Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

Bruno, Oscar P.; Elling, Tim; Paffenroth, Randy; Turc, Catalin

doi:10.1016/j.jcp.2009.05.020

Cited by 52 publications

(80 citation statements)

References 27 publications

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“…However, when k is large, these techniques are limited in terms of stability because the mathematical structure and physics of the underlying operator, that is the Maxwell operators, are lost during the purely algebraic operations. To overcome this problem, recent promising directions [11][12][13]10,9,22,23,2,19,42,21,41] have emerged by producing new preconditioning techniques based on (pseudo differential) operators calculus and integral equations that are then discretized to get a matrix representation. One crucial point in these approaches is to build approximate and accurate representations of the operators linking the magnetic (M) and the electric (J) surface currents through the so-called Magnetic-to-Electric (MtE) map [51]: MtE(M, J) = 0 on Γ , where Γ is the scattering surface.…”

Section: Introductionmentioning

confidence: 99%

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Bouajaji¹,

Antoine²,

Geuzaine³

2014

Journal of Computational Physics

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The aim of this paper is to propose new local and accurate approximate magnetic-toelectric surface boundary operators for the three-dimensional time-harmonic Maxwell's equations. After their construction where their accuracy is improved through a regularization process, a localization of these operators and a full finite element approximation is introduced. Next, their numerical efficiency and accuracy is investigated in detail for different scatterers when these operators are used in the extreme situation of On-Surface Radiation Conditions methods.

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Section: Introductionmentioning

confidence: 99%

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Bouajaji¹,

Antoine²,

Geuzaine³

2014

Journal of Computational Physics

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“…We have explained, in Section 5, how to do this for partial wave expansions, plane waves, and (of course) the potentials induced by known impressed currents and charges. We have also developed integral representations for [15], the Calderon preconditioning combined source integral equation (CP-CSIE) [12], and the regularized combined source integral equation (RCSIE) [7]. the vector and scalar potentials that lead to well-conditioned second kind integral equations (the decoupled potential integral equations or DPIE).…”

Section: Discussionmentioning

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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“…Instead, one usually turns to preconditioned Krylov subspace iterative methods. When such iterative solutions are employed, the efficient and parallel computation of effective preconditioners poses an immense challenge [6,12,[36][37][38][39][40][41][42]. This work proposes a one-level non-overlapping additive Schwarz DD preconditioner [43] for the solution of the DG-BEM linear system equation, Ax = b.…”

Section: Domain Decomposition Solvermentioning

confidence: 99%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

Cited by 52 publications

References 27 publications

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

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