Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl–curl Maxwell's equations

Dolean, Victorita; Gander, Martin J.; Lanteri, Stéphane; Lee, Jin‐Fa; Peng, Zhen

doi:10.1016/j.jcp.2014.09.024

Cited by 58 publications

(29 citation statements)

References 36 publications

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“…It admits two major benefits: the localized BIE for the homogeneous sub-domain problem is immune from cavity resonance effects, and the resulting linear systems of equations readily lend themselves to multiplicative Schwarz preconditioning [23].…”

Section: Local Trace Spacesmentioning

confidence: 99%

“…For a pair of sub-domain interfaces between Ω m and Ω n , S mn and S nm , optimized 2 nd TCs proposed in [23], [41] are employed, which can be expressed as: (20) where I is the identity operator. In reference [41], optimized choices of parameters, κ TE and κ TM , are suggested according to:…”

Section: E Transmission Condititionsmentioning

confidence: 99%

“…Of particular interest is the class of optimized Schwarz methods [17], [18]. Effective transmission conditions have been investigated for the Helmholtz equations [19]- [21] and the Maxwell equations [22], [23]. Recently, DD methods have also been extended to solution of boundary integral equation (BIE) methods [24]- [26].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in the spirit of DD methods, the coupling between adjacent sub-domains are imposed locally through transmission conditions at subdomain interfaces. In particular, optimized second order (2 nd ) transmission conditions [23], [41] are derived to improve the convergence in the DD algorithm.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Multitrace Boundary Integral Equation Formulation for Electromagnetic Cavity Scattering Problems

Peng

2015

IEEE Trans. Antennas Propagat.

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We present a new multi-trace boundary integral equation formulation for the solutions of the time harmonic electromagnetic scattering from large and deep cavities. Comparing to previously integral equation formulations, the new formulation has two major benefits: (1) it leads to a well-conditioned system equation after multiplicative Schwarz preconditioning, and (2) the localized impedance matrices arising from decomposed boundary value problems are immune from cavity resonances effects. We outline the key technical aspects of the new multitrace formulation, give the details of the numerical analysis, and report numerical experiments verifying the analysis and display the capabilities of the proposed methods.Index Terms-Maxwell's Equations, Electromagnetic scattering, Domain decomposition method, Boundary integral equation 0018-926X (c)

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Section: Local Trace Spacesmentioning

confidence: 99%

Section: E Transmission Condititionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Novel Multitrace Boundary Integral Equation Formulation for Electromagnetic Cavity Scattering Problems

Peng

2015

IEEE Trans. Antennas Propagat.

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“…(3) and (1) is guaranteed provided that ( β α ) = 0 or ( β α ) ≥ 0 and (γ ) = 0 or (γ ) ≥ 0. See Dolean et al (2015) for a more detailed discussion.…”

Section: Time-harmonic Boundary Value Problemmentioning

confidence: 99%

Is model-order reduction viable for the broadband finite-element analysis of electrically large antenna arrays?

et al. 2015

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Abstract. Model-order reduction provides an efficient way of computing frequency sweeps for finite-element models, because the dimension of the reduced-order system depends on the complexity of the frequency response rather than the size of the original model. For electrically large domains, however, the applicability of such methods is unclear because the system response may be very complicated. This paper provides a numerical study of the effects of bandwidth, electrical size, and scan angle on the size and convergence of the ROM, by considering linear antenna arrays. A mathematical model is proposed and validated against numerical experiments.

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Schwarz Preconditioning for High Order Edge Element Discretizations of the Time-Harmonic Maxwell’s Equations

Bonazzoli¹,

Dolean

Pasquetti³

et al. 2017

Lecture Notes in Computational Science and Engineering

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Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl–curl Maxwell's equations

Cited by 58 publications

References 36 publications

A Novel Multitrace Boundary Integral Equation Formulation for Electromagnetic Cavity Scattering Problems

A Novel Multitrace Boundary Integral Equation Formulation for Electromagnetic Cavity Scattering Problems

Is model-order reduction viable for the broadband finite-element analysis of electrically large antenna arrays?

Schwarz Preconditioning for High Order Edge Element Discretizations of the Time-Harmonic Maxwell’s Equations

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