An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

Sayed, Sadeed Bin; Ülkü, H. Arda; Bağcı, Hakan

doi:10.1109/apusncursinrsm.2017.8072610

Cited by 4 publications

(7 citation statements)

References 6 publications

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“…These results clearly show that the proposed method is more accurate than FDTD that is traditionally used for analyzing electromagnetic scattering from nonlinear objects. Note that preliminary versions of the method proposed in this work have been described in [61,62] as conference contributions.…”

Section: Introductionmentioning

confidence: 99%

A Time Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering from Nonlinear Dielectric Objects

Sayed¹,

Chen²,

Ülkü³

et al. 2022

Preprint

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A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and electric field induced in the scatterer is used as an auxiliary equation that complements TD-EFVIE. The ordinary differential equation system that arises from TD-EFVIE's Schaubert-Wilton-Glisson (SWG)-based discretization is integrated in time using a P E(CE) m scheme for the unknown expansion coefficients of the electric field. Matrix systems that arise from the SWG-based discretization of the nonlinear constitutive relation and its inverse obtained using the Padé approximant are used to carry out explicit updates of electric field and electric flux expansion coefficients at the predictor (PE) and the corrector (CE) stages. The resulting explicit marching-on-in-time (MOT) scheme does not call for any Newton-like nonlinear solver and only requires solution of sparse and well-conditioned Gram matrix systems at every step. Numerical results show that the proposed explicit MOT-based TD-EFVIE solver is more accurate than the finite-difference time-domain method that is traditionally used for analyzing transient electromagnetic scattering from nonlinear objects.

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Section: Introductionmentioning

confidence: 99%

A Time Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering from Nonlinear Dielectric Objects

Sayed¹,

Chen²,

Ülkü³

et al. 2022

Preprint

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“…Uysal et al [18] develop a time-domain surface integral equation solver for analysing electromagnetic field interactions on plasmonic nanostructures. Sayed et al [19] propose an explicit marching-on-in-time scheme to describe the nonlinear and dispersive scatterers. With the electrodynamic approach [13,20] and equivalent circuit approach [21], a power loss density [22] is derived to overcome the constraint of frequency domain, but the coupling mechanism between the electromagnetic field and Debye media is still not be explicitly revealed.…”

Section: Introductionmentioning

confidence: 99%

Transient analysis of power loss density with time-harmonic electromagnetic waves in Debye media

et al. 2021

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Due to the complex permittivity, it is difficult to directly clarify the transient mechanism between electromagnetic waves and Debye media. To overcome the above problem, the temporal relationship between the electromagnetic waves and permittivity is explicitly derived by applying the Fourier inversion and introducing the remnant displacement. With the help of the Poynting theorem and energy conservation equation, the transient power loss density is derived to describe the transient dissipation of electromagnetic field and the mechanism on phase displacement has been explicitly revealed. Besides, the unique solution can be obtained by applying the time-domain analysis method rather than involving the frequency-domain characteristics. The effectiveness of transient analysis is demonstrated by giving a comparison simulation on one-dimensional example.

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“…A Nalysis of electromagnetic scattering from inhomogeneous dielectric objects finds applications in numerous areas ranging from medical diagnostics to geophysical surveys. Simulation tools developed for these applications often rely on finite difference time domain (FDTD) techniques [1]- [4], frequency and time domain finite element methods (FEM) [5]- [8], time domain discontinuous Galerkin (TD-DG) schemes [9]- [13], or frequency and time domain volume integral equation (VIE) solvers [14]- [31]. VIE solvers are often preferred over differential equation solvers (such as FDTD, FEM, TD-DG), for open region scattering problems, since they require only the scatterer to be discretized and implicitly enforce the radiation condition without the need for (approximate) absorbing boundary conditions to terminate the computation domain [32].…”

Section: Introductionmentioning

confidence: 99%

“…VIE solvers are often preferred over differential equation solvers (such as FDTD, FEM, TD-DG), for open region scattering problems, since they require only the scatterer to be discretized and implicitly enforce the radiation condition without the need for (approximate) absorbing boundary conditions to terminate the computation domain [32]. Time domain volume integral equation (TD-VIE) solvers are preferred over their frequency domain counterparts (FD-VIE solvers) for broadband scattering problems [23]- [31] and/or when the scatterer's permittivity is a (nonlinear) function of the fields [30], [31]. VIEs on dielectric scatterers are constructed by enforcing the fundamental field relation (the total field is equal to the summation of the scattered and incident fields) in the (volumetric) support of the scatterer.…”

Section: Introductionmentioning

confidence: 99%

“…The scattered field is represented in terms of the equivalent (unknown) total field/flux induced inside the scatterer. If the electric field is used in the fundamental field relation, then the resulting VIE is termed the electric field volume integral equation (EFVIE) [23]- [31] and the unknown is either the electric flux or the electric field induced inside the scatterer. On the other hand, if the magnetic field is used in the fundamental field relation and the unknown is the total magnetic field, then the magnetic field volume integral equation (MFVIE) is obtained [14].…”

Section: Introductionmentioning

confidence: 99%

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Explicit Time Marching Schemes for Solving the Magnetic Field Volume Integral Equation

Sayed

Ülkü

Bağcı

2020

IEEE Trans. Antennas Propagat.

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A method for constructing explicit marching-on-intime (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.

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An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

Cited by 4 publications

References 6 publications

A Time Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering from Nonlinear Dielectric Objects

A Time Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering from Nonlinear Dielectric Objects

Transient analysis of power loss density with time-harmonic electromagnetic waves in Debye media

Explicit Time Marching Schemes for Solving the Magnetic Field Volume Integral Equation

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