Estimates of scattered electromagnetic fields

Wellander, Niklas; Kristensson, Gerhard

doi:10.1002/mma.2831

Cited by 3 publications

(8 citation statements)

References 17 publications

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“…Several of the results in a previous paper [4] have been generalized and extended in this paper. In Section 2, the scattering problem is formulated in a variational setting.…”

Section: Introductionmentioning

confidence: 91%

“…Here, we use the Riccati-Bessel functions l .x/ D xh .1/ l .x/, where h .1/ l .k 0 x/ is the spherical Hankel function of the first kind [15]. These vector waves satisfy r .r u n .k 0 x// k 2 0 u n .k 0 x/ D 0, D 1, 2 and they also satisfy the radiation condition in (4). Another representation of the definition of the vector waves is 8 <…”

Section: A2 Lax-milgram's Theoremmentioning

confidence: 99%

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Some a priori estimates of solutions to the Maxwell equations

Kristensson

Wellander

2014

Math. Meth. Appl. Sci.

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In this paper, we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calderón operator for a sphere is investigated and depicted as a function of the frequency.

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“…Several of the results in a previous paper [4] have been generalized and extended in this paper. In Section 2, the scattering problem is formulated in a variational setting.…”

Section: Introductionmentioning

confidence: 91%

Section: A2 Lax-milgram's Theoremmentioning

confidence: 99%

Some a priori estimates of solutions to the Maxwell equations

Kristensson

Wellander

2014

Math. Meth. Appl. Sci.

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“…Theorem 5 There exist constants C 1 , C 2 > 0 such that the scattered fields on the surface ∂ Ω satisfy

| | γ_{t}^{+} (E_{s}) | |_{T (\partial Ω)} \leq C_{1} | | E_{i} | |_{H (curl, Ω)}

and

| | γ_{t}^{+} (H_{s}) | |_{T (\partial Ω)} \leq C_{2} | | E_{i} | |_{H (curl, Ω)} .

…”

Section: Estimates For the Scattered Fieldsmentioning

confidence: 99%

“…Now, there is a well‐known integral representation of the scattered field: 5

\begin{matrix} right E_{s} (x) = \frac{i}{k_{0}} \nabla \times [\nabla \times \int_{\partial Ω} I_{3 \times 3} g (| x - y |) C^{e} (γ_{t}^{+} (E_{s})) (y) d σ (y)] \\ right + \nabla \times \int_{\partial Ω} I_{3 \times 3} g (| x - y |) γ_{t}^{+} (E_{s}) (y) d σ (y), x \in Ω_{e} \end{matrix}

where

g false(z false) = e^{i k_{0} z} false/ false(4 π z false)

is the fundamental solution of the Helmholtz equation. From this representation coupled with Proposition 4.2 in Kristensson and Wellander, 1 we obtain the following explicit estimate:…”

Section: Estimates For the Scattered Fieldsmentioning

confidence: 99%

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Quantitative trace estimates for the Maxwell system in Lipschitz domains

Stachura

Wellander

2021

Math Methods in App Sciences

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We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and extension operators over certain Sobolev spaces. Finally, we provide a weak formulation of the interior scattering problem in terms of the exterior Calderón operator and provide explicit bounds for the solution of the interior problem in terms of the incident fields and the Lipschitz character of the domain.

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Quantitative Trace Estimates for the Maxwell system in Lipschitz Domains

Stachura,

Wellander

2020

Preprint

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We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and extension operators over certain Sobolev spaces. Finally, we provide a weak formulation of the interior scattering problem in terms of the exterior Calderón operator, and provide explicit bounds for the solution of the interior problem in terms of the incident fields and the Lipschitz character of the domain.

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Estimates of scattered electromagnetic fields

Cited by 3 publications

References 17 publications

Some a priori estimates of solutions to the Maxwell equations

Some a priori estimates of solutions to the Maxwell equations

Quantitative trace estimates for the Maxwell system in Lipschitz domains

Quantitative Trace Estimates for the Maxwell system in Lipschitz Domains

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