An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

Chen, Rui; Sayed, Sadeed Bin; Bağcı, Hakan

doi:10.1109/apusncursinrsm.2018.8608706

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…The predictor and corrector coefficient vectors, p and c are obtained using the sixthorder Adams-Bashforth and backward difference formulas [50], respectively. The convergence threshold for the corrector updates [(CE) m ] is set to PECE = 10 −13 [see (54)]. The matrix equations in ( 43), ( 46), (50), and ( 53) are iteratively solved using the transpose-free quasi-minimal residual (TFQMR) method [67].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Inserting these expansions into TD-EFVIE and testing the resulting equation using SWG functions yield a system of ordinary differential equations (ODEs) in timedependent expansion coefficients of the SWG basis functions. A P E(CE) m scheme is used to integrate this system of ODEs in time for the unknown electric field expansion coefficients [38,39,43,[47][48][49][50][51][52][53][54][55][56][57]. Similarly, expansions of the electric field and the electric flux are inserted into the nonlinear constitutive relation and its "inverse" obtained using the Padé approximant [58][59][60].…”

Section: Introductionmentioning

confidence: 99%

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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: Numerical Resultsmentioning

confidence: 99%

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

Self Cite

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“…It should be noted here that TDCPIE is obtained by linearly combining TDPIE with its normal derivative. Coupling parameters of this combination are carefully selected to enable the computation of the singular integrals that appear in the expressions of the matrix elements resulting from the Nyström discretization in space [28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

On the Spurious Interior Resonance Modes of Time Domain Integral Equations for Analyzing Acoustic Scattering from Penetrable Objects

Chen,

Shi,

Sayed

et al. 2021

Preprint

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The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the time domain potential integral equation (TDPIE) (in unknowns velocity potential and its normal derivative), suffers from the interior resonance problem, i.e., its solution is replete with spurious modes that are excited at the resonance frequencies of the acoustic cavity in the shape of the scatterer. Numerical experiments demonstrate that, unlike the frequencydomain integral equations, the amplitude of these modes in the time domain could be suppressed to a level that does not significantly affect the solution. The second equation is obtained by linearly combining TDPIE with its normal derivative. Weights of the combination are carefully selected to enable the numerical computation of the singular integrals. The solution of this equation, which is termed the time domain combined potential integral equation (TDCPIE), does not involve any spurious interior resonance modes.

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On the Internal Resonance Modes of Time Domain Surface Integral Equations for Acoustic Transmission Problems

Chen

Bağcı

2021

2021 XXXIVth General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS)

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The internal resonance problem pertinent to time domain surface integral equations (SIEs) for analyzing transient acoustic scattering from penetrable objects is investigated. The first equation considered here is constructed by combining SIE representations of the internal and external problems via the continuity of the velocity potential and its normal derivative. Just like its frequency-domain counterpart, this equation suffers from the internal resonance problem. But it is demonstrated in this work that, unlike the frequency-domain solution, by increasing the accuracy of the discretization, the amplitude of these spurious modes can be suppressed to a level that does not significantly affect the solution. The second equation considered here is obtained by linearly combining the first equation with its normal derivative and its solution is completely free from spurious internal resonance modes.

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An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

Cited by 3 publications

References 9 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

On the Spurious Interior Resonance Modes of Time Domain Integral Equations for Analyzing Acoustic Scattering from Penetrable Objects

On the Internal Resonance Modes of Time Domain Surface Integral Equations for Acoustic Transmission Problems

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