Current and Charge Integral Equation Formulation

Taskinen, Matti; Ylä‐Oijala, Pasi

doi:10.1109/tap.2005.861580

Cited by 163 publications

(119 citation statements)

References 15 publications

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“…This avoids terms of the order O.! 1 / (see [6,27,28,30,35]). Unfortunately, all of these approaches encounter a second difficulty in multiply connected domains-a phenomenon that we refer to as "topological low-frequency breakdown" [10,13].…”

Section: The Vector and Scalar Potentialmentioning

confidence: 99%

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A; in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a wellconditioned second-kind Fredholm integral equation that has no spurious resonances, avoids low-frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, scat , is determined entirely by the incident scalar potential inc . Likewise, the unknown vector potential defining the scattered field, A scat , is determined entirely by the incident vector potential A inc . This decoupled formulation is valid not only in the static limit but for arbitrary ! 0.

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Section: The Vector and Scalar Potentialmentioning

confidence: 99%

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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“…To obtain a numerical solution, the problem was recast as a variant of the magnetic field integral equation [25] with surface charge and current densities ρ and J as unknowns [26,27] …”

Section: Calculation Of Electromagnetic Fieldsmentioning

confidence: 99%

Visualizing skin effects in conductors with MRI: 7Li MRI experiments and calculations

Ilott

Chandrashekar

Klöckner

et al. 2014

Journal of Magnetic Resonance

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While experiments on metals have been performed since the early days of NMR (and DNP), the use of bulk metal is normally avoided. Instead, often powders have been used in combination with low fields, so that skin depth effects could be neglected. Another complicating factor of acquiring NMR spectra or MRI images of bulk metal is the strong signal dependence on the orientation between the sample and the radio frequency (RF) coil, leading to non-intuitive image distortions and inaccurate quantification. Such factors are particularly important for NMR and MRI of batteries and other electrochemical devices. Here, we show results from a systematic study combining RF field calculations with experimental MRI of 7 Li metal to visualize skindepth effects directly and to analyze the RF field orientation effect on MRI of bulk metal. It is shown that a certain degree of selectivity can be achieved for particular faces of the metal, simply based on the orientation of the sample. By combining RF field calculations with bulk magnetic susceptibility calculations accurate NMR spectra can be obtained from first principles. Such analyses will become valuable in many applications involving battery systems, but also metals, in general.

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“…In [19] and [16] a new idea to improve conditioning of the electromagnetic surface integral equations was proposed. This idea is based on the use of normalized fields and currents, defined as follows…”

Section: Stabilizing Jm-cfie(α) Formulationsmentioning

confidence: 99%

“…The formulations with the normalized fields and currents, and with various scaling factors, are defined as follows ssJM-CFIEj(α) : α ssJM-CFIEj(1) + β ssJM-CFIEj(0) (19) tsJM-CFIEj(α) : α tsJM-CFIEj(1) + β tsJM-CFIEj(0) (20) rsJM-CFIEj(α) : α rsJM-CFIEj(1) + β rsJM-CFIEj(0).…”

Section: Stabilizing Jm-cfie(α) Formulationsmentioning

confidence: 99%

“…The conditioning of the integral equations of the second kind decreases as the permittivity contrast increases. As a remedy to this problem we propose to use normalized field quantities [16,19]. With the normalized fields and currents the properties of both new JM-CFIE(α) formulations can be stabilized and the optimal values of α minimizing the number of iterations become only weakly dependent on the permittivity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Analysis of Combined Field Integral Equation Formulations for Electromagnetic Scattering by Dielectric and Composite Objects

Ylä‐Oijala¹

2008

PIER C

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Abstract-Numerical analysis of a generalized form of the recently developed electric and magnetic current combined field integral equation (JM-CFIE) for electromagnetic scattering by homogeneous dielectric and composite objects is presented. This new formulation contains a similar coupling parameter α as CFIE contains in the case of perfectly conducting objects. Two alternative JM-CFIE(α) formulations are introduced and their numerical properties (solution accuracy and convergence of iterative Krylov subspace methods) are investigated. The properties of these formulations are found to be very sensitive to the choice of α and to the permittivity of the object. By using normalized fields and currents the optimal value of α minimizing the number of iterations becomes only weakly dependent on the permittivity object. Using linear-linear basis functions instead of the more conventional constant-linear (RWG) basis functions the solution accuracy can be made less dependent on the choice of α.

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Current and Charge Integral Equation Formulation

Cited by 163 publications

References 15 publications

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Visualizing skin effects in conductors with MRI: 7Li MRI experiments and calculations

Numerical Analysis of Combined Field Integral Equation Formulations for Electromagnetic Scattering by Dielectric and Composite Objects

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