Greeshma Pisharody

A novel scheme for the solution of the time-domain integral equations of electromagnetics

A new method to numerically solve time-domain integral equations pertinent to electromagnetic surface scattering phenomena is presented. The method uses approximate prolate spheroidal wave functions and standard Rao-Wilton-Glisson basis functions to effect the temporal and spatial discretization of the integral equations, respectively. Because the temporal basis functions are noncausal, an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time. Numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time-bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency-domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time-domain solver.

An accurate scheme for the solution of the time-domain Integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation

Despite the numerous advances made in increasing the computational efficiency of time-domain integral equation (TDIE)-based solvers, the stability and accuracy of TDIE solvers remain problematic. This paper introduces a new numerical method for the accurate solution of TDIEs for scattering from arbitrary perfectly conducting surfaces. The work described in this paper uses the higher order divergence-conforming basis functions of Graglia et al. for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations. Since the basis functions used for the temporal representation are noncausal, an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time. Numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization.

Robust solution of time-domain integral equations using loop-tree decomposition and bandlimited extrapolation

A stabilization method that eradicates low frequency instabilities in the solution of the time-domain integral equations of electromagnetic scattering is presented. The method uses the loop-tree decomposition originally suggested for the solution of low frequency scattering problems via the method of moments. Specifically, a temporally differentiated form of the pertinent integral equation is tested using tree basis functions, and the undifferentiated form is tested using solenoidal basis functions. The underlying solution method uses bandlimited interpolation functions (BLIFs) and the higher-order divergence-conforming vector bases of Graglia et al. for the temporal and spatial discretization of the integral equations, respectively. An extrapolation technique has been implemented to overcome the noncausality introduced into the system by the BLIFs. Numerical results will demonstrate the stability and accuracy of the proposed technique.

Electromagnetic scattering from homogeneous dielectric bodies using time-domain integral equations

This paper presents a stable and accurate method to compute the electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies using time-domain integral equations (TDIEs). Unlike previous TDIE-based scattering work, the formulation presented here is based on the equations of Poggio, Miller, Chang, Harrington, Wu, and Tsai formulation. The method employs the higher-order divergence-conforming basis functions described by Graglia et al. and bandlimited interpolation functions to effect the spatial and temporal discretization of the integral equations, respectively. As the temporal basis functions are noncausal, an extrapolation mechanism is used to modify the noncausal system of equations to a form solvable by standard marching-on-in-time procedure. This work also explains the reason for late-time low-frequency instabilities encountered in current TDIE implementations and details a stabilization technique employed to overcome them. Numerical results demonstrate the accuracy and stability of the proposed technique.

Accurate solution of time domain integral equations using higher order vector bases and bandlimited extrapolation

Time domain integral equations (TDIE) based solvers have been gaining a lot of attention in the past few years for the solution of electromagnetic problems. The widespread acceptance of TDIE based solvers was historically hindered by the instability and inefficiency of their original implementations. As a consequence of this, the art of TDIE based solvers is not as refined as that for more conventional methods. While higher-order spatial discretizations have been used in the past, few claims of higher order temporal convergence can be found in the literature. This paper presents a stable and accurate scheme to solve TDIEs using higher order vector bases, coupled with bandlimited temporal basis functions and bandlimited extrapolation. It will be demonstrated that the proposed scheme demonstrates enhanced convergence in space and time.

Electromagnetic scattering from a homogeneous material body using time domain integral equations and bandlimited extrapolation

In recent years, the time domain integral equation based solvers for Maxwells equations have been gaining popularity. Although for certain types of problems they possess a number of advantages over other computational methods, their widespread usage has been hampered because of the instability and inefficiency encountered in early implementations. One new scheme that seems to overcome these instability problems is time marching using bandlimited extrapolation, which uses bandlimited basis functions for temporal representation, and bandlimited extrapolation to create a causal scheme from these noncausal basis functions. This paper presents an extension of this scheme to compute the scattering from homogeneous dielectric bodies. The results obtained from the new method show an excellent correspondence with those obtained from the standard, frequency domain method of moments.

An accurate solution to time domain integral equations for homogeneous dielectric bodies using loop-tree decomposition and bandlimited extrapolation

This work presents a stable and accurate method to solve the electromagnetic scattering from homogeneous dielectric scatterers using time domain integral equations (TDIE). In particular, it applies a loop-tree decomposition to the spatial testing functions and separately handles the solenoidal testing functions. For this purpose, the presented TDIE solver uses Rao-Wilton-Glisson (RWG) basis functions and bandlimited interpolatory functions (BLIF) to discretize the integral equations spatially and temporally, respectively, and implements a bandlimited extrapolation technique to overcome the noncausality introduced by the BLIF. Numerical results presented in this paper demonstrate the accuracy and stability of the method and illustrate the exponential convergence with respect to a temporal discretization parameter.

An accurate solution to time domain integral equations for inhomogeneous dielectric bodies using higher-order volume bases

Time domain integral equation (TDIE) based solvers possess a number of advantages over other computational methods for the solution of wideband, nonlinear, and time-varying electromagnetic scattering and radiation phenomenon. Widespread use of TDIE solvers has been hindered by their historical inefficiency and instability. In the recent past, a new time marching method was proposed that used special bandlimited interpolation functions (BLIFs) for the temporal discretization of the TDIEs and a bandlimited extrapolation to create a causal scheme from these noncausal BLIFs, that overcame previous inaccuracy and instability issues. This paper presents an extension of this scheme to compute the scattering from inhomogeneous dielectric bodies using higher-order volume spatial basis functions. The results obtained from the new method show an excellent correspondence with those obtained from the standard, frequency domain method of moments

A robust solution to time domain integral equations for perfect electric conductors using loop-tree decomposition and bandlimited extrapolation

Time domain integral equation (TDIE) solution methods have received more limited attention than other methods in computational electromagnetics because their early implementations were inaccurate, inefficient, and, worst of all, unstable. In spite of the advances made towards improving the efficiency of TDIEs, no consensus has so far been reached on how to stabilize TDIE solvers. The paper offers a novel and robust solution to the low frequency instability encountered in the implementation of currently available TDIE solvers. Specifically, the approach implements a loop-tree decomposition to the space of spatial testing functions, and treats the equations tested with solenoidal testing functions differently than the other equations. The underlying TDIE solver uses higher order divergence-conforming basis functions and bandlimited interpolatory functions (BLIFs) to effect, respectively, the spatial and temporal discretizations of the integral equation, and implements a bandlimited extrapolation technique to recover causality from the noncausal system generated by the BLIFs. Numerical results show that the proposed method is stable and exhibits exponential convergence with respect to a parameter of the temporal discretization.