A Novel Scheme for the Solution of the Time-Domain Integral Equations of Electromagnetics

Weile, D.S.; Pisharody, G.; Chen, Nan-Wei; Shanker, B.; Michielssen, E.

doi:10.1109/tap.2003.822450

Cited by 212 publications

(157 citation statements)

References 30 publications

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“…Linearly increasing and constant current components are often observed in marching on-in-time (MOT) solution of time domain surface integral equations (TD-SIEs) [1]- [4]. The presence of these spurious components is attributed to the fact that initial conditions on time derivatives of unknown equivalent currents are not enforced properly [3], [4].…”

Section: Introductionmentioning

confidence: 99%

On the initial condition problem of the time domain PMCHWT surface integral equation

Uysal

Bağcı

Ergin

et al. 2017

2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES)

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Abstract-Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-MillerChan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.

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Section: Introductionmentioning

confidence: 99%

On the initial condition problem of the time domain PMCHWT surface integral equation

Uysal

Bağcı

Ergin

et al. 2017

2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES)

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“…While this does result in the elimination of the linear-in-time spurious currents, it does not solve constantin-time DC instability. In [26], a loop-tree decomposition is used to filter out static loop modes after they emerge.…”

Section: Introductionmentioning

confidence: 99%

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

Beghein

Cools

Andriulli

2015

IEEE Trans. Antennas Propagat.

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Abstract-The marching-on-in-time solution of the time domain electric field integral equation (TD-EFIE) has traditionally suffered from a number of issues, including the emergence of spurious static currents (DC instability) and ill-conditioning at large time steps (low frequencies). In this contribution, a spacetime Galerkin discretization of the TD-EFIE is proposed, which separates the loop and star components of both the equation and the unknown. Judiciously integrating or differentiating these components with respect to time leads to an equation which is free from DC instability. By choosing the correct temporal basis and testing functions for each of the components, a stable marchingon-in-time system is obtained. Furthermore, the scaling of these basis and testing functions ensure that the system remains wellconditioned for large time steps. The loop-star decomposition is performed using quasi-Helmholtz projectors in order to avoid the explicit transformation to the unstable bases of loops and stars (or trees), and to avoid the search for global loops, which is a computationally expensive operation.Index Terms-time domain, electric field integral equation, DC instability, low frequency breakdown.

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“…However, this technique suffers from late time instability. Many measures [7][8][9][10] have attempted to overcome this instability as the choice of appropriate temporal basis functions. In [10,11], the authors applied the weighted Laguerre Polynomials as temporal basis functions and obtained an accurate and stable solution.…”

Section: Introductionmentioning

confidence: 99%

Transient Analysis of a Rectangular Cavity Containing an Interior Scatterer Using Td-Efie With Weighted Laguerre Polynomials as Temporal Basis Functions

Omri¹,

Aguili²

2014

PIER M

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Abstract-Novel 2-D Time Domain Electric FieldIntegral Equations (TD-EFIE) are established in order to predict transient response of a wire enclosed within a rectangular cavity. The wire and cavity are excited by an external incident transient electromagnetic wave through a slot in the cavity wall. The formulation of the TD-EFIE is based on equivalence principle and boundary conditions taking account the effect of reflection from cavity walls. The equations are efficiently solved by Method of Moments. The transient unknown coefficients of the electric current at the wire and magnetic current at the slot are approximated using a set of orthonormal temporal basis functions derived from Laguerre Polynomials. The analysis demonstration is presented to prove that the novel TD-EFIE combined to MoM is able to solve this critical problem. No late-time instability is encountered.

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A Novel Scheme for the Solution of the Time-Domain Integral Equations of Electromagnetics

Cited by 212 publications

References 30 publications

On the initial condition problem of the time domain PMCHWT surface integral equation

On the initial condition problem of the time domain PMCHWT surface integral equation

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

Transient Analysis of a Rectangular Cavity Containing an Interior Scatterer Using Td-Efie With Weighted Laguerre Polynomials as Temporal Basis Functions

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