Polar Integration for Exact Space-Time Quadrature in Time-Domain Integral Equations

Pingenot, J.; Chakraborty, Shiladri; Jandhyala, Vikram

doi:10.1109/tap.2006.882195

Cited by 25 publications

(20 citation statements)

References 12 publications

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“…Similarly, the scalar potential can be written as (4) where denotes the integration with respect to time. In (3) and (4), are chosen as the SWG functions.…”

Section: Evaluation Of the Potentialsmentioning

confidence: 99%

“…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]. Later, it was shown that by using the closed-form expressions, more accurate results were obtained in the solutions of SIEs [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Similarly, the scalar potential can be written as (4) where denotes the integration with respect to time. In (3) and (4), are chosen as the SWG functions.…”

Section: Evaluation Of the Potentialsmentioning

confidence: 99%

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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“…Fortunately, the inclusion of additional uncoupled filtering circuit elements is relatively inexpensive in comparison to the computationally more demanding coupled circuit elements. As an alternative approach to our filtering approach, the geometrical arrangements of the delay distances is used in [11] to improve the phase response for very high frequencies.…”

Section: High Frequency Filteringmentioning

confidence: 99%

Toward improved time domain stability and passivity for full-wave PEEC models

Ekman

Antonini²,

Ruehli³

2006

2006 IEEE International Symposium on Electromagnetic Compatibility, 2006. EMC 2006.

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Abstract-It is well known that time domain integral equation techniques may suffer from stability problems and frequency domain models may provide non-passive results. A main source of these issues is the delay of the coupled elements. In the classical Partial Element Equivalent Circuit (PEEC) method, a single delay was used for each couple of partial element which results in a delay differential equation with reduced stability and accuracy. In this paper, we consider multiple delay coefficients which can be used for both the time and frequency domain. Also, filters are introduced which remove unwanted eigenvalues or resonances in the partial element couplings. This can substantially improve the response of the frequency domain and the time domain models. Stability improvements also means passivity improvements.

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“…Later, implicit time stepping algorithms and appropriate smooth temporal basis functions are also proposed to overcome the above mentioned drawbacks [5][6][7][8][9][10]. Recent studies show that accuracy computation of the MOT impedance matrix is considered as a cure factor, effecting the late time stability and accuracy of the MOT solver [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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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Polar Integration for Exact Space-Time Quadrature in Time-Domain Integral Equations

Cited by 25 publications

References 12 publications

On the Evaluation of Retarded-Time Potentials for SWG Bases

On the Evaluation of Retarded-Time Potentials for SWG Bases

Toward improved time domain stability and passivity for full-wave PEEC models

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

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