Research Group of Prof. Dr. Barbara Verfürth

Address:
Institut für Numerische Simulation
Friedrich-Hirzebruch-Allee 7
53115 Bonn
Germany
Phone: +49 228 73-69833
Office: FHA7 3.030
E-Mail: ed tod nnob-inu tod sni ta htreufreva tod b@foo tod de

Open position

In the research group, we currently have an open PhD position (3 years contract, 75% TV-L E13, possibility to earn a PhD is given, starting date October 1, 2025 or later). The envisioned topic is about numerical multiscale methods (e.g., Heterogeneous Multiscale Method) for linear elasticity with high-contrast coeffcients. We are looking for a candidate with a Master degree in mathematics, a strong background in numerical methods for PDEs and their theoretical error analysis (knowledge about multiscale method not necessary), and some programming knowledge. If you are interested, please contact Barbara Verfürth (ed tod nnob-inu tod sni ta htreufreva tod b@foo tod de) for further information and how to apply.

Research interests

  • numerical methods for partial differential equations
  • multiscale (finite element) methods
  • (numerical) homogenization
  • (time-harmonic) wave propagation: Helmholtz and Maxwell equations
  • nonlinear PDEs (nonlinear diffusion, nonlinear Helmholtz,…)

Short CV

  • since 10/2022: Professor at INS, University of Bonn
  • 2020 – 2022: Junior research group leader and Tenure-Track-Professor at Karlsruhe Institute of Technology (KIT)
  • 2018 – 2020: PostDoc at University of Augsburg
  • 2015 – 2018: PhD at University of Münster

Teaching

Winter semester 2025/26

Summer semester 2025

Winter semester 2024/25

See teaching activities of the whole group.

Research Projects

Current

Homogenization of time-varying metamaterials

Project B4, DFG CRC 1173.

Homepage.

Numerical methods for nonlinear, random and dynamical multiscale problems

Project 496556642, DFG Emmy Noether.

Show description. Homepage.

Completed

TEEMLEAP - A new TEstbed for Exploring Machine LEarning in Atmospheric Prediction

KIT Future Fields.

Homepage.

See all projects of the group.

Publications

Preprints

  1. Local and nonlocal homogenization of wave propagation in time-varying media. C. Döding and B. Verfürth. preprint, 2025. BibTeX arXiv
  2. Linearized localized orthogonal decomposition for quasilinear nonmonotone elliptic pde. M. Khrais and B. Verfürth. arXiv preprint 2502.13831, 2025. BibTeX arXiv
  3. Error analysis of an implicit-explicit time discretization scheme for semilinear wave equations with application to multiscale problems. D. Eckhardt, M. Hochbruck, and B. Verfürth. arXiv preprint 2406.19889, 2024. BibTeX arXiv

Articles

  1. Offline-online approximation of multiscale eigenvalue problems with random defects. D. Kolombage and B. Verfürth. ESAIM Math. Model. Numer. Anal., 2025. to appear; preprint available as arXiv:2411.19614. BibTeX DOI
  2. TEEMLEAP - a new testbed for exploring machine learning in atmospheric prediction for research and education. J. Wilhelm, J. F. Quinting, M. Burba, S. Hollborn, U. Ehret, I. P. Sanchez, S. Lerch, J. Meyer, B. Verfürth, and P. Knippertz. Journal of Advances in Modeling Earth Systems, 17(7):e2024MS004881, 2025. BibTeX DOI preprint
  3. Statistical variational data assimilation. A. Benaceur and B. Verfürth. Comput. Methods Appl. Mech. Engrg., 432:117402, 2024. BibTeX DOI
  4. Wave propagation in high-contrast media: periodic and beyond. É. Fressart and B. Verfürth. Comput. Methods Appl. Math., 24(2):337–354, 2024. BibTeX DOI
  5. Two-step homogenization of spatiotemporal metasurfaces using an eigenmode-based approach. P. Garg, A. G. Lamprianidis, S. Rahman, N. Stefanou, E. Almpanis, N. Papanikolaou, B. Verfürth, and C. Rockstuhl. Opt. Mater. Express, 14(2):549–563, 2024. See supplement https://doi.org/10.6084/m9.figshare.24849822.v2. BibTeX DOI
  6. Metamaterial applications of TMATSOLVER, an easy-to-use software for simulating multiple wave scattering in two dimensions. S. C. Hawkins, L. G. Bennetts, M. A. Nethercote, M. A. Peter, D. Peterseim, H. J. Putley, and B. Verfürth. Proc. R. Soc. A, 2024. BibTeX DOI
  7. Higher-Order Finite Element Methods for the Nonlinear Helmholtz Equation. B. Verfürth. J. Sci. Comput., 98(3):article number 66, 2024. BibTeX DOI
  8. Numerical Multiscale Methods for Waves in High-Contrast Media. B. Verfürth. Jahresber. Dtsch. Math.-Ver., 126(1):37–65, 2024. BibTeX DOI
  9. Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales. D. Eckhardt and B. Verfürth. BIT, 63(2):Paper No. 35, 26, 2023. BibTeX DOI
  10. Modeling four-dimensional metamaterials: a T-matrix approach to describe time-varying metasurfaces. P. Garg, A. G. Lamprianidis, D. Beutel, T. Karamanos, B. Verfürth, and C. Rockstuhl. Opt. Express, 30(25):45832–45847, dec 2022. BibTeX DOI
  11. Numerical upscaling for wave equations with time-dependent multiscale coefficients. B. Maier and B. Verfürth. Multiscale Model. Simul., 20(4):1169–1190, 2022. BibTeX DOI
  12. Multiscale scattering in nonlinear Kerr-type media. R. Maier and B. Verfürth. Math. Comp., 91(336):1655–1685, 2022. BibTeX DOI
  13. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. R. Mandel, Zo¨ıs Moitier, and B. Verfürth. C. R. Math. Acad. Sci. Paris, 360:513–538, 2022. BibTeX DOI
  14. An offline-online strategy for multiscale problems with random defects. A. Målqvist and B. Verfürth. ESAIM Math. Model. Numer. Anal., 56(1):237–260, 2022. BibTeX DOI
  15. Numerical homogenization for nonlinear strongly monotone problems. B. Verfürth. IMA J. Numer. Anal., 42(2):1313–1338, 2022. BibTeX DOI
  16. A multiscale method for heterogeneous bulk-surface coupling. R. Altmann and B. Verfürth. Multiscale Model. Simul., 19(1):374–400, 2021. BibTeX DOI
  17. A generalized finite element method for problems with sign-changing coefficients. T. Chaumont-Frelet and B. Verfürth. ESAIM Math. Model. Numer. Anal., 55(3):939–967, 2021. BibTeX DOI
  18. A diffuse modeling approach for embedded interfaces in linear elasticity. P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, and M. Kästner. GAMM-Mitt., 43(1):e202000001, 16, 2020. BibTeX DOI
  19. Mathematical analysis of transmission properties of electromagnetic meta-materials. M. Ohlberger, B. Schweizer, M. Urban, and B. Verfürth. Netw. Heterog. Media, 15(1):29–56, 2020. BibTeX DOI
  20. Computational high frequency scattering from high-contrast heterogeneous media. D. Peterseim and B. Verfürth. Math. Comp., 89(326):2649–2674, 2020. BibTeX DOI
  21. Heterogeneous multiscale method for the Maxwell equations with high contrast. B. Verfürth. ESAIM Math. Model. Numer. Anal., 53(1):35–61, 2019. BibTeX DOI
  22. Numerical homogenization of H(curl)-problems. D. Gallistl, P. Henning, and B. Verfürth. SIAM J. Numer. Anal., 56(3):1570–1596, 2018. BibTeX DOI
  23. A new heterogeneous multiscale method for the Helmholtz equation with high contrast. M. Ohlberger and B. Verfürth. Multiscale Model. Simul., 16(1):385–411, 2018. BibTeX DOI
  24. Localized Orthogonal Decomposition for two-scale Helmholtz-type problems. M. Ohlberger and B. Verfürth. AIMS Math., 2(3):458–478, 2017. BibTeX DOI
  25. A new heterogeneous multiscale method for time-harmonic Maxwell's equations. P. Henning, M. Ohlberger, and B. Verfürth. SIAM J. Numer. Anal., 54(6):3493–3522, 2016. BibTeX DOI

Proceedings

  1. Numerical methods for wave propagation in metamaterials. B. Verfürth. In L. Gizon, editor, Book of Abstracts, The 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2024), pages 40–45. Edmond, 2024. BibTeX DOI
  2. From domain decomposition to homogenization theory. D. Peterseim, D. Varga, and B. Verfürth. In Domain decomposition methods in science and engineering XXV, volume 138 of Lect. Notes Comput. Sci. Eng., pages 29–40. Springer, Cham, 2020. BibTeX DOI
  3. Computational multiscale method for nonlinear monotone elliptic equations. B. Verfürth. In Oberwolfach Reports, number 35. 2019. BibTeX
  4. Numerical homogenization for indefinite H(curl)-problems. B. Verfürth. In K. Mikula, D. Ševčovič, and J. Urb\´an, editors, Proceedings of Equadiff 2017 conference, 137–146. 2017. BibTeX url
  5. Analysis of multiscale methods for time-harmonic Maxwell's equations. P. Henning, M. Ohlberger, and B. Verfürth. In PAMM, volume 16, 559–560. 2016. BibTeX DOI

Thesis

  1. Numerical multiscale methods for Maxwell's equations in heterogeneous media. B. Verfürth. PhD thesis, WWU Münster, 2018. BibTeX url