| Kirsch A and Schweizer B (2025), "Time-harmonic Maxwell's equations in periodic waveguides", Arch. Rat. Mech. Anal. (accepted). Vol. n/a(n/a), pp. n/a.
[BibTeX] [URL]
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BibTeX:
@article{Kirsch-Schweizer-Maxwell-2024,
author = {Kirsch, Andreas and Schweizer, Ben},
title = {Time-harmonic Maxwell's equations in periodic waveguides},
journal = {Arch. Rat. Mech. Anal. (accepted)},
year = {2025},
volume = {n/a},
number = {n/a},
pages = {n/a},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Closed-WG-Maxwell-Revision.pdf}
}
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| Lamacz-Keymling A, Schubert T and Schweizer B (2025), "Existence result for Maxwell's equations in half-waveguides", (submitted) TU Dortmund 2025-02.
[BibTeX] [URL]
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BibTeX:
@techreport{HalfWG-Maxwell-LSS-2025,
author = {Lamacz-Keymling, Agnes and Schubert, Tim and Schweizer, Ben},
title = {Existence result for Maxwell's equations in half-waveguides},
journal = {(submitted) TU Dortmund 2025-02},
year = {2025},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/existence-Maxwell-preprint.pdf}
}
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| Schweizer B and Wiedemann D (2025), "Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization", (submitted) TU Dortmund 2025-01.
[BibTeX] [URL]
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BibTeX:
@techreport{Schweizer-Wiedemann-Pol-2025,
author = {Schweizer, Ben and Wiedemann, David},
title = {Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization},
journal = {(submitted) TU Dortmund 2025-01},
year = {2025},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Polarization-Maxwell-BS-DW-2025.pdf}
}
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| Kirsch A and Schweizer B (2024), "Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions", Mathematical Methods in the Applied Sciences. Vol. n/a(n/a)
[Abstract] [BibTeX] [DOI] [URL]
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| Abstract: We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self-contained exposition. In this context, we simplify the non-degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem. |
BibTeX:
@article{Kirsch-Schweizer-radiation-2024,
author = {Kirsch, Andreas and Schweizer, Ben},
title = {Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions},
journal = {Mathematical Methods in the Applied Sciences},
year = {2024},
volume = {n/a},
number = {n/a},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Periodic-wave-guides-revisited.pdf},
doi = {10.1002/mma.10435}
}
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| Schweizer B (2024), "Effective sound absorbing boundary conditions for complex geometries", (submitted) TU Dortmund 2024-02.
[BibTeX] [URL]
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BibTeX:
@techreport{Schweizer-Sound-2024,
author = {Schweizer, Ben},
title = {Effective sound absorbing boundary conditions for complex geometries},
journal = {(submitted) TU Dortmund 2024-02},
year = {2024},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/impedance-preprint.pdf}
}
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| Schweizer B (2023), "Inhomogeneous Helmholtz equations in wave guides -- existence and uniqueness results with energy methods", European J. Appl. Math.. Vol. 34(2), pp. 211-237.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Schweizer-Helmholtz-existence-2023,
author = {Schweizer, B.},
title = {Inhomogeneous Helmholtz equations in wave guides -- existence and uniqueness results with energy methods},
journal = {European J. Appl. Math.},
year = {2023},
volume = {34},
number = {2},
pages = {211--237},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Helmholtz-existence-preprint.pdf},
doi = {10.1017/S0956792522000080}
}
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| Donato P, Lamacz A and Schweizer B (2022), "Sound absorption by perforated walls along boundaries", Applicable Analysis. An International Journal. Vol. 101(13), pp. 4397-4411.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Donato-L-S-2022,
author = {Donato, P. and Lamacz, A. and Schweizer, B.},
title = {Sound absorption by perforated walls along boundaries},
journal = {Applicable Analysis. An International Journal},
year = {2022},
volume = {101},
number = {13},
pages = {4397--4411},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/sound-absorption.pdf},
doi = {10.1080/00036811.2020.1855329}
}
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| Poelstra KH, Schweizer B and Urban M (2021), "The geometric average of curl-free fields in periodic geometries", Analysis (Berlin). Vol. 41(3), pp. 179-197.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Poelstra-S-U-2021,
author = {Poelstra, K. H. and Schweizer, B. and Urban, M.},
title = {The geometric average of curl-free fields in periodic geometries},
journal = {Analysis (Berlin)},
year = {2021},
volume = {41},
number = {3},
pages = {179--197},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/geom-average-preprint.pdf},
doi = {10.1515/anly-2020-0053}
}
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| Ohlberger M, Schweizer B, Urban M and Verführt B (2020), "Mathematical analysis of transmission properties of electromagnetic meta-materials", Networks and Heterogeneous Media. Vol. 15(1), pp. 29-56.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Ohlberger-Schweizer-Urban-Verfuehrt-2020,
author = {Ohlberger, Mario and Schweizer, Ben and Urban, Maik and Verführt, Barbara},
title = {Mathematical analysis of transmission properties of electromagnetic meta-materials},
journal = {Networks and Heterogeneous Media},
year = {2020},
volume = {15},
number = {1},
pages = {29--56},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/maxwell-microstructures-preprint.pdf},
doi = {10.3934/nhm.2020002}
}
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| Schweizer B (2020), "Effective Helmholtz problem in a domain with a Neumann sieve perforation", Journal de Mathématiques Pures et Appliquées. Neuvième Série. Vol. 142, pp. 1-22.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Schweizer-Neumann-sieve-2020,
author = {Schweizer, Ben},
title = {Effective Helmholtz problem in a domain with a Neumann sieve perforation},
journal = {Journal de Mathématiques Pures et Appliquées. Neuvième Série},
year = {2020},
volume = {142},
pages = {1--22},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/thinlayer-preprint.pdf},
doi = {10.1016/j.matpur.2020.08.002}
}
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| Schweizer B and Urban M (2020), "On a limiting absorption principle for sesquilinear forms with an application to the Helmholtz equation in a waveguide", In Mathematics of Wave Phenomena.
[BibTeX] [URL]
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BibTeX:
@inproceedings{Schweizer-Urban-LimAbs-2019,
author = {Schweizer, B. and Urban, M.},
editor = {Willy Dörfler and Marlis Hochbruck and Dirk Hundertmark and Wolfgang Reichel and Andreas Rieder and Roland Schnaubelt and Birgit Schörkhuber},
title = {On a limiting absorption principle for sesquilinear forms with an application to the Helmholtz equation in a waveguide},
booktitle = {Mathematics of Wave Phenomena},
year = {2020},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Limiting-absorption-preprint.pdf}
}
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| Dohnal T and Schweizer B (2018), "A Bloch wave numerical scheme for scattering problems in periodic wave-guides", SIAM J Numer Anal. Vol. 56(3), pp. 1848-1870.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Dohnal-Schweizer-2018,
author = {Dohnal, T and Schweizer, B},
title = {A Bloch wave numerical scheme for scattering problems in periodic wave-guides},
journal = {SIAM J Numer Anal},
year = {2018},
volume = {56},
number = {3},
pages = {1848--1870},
url = {https://eldorado.tu-dortmund.de/handle/2003/36118},
doi = {10.1137/17M1141643}
}
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| Lamacz A and Schweizer B (2018), "Outgoing wave conditions in photonic crystals and transmission properties at interfaces", ESAIM Math. Model. Numer. Anal.. Vol. 52(5), pp. 1913-1945.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Lamacz-Schweizer-2018,
author = {Lamacz, Agnes and Schweizer, Ben},
title = {Outgoing wave conditions in photonic crystals and transmission properties at interfaces},
journal = {ESAIM Math. Model. Numer. Anal.},
year = {2018},
volume = {52},
number = {5},
pages = {1913--1945},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/bloch-transmission-rev2016-12.pdf},
doi = {10.1051/m2an/2018026}
}
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| Lipton R and Schweizer B (2018), "Effective Maxwell's equations for perfectly conducting split ring resonators", Arch Ration Mech Anal. Vol. 229(3), pp. 1197-1221.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Lipton-Schweizer-2018,
author = {Lipton, Robert and Schweizer, Ben},
title = {Effective Maxwell's equations for perfectly conducting split ring resonators},
journal = {Arch Ration Mech Anal},
year = {2018},
volume = {229},
number = {3},
pages = {1197--1221},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/perfectcondrings-preprint.pdf},
doi = {10.1007/s00205-018-1237-1}
}
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| Schweizer B (2018), "On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma", In Trends in applications of mathematics to mechanics. Vol. 27, pp. 65-79. Springer, Cham.
[BibTeX] [URL]
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BibTeX:
@incollection{Schweizer-Friedrich-2018,
author = {Schweizer, Ben},
title = {On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma},
booktitle = {Trends in applications of mathematics to mechanics},
publisher = {Springer, Cham},
year = {2018},
volume = {27},
pages = {65--79},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Friedrichs-Helmholtz-divcurl-revised.pdf}
}
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| Schweizer B and Urban M (2018), "Effective Maxwell's equations in general periodic microstructures", Applicable Analysis. An International Journal. Vol. 97(13), pp. 2210-2230.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Schweizer-Urban-2018,
author = {Schweizer, B. and Urban, M.},
title = {Effective Maxwell's equations in general periodic microstructures},
journal = {Applicable Analysis. An International Journal},
year = {2018},
volume = {97},
number = {13},
pages = {2210--2230},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Effective-Maxwell-BS-MU-preprint.pdf},
doi = {10.1080/00036811.2017.1359563}
}
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| Dörlemann C, Heida M and Schweizer B (2017), "Transmission conditions for the Helmholtz-equation in perforated domains", Vietnam J. Math.. Vol. 45(1-2), pp. 241-253.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Doerlemann-Heida-Schweizer-2017,
author = {Dörlemann, Christina and Heida, Martin and Schweizer, Ben},
title = {Transmission conditions for the Helmholtz-equation in perforated domains},
journal = {Vietnam J. Math.},
year = {2017},
volume = {45},
number = {1-2},
pages = {241--253},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Transmission-revision.pdf},
doi = {10.1007/s10013-016-0222-y}
}
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| Lamacz A and Schweizer B (2017), "Effective acoustic properties of a meta-material consisting of small Helmholtz resonators", Discrete Contin. Dyn. Syst. Ser. S. Vol. 10(4), pp. 815-835.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Lamacz-Schweizer-2017,
author = {Lamacz, Agnes and Schweizer, Ben},
title = {Effective acoustic properties of a meta-material consisting of small Helmholtz resonators},
journal = {Discrete Contin. Dyn. Syst. Ser. S},
year = {2017},
volume = {10},
number = {4},
pages = {815--835},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/SmallResonatorsFinal.pdf},
doi = {10.3934/dcdss.2017041}
}
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| Schweizer B (2017), "Resonance meets homogenization: construction of meta-materials with astonishing properties", Jahresber. Dtsch. Math.-Ver.. Vol. 119(1), pp. 31-51.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Schweizer-Resonance-2017,
author = {Schweizer, Ben},
title = {Resonance meets homogenization: construction of meta-materials with astonishing properties},
journal = {Jahresber. Dtsch. Math.-Ver.},
year = {2017},
volume = {119},
number = {1},
pages = {31--51},
url = {https://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/Resonances-Preprint.pdf},
doi = {10.1365/s13291-016-0153-2}
}
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| Lamacz A and Schweizer B (2016), "A negative index meta-material for Maxwell's equations", SIAM J Math Anal. Vol. 48(6), pp. 4155-4174.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Lamacz-Schweizer-2016,
author = {Lamacz, A. and Schweizer, B.},
title = {A negative index meta-material for Maxwell's equations},
journal = {SIAM J Math Anal},
year = {2016},
volume = {48},
number = {6},
pages = {4155--4174},
url = {https://eldorado.tu-dortmund.de/handle/2003/34176},
doi = {10.1137/16M1064246}
}
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| Schweizer B (2015), "The low-frequency spectrum of small Helmholtz resonators", Proceedings A. Vol. 471(2174), pp. 20140339, 18.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Schweizer-Spectrum-2015,
author = {Schweizer, B.},
title = {The low-frequency spectrum of small Helmholtz resonators},
journal = {Proceedings A},
year = {2015},
volume = {471},
number = {2174},
pages = {20140339, 18},
url = {https://eldorado.tu-dortmund.de/handle/2003/33030},
doi = {10.1098/rspa.2014.0339}
}
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| Bouchitté G and Schweizer B (2013), "Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings", Netw. Heterog. Media. Vol. 8(4), pp. 857-878.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Bouchitte-Schweizer-Plasmonic-2013,
author = {Bouchitté, Guy and Schweizer, Ben},
title = {Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings},
journal = {Netw. Heterog. Media},
year = {2013},
volume = {8},
number = {4},
pages = {857--878},
url = {http://www.mathematik.tu-dortmund.de/lsi/schweizer/Preprints/plasmons-revised.pdf},
doi = {10.3934/nhm.2013.8.857}
}
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| Lamacz A and Schweizer B (2013), "Effective Maxwell equations in a geometry with flat rings of arbitrary shape", SIAM J Math Anal. Vol. 45(3), pp. 1460-1494.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Lamacz-Schweizer-flat-2013,
author = {Lamacz, Agnes and Schweizer, Ben},
title = {Effective Maxwell equations in a geometry with flat rings of arbitrary shape},
journal = {SIAM J Math Anal},
year = {2013},
volume = {45},
number = {3},
pages = {1460--1494},
url = {https://eldorado.tu-dortmund.de/handle/2003/29427},
doi = {10.1137/120874321}
}
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| Bouchitté G and Schweizer B (2010), "Homogenization of Maxwell's equations in a split ring geometry", Multiscale Model Simul. Vol. 8(3), pp. 717-750.
[BibTeX] [DOI] [URL]
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BibTeX:
@article{Bouchitte-Schweizer-Max-2010,
author = {Bouchitté, Guy and Schweizer, Ben},
title = {Homogenization of Maxwell's equations in a split ring geometry},
journal = {Multiscale Model Simul},
year = {2010},
volume = {8},
number = {3},
pages = {717--750},
url = {https://eldorado.tu-dortmund.de/handle/2003/25743},
doi = {10.1137/09074557X}
}
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