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Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators.

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Τίτλος: Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators.
Συγγραφείς: Burbano-Gallegos, Juan, Pérez-Arancibia, Carlos, Turc, Catalin
Πηγή: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN); Jan/Feb2026, Vol. 60 Issue 1, p273-315, 43p
Θεματικοί όροι: Electromagnetic wave scattering, Electrical conductors, Helmholtz free energy, Free energy (Thermodynamics), Integral operators
Περίληψη: This paper introduces a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems involving smooth perfectly electric conductors (PECs) in three dimensions. These combined-field-type BIE formulations rely exclusively on classical Helmholtz boundary operators, resulting in provably well-posed, frequency-robust, Fredholm second-kind BIEs. Notably, we prove that the proposed formulations are free from spurious resonances, while retaining the versatility of Helmholtz integral operators. The approach is based on the equivalence between the Maxwell PEC scattering problem and two independent vector Helmholtz boundary value problems for the electric and magnetic fields, with boundary conditions defined in terms of the Dirichlet and Neumann traces of the corresponding vector Helmholtz solutions. While certain aspects of this equivalence (for the electric field) have been previously exploited in the so-called field-only BIE formulations, we here rigorously establish and generalize the equivalence between Maxwell and Helmholtz problems for both fields. Finally, a variety of numerical examples highlights the robustness and accuracy of the proposed approach when combined with Density Interpolation-based Nyström methods and fast linear algebra solvers, implemented in the open-source Julia package Inti.jl. [ABSTRACT FROM AUTHOR]
Copyright of ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 192513558
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators.
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  Data: <searchLink fieldCode="AR" term="%22Burbano-Gallegos%2C+Juan%22">Burbano-Gallegos, Juan</searchLink><br /><searchLink fieldCode="AR" term="%22Pérez-Arancibia%2C+Carlos%22">Pérez-Arancibia, Carlos</searchLink><br /><searchLink fieldCode="AR" term="%22Turc%2C+Catalin%22">Turc, Catalin</searchLink>
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  Data: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN); Jan/Feb2026, Vol. 60 Issue 1, p273-315, 43p
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  Data: <searchLink fieldCode="DE" term="%22Electromagnetic+wave+scattering%22">Electromagnetic wave scattering</searchLink><br /><searchLink fieldCode="DE" term="%22Electrical+conductors%22">Electrical conductors</searchLink><br /><searchLink fieldCode="DE" term="%22Helmholtz+free+energy%22">Helmholtz free energy</searchLink><br /><searchLink fieldCode="DE" term="%22Free+energy+%28Thermodynamics%29%22">Free energy (Thermodynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+operators%22">Integral operators</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This paper introduces a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems involving smooth perfectly electric conductors (PECs) in three dimensions. These combined-field-type BIE formulations rely exclusively on classical Helmholtz boundary operators, resulting in provably well-posed, frequency-robust, Fredholm second-kind BIEs. Notably, we prove that the proposed formulations are free from spurious resonances, while retaining the versatility of Helmholtz integral operators. The approach is based on the equivalence between the Maxwell PEC scattering problem and two independent vector Helmholtz boundary value problems for the electric and magnetic fields, with boundary conditions defined in terms of the Dirichlet and Neumann traces of the corresponding vector Helmholtz solutions. While certain aspects of this equivalence (for the electric field) have been previously exploited in the so-called field-only BIE formulations, we here rigorously establish and generalize the equivalence between Maxwell and Helmholtz problems for both fields. Finally, a variety of numerical examples highlights the robustness and accuracy of the proposed approach when combined with Density Interpolation-based Nyström methods and fast linear algebra solvers, implemented in the open-source Julia package Inti.jl. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1051/m2an/2025101
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      – Code: eng
        Text: English
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        PageCount: 43
        StartPage: 273
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        Type: general
      – SubjectFull: Electrical conductors
        Type: general
      – SubjectFull: Helmholtz free energy
        Type: general
      – SubjectFull: Free energy (Thermodynamics)
        Type: general
      – SubjectFull: Integral operators
        Type: general
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      – TitleFull: Maxwell à la Helmholtz: Electromagnetic scattering by 3D perfect electric conductors via Helmholtz integral operators.
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              M: 01
              Text: Jan/Feb2026
              Type: published
              Y: 2026
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