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Thöns-Zueva, A., Schmidt, K. and Semin, A. Multiharmonic analysis for nonlinear acoustics with different scales. arXiv:1701.02097, TU Berlin, 2017. [PDF], [BibTeX]

Schmidt, K. and Thöns-Zueva, A. Impedance boundary conditions for acoustic time harmonic wave propagation in viscous gases. Preprint series of the Institute of Mathematics, 6-2014, Technische Universität Berlin, 2014. [PDF], [BibTeX]

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Reviewed Articles


Schmidt, K. and Hiptmair, R. Asymptotic expansion techniques for singularly perturbed boundary integral equations. Numer. Math., 137(2): 397–415, 2017. [DOI], [BibTeX]

Semin, A., Delourme, B. and Schmidt, K. On the homogenization of the Helmholtz problem with thin perforated walls of finite length. ESAIM Math. Model. Numer. Anal., 2017. [BibTeX]

Drescher, L., Heumann, H. and Schmidt, K. A High Order Galerkin Method for Integrals over Contour Lines with an Application to Plasma Physics. SIAM Numer. Math., 2017. [PDF], [BibTeX]


Semin, A. and Schmidt, K. Absorbing boundary conditions for the viscous acoustic wave equation. Math. Meth. Appl. Sci., 39(17): 5043–5065, 11 2016. [DOI], [BibTeX]

Péron, V., Schmidt, K. and Duruflé, M. Equivalent Transmission Conditions for the time-harmonic Maxwell equations in 3D for a Medium with a Highly Conductive Thin Sheet. SIAM J. Appl. Math., 76(3): 1031–1052, May 2016. [DOI], [PDF], [BibTeX]

Delourme, B., Schmidt, K. and Semin, A. On the homogenization of thin perforated walls of finite length. Asymptotic Analysis, 97(3-4): 211-264, 2016. [DOI], [PDF], [BibTeX]


Fliss, S., Klindworth, D. and Schmidt, K. Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides. BIT, 55(1): 81–115, 2015. [DOI], [PDF], [BibTeX]

Garnier, J., Papanicolaou, G., Semin, A. and Tsogka, C. Signal to Noise Ratio Analysis in Virtual Source Array Imaging. SIAM Journal on Imaging Sciences, 8(1): 248–279, 2015. [DOI], [PDF], [BibTeX]

Schmidt, K., Diaz, J. and Heier, C. Non-conforming Galerkin finite element methods for local absorbing boundary conditions of higher order. Comput. Math. Appl., 70(9): 2252–2269, 2015. [DOI], [PDF], [BibTeX]

Schmidt, K. and Heier, C. An analysis of Feng's and other symmetric local absorbing boundary conditions. ESAIM Math. Model. Numer. Anal., 49(1): 257–273, 2015. [DOI], [PDF], [BibTeX]

Schmidt, K. and Hiptmair, R. Asymptotic boundary element methods for thin conducting sheets. Discrete Contin. Dyn. Syst. Ser. S, 8(3): 619–647, 2015. [DOI], [BibTeX]


Klindworth, D. and Schmidt, K. Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides. IEEE Trans. Magn., 50: 217–220, Feb 2014. [DOI], [PDF], [BibTeX]

Schmidt, K. and Chernov, A. Robust transmission conditions of high order for thin conducting sheets in two dimensions. IEEE Trans. Magn., 50(2): 41–44, Feb 2014. [DOI], [PDF], [BibTeX]

Schmidt, K. and Hiptmair, R. Asymptotic boundary element methods for thin conducting sheets in two dimensions. IEEE Trans. Magn., 50: 469–472, Feb 2014. [DOI], [PDF], [BibTeX]

Klindworth, D. and Schmidt, K. An efficient calculation of photonic crystal band structures using Taylor expansions. Commun. Comput. Phys., 16(5): 1355–1388, 2014. [PDF], [BibTeX]

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Technical Reports

Schmidt, K. and Chernov, A. Robust families of transmission conditions of high order for thin conducting sheets. INS Report, 1102, pp. 1–33, Institute for Numerical Simulation, University of Bonn, Feb 2011. [PDF], [BibTeX]

Semin, A. and Joly, P. Study of propagation of acoustic waves in junction of thin slots. Research Report, RR-7265, pp. 1–56, INRIA, Apr 2010. [PDF], [BibTeX]

Semin, A. Numerical resolution of the wave equation on a network of slots. Technical Report, RT-369, pp. 1–35, INRIA, 2009. [PDF], [BibTeX]

Joly, P. and Semin, A. Propagation of an acoustic wave in a junction of two thin slots. Research Report, RR-6708, pp. 1–61, INRIA, 2008. [PDF], [BibTeX]

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Robust transmission conditions of high-order for thin conducting sheets
Zitatschlüssel Schmidt.Chernov:2011:WAVES
Autor K. Schmidt and A. Chernov
Buchtitel Proc. 10th International Conference on Mathematical and Numerical Aspects of Wave Propagation
Seiten 691–694
Jahr 2011
Monat Jul
Zusammenfassung For conducting thin sheets we derive approximative transmission conditions of high orders within the time-harmonic eddy current model, and discuss an application to time-harmonic wave propagation. With the transmission conditions the sheet has not to be resolved by a FE mesh, but only its middle curve. We investigate three families of transmission conditions which are derived by asymptotic expansion for small sheet thicknesses $\eps$, where each family results from a different asymptotic framework. In the first asymptotic framework the conductivity remains constant, scales with $1/\eps$ in the second and with $1/\eps^2$ in the third. The conditions of different asymptotics differ from they robustness, i.e., they applicability and accurary for a wide range of sheet thicknesses and conductivities. We observe that the condition derived for the $1/\eps$ asymptotics is the most robust limit condition, contrary to higher orders, where the transmission conditions derived for the $1/\eps^2$ asymptotics turn out to be most robust.
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Chapters in Books

Klindworth, D., Ehrhardt, M. and Koprucki, T. Discrete Transparent Boundary Conditions for Multi-Band Effective Mass Approximations. In Ehrhardt, M. and Koprucki, T. (editors), Multi-Band Effective Mass Approximations, Lecture Notes in Computational Science and Engineering, Vol. 94, Chapter 8, pp. 273–318, 2014. [DOI], [BibTeX]

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PhD Theses

Klindworth, D. On the numerical computation of photonic crystal waveguide band structures. Technische Universität Berlin, 2015. [PDF], [BibTeX]

Semin, A. Propagation d'ondes dans des jonctions de fentes minces. Université de Paris-Sud 11, Nov 2010. [BibTeX]

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