An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation

Chen, Rui; Sayed, Sadeed Bin; Al-Harthi, Noha; Keyes, David E.; Bağcı, Hakan

doi:10.1121/1.5125259

Cited by 12 publications

(12 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Substituting (3) in (2) and spatially testing with u(rjq) and v(rjq), j = 1, ..., Nn, q = 1, ..., Np yield a time-dependent semi-discrete system of ODEs. This system has to be sampled at times t = h∆t to carry out the time integration using a PE(CE) m -type scheme [8], [20], [22]. Consequently one has to use temporal interpolation on…”

Section: Explicit Mot Scheme (E-mot)mentioning

confidence: 99%

“…A PE(CE) m scheme is used to integrate the ODE system (5) to yield I h , h = 1, ..., Nt [8], [20], [22]. Steps of this scheme are briefly summarized as follows:…”

Section: Explicit Mot Scheme (E-mot)mentioning

confidence: 99%

“…This sparse matrix inversion required at every step can be eliminated if a spatial discretization scheme, which does not use basis functions defined over two mesh elements, is used. Indeed in [20], an MOT scheme that makes use of this idea is used to solve the time domain integral equations of acoustics. In this work, this scheme is extended to solve the TD-MFIE efficiently when ∆t is large.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies

Chen

Sayed

Ülkü

et al. 2021

IEEE Trans. Antennas Propagat.

Self Cite

View full text Add to dashboard Cite

An explicit marching-on-in-time (MOT) scheme to efficiently solve the time domain magnetic field integral equation (TD-MFIE) with a large time step size (under a low-frequency excitation) is developed. The proposed scheme spatially expands the current using high-order nodal functions defined on curvilinear triangles discretizing the scatterer surface. Applying Nyström discretization, which uses this expansion, to the TD-MFIE, which is written as an ordinary differential equation (ODE) by separating self-term contribution, yields a system of ODEs in unknown time-dependent expansion coefficients. A predictor-corrector method is used to integrate this system for samples of these coefficients. Since the Gram matrix arising from the Nyström discretization is blockdiagonal, the resulting MOT scheme replaces the matrix "inversion" required at each time step by a product of the inverse block-diagonal Gram matrix and the right-hand side vector. It is shown that, upon convergence of the corrector updates, this explicit MOT scheme produces the same solution as its implicit counterpart, and is faster for large time step sizes. Index Terms-Marching-on-in-time (MOT), magnetic field integral equation (MFIE), Nyström method, predictor-corrector scheme.

show abstract

Section: Explicit Mot Scheme (E-mot)mentioning

confidence: 99%

“…A PE(CE) m scheme is used to integrate the ODE system (5) to yield I h , h = 1, ..., Nt [8], [20], [22]. Steps of this scheme are briefly summarized as follows:…”

Section: Explicit Mot Scheme (E-mot)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies

Chen

Sayed

Ülkü

et al. 2021

IEEE Trans. Antennas Propagat.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The strongly-singular integrals in Eq. ( 17) are computed using the approach described in [29]. The strongly-and hyper-singular integrals in Eq.…”

Section: Computation Of Singular Integralsmentioning

confidence: 99%

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Explicit Marching‐on‐in‐time Solvers for Second‐kind Time Domain Integral Equations

Chen¹,

Sayed²,

Ülkü³

et al. 2022

Advances in Time‐Domain Computational Electromagnetic Methods

Self Cite

View full text Add to dashboard Cite

Time domain methods are often preferred over their frequency domain counterparts for numerical electromagnetic analysis since they can produce broadband data from a single simulation, can account for nonlinearities directly, and often provide immediate physical interpretation of the problem's solution. Among the time domain methods, time domain integral equation (TDIE) solvers have recently found widespread use and they have become an attractive alternative to differential equation solvers such 1 as finite difference time domain schemes and time domain finite element method, especially for open region scattering problems. This is because TDIE solvers do not suffer from numerical phase dispersion, do not require approximate radiation boundary conditions (such as absorbing boundary conditions and perfectly matched layers), and their time step size is not restricted by a Courant-Friedrichs-Lewy-like condition. Almost all traditional TDIE solvers utilize an implicit time marching scheme, i.e., they call for solution of a (sparse) matrix at every iteration. This reduces the computational efficiency under low-frequency excitations and makes the use of TDIE solvers in multiphysics frameworks a challenge. To address these challenges, recently, various explicit marching-on-in-time (MOT) schemes have been developed to solve the second kind TDIEs for perfect electrically conducting and dielectric scatterers. This chapter details the formulation and implementation of these TDIE solvers. These schemes cast the second kind TDIE in the form of an ordinary differential equation (ODE).A classical scheme such as those making use of Rao-Wilton-Glisson and Schubert-Wilton-Glisson basis functions and Nyström integration is used for spatial discretization. Then, a predictor-corrector scheme is used to integrate the spatially discretized ODE systems in time for the expansion coefficients of the unknowns. The explicit TDIE solvers described in this chapter use the same time step size as their implicit counterparts without sacrificing from accuracy and stability of the solution. In addition, they are significantly faster under low-frequency excitations. Numerical results are presented to demonstrate these computational benefits.

show abstract

An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation

Cited by 12 publications

References 41 publications

An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies

An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies

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

Explicit Marching‐on‐in‐time Solvers for Second‐kind Time Domain Integral Equations

Contact Info

Product

Resources

About