Analytical Evaluation of Transient Magnetic Fields Due to RWG Current Bases

Ülkü, H. Arda; Ergin, A.A.

doi:10.1109/tap.2007.910366

Cited by 40 publications

(38 citation statements)

References 8 publications

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“…α(r, t) and e(r, t) denote the arc length and bisecting vector of the arc formed by the intersection of the sphere and S n , respectively. The closed-form expressions of α(r, t) and e(r, t) have been derived in details [17,19]. To complete the whole MOT solver, temporal convolutions between the potentials and the temporal basis functions have to be performed as indicated in Eqs.…”

Section: −1 Tmentioning

confidence: 99%

“…Similarly, the un-smooth property still exists in ∂ R α(r, t) or ∂ R e(r, t) in Eq. (11), which has singularity at tangent points [17]. Thus the direct numerical integration method is invalid in calculating the convolutions in Eqs.…”

Section: −1 Tmentioning

confidence: 99%

“…On the other hand, a developed approach was proposed as shown in [16][17][18][19], which was different from the traditional MOT method. The spatial basis integral was performed first, and then the temporal convolution was evaluated, while the conventional MOT method was implemented in the reverse sequence.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Novel Smoothing Scheme of Temporal Basis Function Independent Method in Mot Based Tdie

Jia¹,

Zhao²,

Zheng³

et al. 2016

PIER M

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Abstract-In this paper, a novel numerical temporal convolution method is presented to calculate the convolutions between the retarded-time potentials and temporal basis functions (or its integration, derivation) in marching-on-in-time (MOT) solver. This approach can smooth and eliminate the singularity of integrated functions by variable substitution. It can also effectively control the precision of numerical quadratures over the surface of the source distribution. Thus it is suitable for more types of temporal basis functions, including non-piecewise polynomial functions. Numerical results demonstrate that this improved method can ensure the accuracy and late time stability of the MOT solver with different types of temporal basis functions.

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Section: −1 Tmentioning

confidence: 99%

Section: −1 Tmentioning

confidence: 99%

See 1 more Smart Citation

A Novel Smoothing Scheme of Temporal Basis Function Independent Method in Mot Based Tdie

Jia¹,

Zhao²,

Zheng³

et al. 2016

PIER M

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show abstract

“…Additionally, for polynomial T i (t) , temporal convolution in (3) can be evaluated in analytically [6]- [8].…”

Section: Magnetic Field Integral Equationmentioning

confidence: 99%

On the mixed discretization of the time domain magnetic field integral equation

Ülkü

Bogaert

Cools

et al. 2012

2012 International Conference on Electromagnetics in Advanced Applications

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− Time domain magnetic field integral equation (MFIE) is discretized using divergenceconforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is "proper": Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. INTRODUCTIONMagnetic field integral equation (MFIE) is a second kind integral equation, i.e., it is constructed as a summation of an identity and a linear operator. Because of the identity operator, the domain and range of the MFIE operator are identical and a consistent discretization scheme should use basis and testing functions, which belong to dual spaces of each other [1]. In particular, the testing function should be in the dual space of the MFIE operator's range (and domain) to obtain a "proper" discretization scheme. Classical marching on-intime (MOT) based MFIE solvers expand the unknown surface current density using divergence-conforming Rao-Wilton-Glisson (RWG) functions [2] in space and polynomial functions in time. To obtain a proper discretization, spatial testing should be done using curl-conforming n × RWG functions, which belong to dual space of the divergence conforming RWG basis functions. However, resulting MOT matrix becomes singular and cannot be inverted accurately at every time step as required by the MOT scheme. Therefore, classical implementations use RWG functions (but not their duals) for spatial testing and violates the requirement of the proper discretization described above. Even though the solution of the MOT matrix system resulting from this discretization scheme converges fast, it yields inaccurate results.In this work, time domain MFIE is discretized using the mixed discretization scheme, which is originally proposed for discretizing the frequency domain MFIE [3]. Mixed discretization scheme makes use of recently proposed Buffa-Christiansen (BC) functions [4]-[5] to produce well-conditioned MOT matrices without violating the requirement of the proper discretization described above. Current density is expanded using divergence-conforming RWG functions in space and spatial testing is carried out using curl-conforming n × BC functions, which belong to dual space of the divergence-conforming RWG functions.

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“…In the marching on-in-time (MOT) solutions of such integral equations, inaccurate calculation of the MOT matrix elements may cause unstable solutions. Recently, closed-form expressions of the retarded-time potentials and fields were developed via Radon transform (RT) interpretation of potential integrals that appear in the surface integral equations (SIEs) [2], [3]. Other exact integration approaches for SIEs have also been suggested [4], [5].…”

Section: Introductionmentioning

confidence: 99%

On the Evaluation of Retarded-Time Potentials for SWG Bases

Ülkü

Ergin

Dikmen

2011

Antennas Wirel. Propag. Lett.

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A new approach for obtaining the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Schaubert-Wilton-Glisson (SWG) basis function is presented. The approach is formulated directly in the time domain without any assumptions regarding the temporal behavior of the currents represented by the SWG bases. It is shown that the aforementioned potentials are related to the solid angle formed by the intersection of the tetrahedral supports of the SWG basis and the "hyper-cone" that is centered at the observation point and that has a radius = , where is the speed of light. In particular, the scalar potential is directly proportional to the total solid angle, and the vector potential is a function of the area centroid vector of this solid angle. The validity of the obtained time-domain formulas is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain. IndexTerms-Marching-on-in-time (MOT) method, Schaubert-Wilton-Glisson (SWG) basis, time-domain analysis, volume integral equations (VIEs).

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Analytical Evaluation of Transient Magnetic Fields Due to RWG Current Bases

Cited by 40 publications

References 8 publications

A Novel Smoothing Scheme of Temporal Basis Function Independent Method in Mot Based Tdie

A Novel Smoothing Scheme of Temporal Basis Function Independent Method in Mot Based Tdie

On the mixed discretization of the time domain magnetic field integral equation

On the Evaluation of Retarded-Time Potentials for SWG Bases

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