterizing the time variable enables one to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. We also propose an alternative formulation using a differential form of time domain PMCHW equation with a different expansion for the equivalent currents. Numerical results computed by the two proposed methods are presented and compared.

Solution of time domain electric field integral equation for arbitrarily shaped dielectric bodies using an unconditionally stable methodology

[1]xa0In this work, we present a new and efficient numerical method to obtain an unconditionally stable solution for the time domain electric field integral equation (TD-EFIE) for arbitrary homogeneous dielectric bodies, derived utilizing the surface equivalence principle. This novel method does not utilize the customary marching-on in time solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives in the TD-EFIE formulation can be handled analytically. Since these weighted Laguerre polynomials converge to zero as time progresses, the induced electric and magnetic currents when expanded in a series of weighted Laguerre polynomials also converge to zero. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the temporal testing procedure, the marching-on in time procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the currents, the spatial and the temporal variables can be separated. For convenience, we use the Hertz vector as the unknown variable instead of the equivalent electric current density. However, we use the equivalent magnetic current density as it is. To verify our method, we apply the proposed method to various dielectric scatterers and compare the results of an inverse Fourier transform of a frequency domain EFIE.

Finite element time domain method using Laguerre polynomials

In this work, we present a numerical method to obtain an unconditionally stable solution for the finite element method in time domain (FETD) for two-dimensional TE/sub z/ case. Our method does not utilize the customary marching-on in time solution method often used to solve a hyperbolic partial differential equation. Instead we solve the time domain wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the three derivatives can be handled analytically. To verify our method, we apply it to two-dimensional parallel plate waveguide and compare the result to that of the conventional FETD using the Newmark-Beta method.

Solving the Time-Domain Magnetic Field Integral Equation for Dielectric Bodies without the Time Variable through the Use of Entire Domain Laguerre Polynomials

In this paper, we propose a time-domain magnetic field integral equation (TD-MFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion, and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated as an orthonormal basis function set that is derived from the entire domain Laguerre functions. These basis functions are also used as the temporal testing. Through the use of the Laguerre functions, it is possible to perform the time derivatives in the integral equations analytically. In addition, due to the orthonormality and additivity properties of these basis functions, it is possible to eliminate the time variable completely from the computations, and therefore one does not have to worry about the Courant condition. We also propose an alternative formulation using a different expansion of the electric current. Numerical results involving equivalent currents and far fields computed by the two different implementations of the TD-MFIE are presented and compared.