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Institute for Applied and Numerical Mathematics
Junior Research Group: Numerical analysis of multiscale methods
JProf. Dr. Barbara Verfürth

JProf. Dr. Barbara Verfürth

Since October 1st, 2022, I am at University Bonn. This page is no longer updated. Please visit my new homepage and note my new contact details!

Welcome to my personal homepage. You will find information about my junior research group "Numerical analysis of multiscale methods" on its own homepage and as associated project within the CRC 1173 "Wave phenomena" on the corresponding project page.


News/Open positions

Within the Emmy-Noether project "Numerical methods for nonlinear, random and dynamic multiscale problems" a PhD positions is vacant. If you are interested and have very good knowledge of numerical methods for partial differential equations (in particular finite element method), please contact me for details on the project and the required qualifications.

Current List of Courses
Semester Titel Typ
Summer Semester 2022 Adaptive Finite Elemente Methoden Lecture
Winter Semester 2021/22 Numerical Analysis of Helmholtz Problems Lecture
Ringvorlesung Wavephenomena Lecture
Summer Semester 2021 Analytical and Numerical Homogenization Lecture
Winter Semester 2020/21 Seminar (Numerik partieller Dgl) Seminar

Research interests

  • multiscale (finite element) methods
  • (numerical) homogenization
  • (time-harmonic) wave propagation: Helmholtz and Maxwell equations
  • quasilinear PDEs

Projects

  • Emmy-Noether project "Numerical methods for nonlinear, random and dynamic multiscale problems" (2022-)
  • Co-PI: KIT Future Fields Stage 2 TEEMLEAP (2021-2023)
  • KIT Young Investigator Group Preparation Program Unusual wave phenomena in heterogeneous and nonlinear media (2020-2022)

Short CV

10/10 - 02/15 Bachelor and Master studies in mathematics with minor in physics, WWU Münster
03/15 - 09/18 Research associate, WWU Münster; PhD obtained 06/18
01/17 - 04/17 Participation in trimester programme multiscale problems, Hausdorff-Institute Bonn
10/18 - 05/20 Research associate (PostDoc), University of Augsburg
06/20 - 01/22 Junior research group leader, Karlsruhe Institute of Technology (KIT)
since 02/22 Tenure-Track-Professor for numerics of partial differential equations, KIT

Awards and Prizes

  • Dissertation prize of the University of Münster 2018
  • Dr.-Klaus-Körper-Prize of the GAMM 2019
  • Second prize of IMA Leslie Fox Prize 2021

Teaching in previous semesters (Universities of Augsburg and Münster)

Winter 2019/20 Lecture: Selected topics in numerics - Numerical analysis of acoustic and electromagnetic scattering problems
Seminar: Exponential (time) integrators (Bachelor)
Summer 2019 Lecture: Numerics of ordinary differential equations (together with D. Peterseim)
Seminar: Numerical methods and their applications (Bachelor) (together with D. Peterseim)
Seminar: Seminar on numerics (Master)
Winter 2018/19 Seminar: Introduction to differential equations in 1D (Bachelor)
Tutorials for the Lecture: Introduction to numerical mathematics (Numerics I)
Summer 18 Tutorials to Numerical Analysis

Publications

Submitted Preprints

  1. B. Verfürth. Higher-order finite element methods for the nonlinear Helmholtz equation. ArXiv Preprint 2208.11027, 2022.
  2. B. Maier, B. Verfürth. Numerical upscaling of wave equations with time-dependent multiscale coefficients. ArXiv Preprint 2107.14069, 2021. Accepted in Multiscale Model. Simul.

Journal articles

  1. A. Målqvist, B. Verfürth. An offline-online strategy for multiscale problems with random defects. ESAIM Math. Model. Numer. Anal. Vol. 56, No.1, 2022, pp. 237-260.
  2. R. Mandel, Z. Moitier, B. Verfürth. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. C. R. Math. Acad. Sci. Paris, Vol. 360, 2022, pp. 513–538.
  3. R. Maier, B. Verfürth. Multiscale scattering in nonlinear Kerr-type media. Math. Comp., Vol. 91, No. 361, 2022, pp. 1655–1685.
  4. T. Chaumont-Frelet, B. Verfürth. A generalized finite element method for problems with sign-changing coefficients. ESAIM Math. Model. Numer. Anal., Vol. 55, No.3, 2021, pp. 939-967.
  5. B. Verfürth. Numerical homogenization for nonlinear strongly monotone problems. IMA J. Numer. Anal., Vol. 42, No.2, 2022, pp. 1313–1338.
  6. R. Altmann, B. Verfürth. A multiscale method for heterogeneous bulk-surface coupling. Multiscale Model. Simul., Vol. 19, No. 1, 2021, pp.374–400.
  7. D. Peterseim, B. Verfürth. Computational high frequency scattering from high contrast heterogeneous media. Math. Comp., Vol. 89, No. 326, 2020, pp. 2649-2674.
  8. P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, M. Kästner. A diffuse modeling approach for embedded interfaces in linear elasticity. GAMM Mitteilungen, Vol. 43, No. 1, e202000001, 2020.
  9. M. Ohlberger, B. Schweizer, M. Urban, B. Verfürth. Mathematical analysis of transmission properties of electromagnetic meta-materials. Netw. Het. Media, Vol. 15, No. 1, 2020, pp. 29–56.
  10. B. Verfürth. Heterogeneous Multiscale Method for the Maxwell equations with high contrast. ESAIM Math. Model. Numer. Anal., Vol. 53, No. 1, 2019, pp. 35–61.
  11. D. Gallistl, P. Henning, B. Verfürth. Numerical homogenization of H(curl)-problems. SIAM J. Numer. Anal., Vol. 56, No. 3, 2018, pp. 1570–1596.
  12. M. Ohlberger, B. Verfürth. A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast. Multiscale Model. Simul., Vol. 16, No. 1, 2018, pp. 385–411.
  13. M. Ohlberger, B. Verfürth. Localized Orthogonal Decomposition for two-scale Helmholtz-type problems. AIMS Mathematics, Vol. 2, No. 3, 2017, pp. 458–478.
  14. P. Henning, M. Ohlberger, B. Verfürth. A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations. SIAM J. Numer. Anal., Vol. 454, No. 6, 2016, pp. 3493–3522.

Conference Proceedings

  1. D. Peterseim, D. Varga, B. Verfürth. From Domain Decomposition to Homogenization Theory. In Domain Decomposition Methods in Science and Engineering XXV, Vol. 138 of Lect. Notes Comp. Sci. Eng., Springer, pp. 29–40, 2020.
  2. B. Verfürth. Computational multiscale method for nonlinear monotone elliptic equations. Oberwolfach Reports 35, 2019.
  3. B. Verfürth. Numerical homogenization for indefinite H(curl)-problems. In Proceedings of Equadiff 2017 conference, edited by K. Mikula, D. Sevcovic, J. Urban, pp. 137–146, 2017.
  4. P. Henning, M. Ohlberger, B. Verfürth. Analysis of multiscale methods for time-harmonic Maxwell's equations. In Proc. Appl. Math. Mech. 16, pp. 559–560, 2016.

Theses

  1. B. Verfürth. Numerical multiscale methods for Maxwell's equations in heterogeneous media. Dissertation, WWU Münster, 2018.
  2. B. Verfürth. Numerical analysis of multiscale methods for Maxwell equations. Masterarbeit, WWU Münster, 2015.
  3. B. Verfürth. Homogenisierung für nichtlineare Hindernisprobleme. Bachelorarbeit, WWU Münster, 2013.


Talks

2022

07/22 Workshop Numerical analysis of nonlinear and multiscale problems, Jena, Germany. (Inivited talk)
06/22 Workshop Solvers for frequency-domain wave problems and applications, Glasgow, UK. (Invited talk)
05/22 Zurich Colloquium on Applied and Computational Mathematics, Zurich, Switzerland. (Invited seminar talk)
04/22 Workshop Adaptivity, high-dimensionality and randomness, ESI Wien. (Invited talk)
02/22 Organization of a minisymposium (together with D. Gallistl, P. Henning), Conference on Analysis and Numerics of Waves, online
02/22 Conference on Analysis and Numerics of Waves, online (Invited talk in a minisymposium)

2021

09/21 Workshop Scattering by random heterogeneous media, Augsburg, Germany. (Invited Talk)
07/21 Workshop New trends in numerical multiscale methods and beyond, Mittag-Leffler-Institute, Sweden. (Invited Talk)
06/21 IMA Leslie Fox prize event
03/21 MATHLEC-2021, online. (Invited talk)

2020

09/20 DMV Annual meeting & Chemnitz FE Symposium, online. (Contributed talk)
03/20 Seminar Numerical Analysis, Royal Institute of Technology, Stockholm, Sweden. (Invited seminar talk)
01/20 Bayerische Akademie der Wissenschaften. (Invited talk)

2019

10/19 ENUMATH, Egmond an Zee, The Netherlands. (Invited Talk in a minisymposium)
10/19 Organization of a minisymposium (together with D. Gallistl, M. Schlottbom), ENUMATH, Egmond an Zee, The Netherlands.
09/19 9th Singular Days, Kassel. (Contributed talk)
09/19 Annual meeting of the GAMM workgoup on Numerical Analysis, Essen. (Contributed talk)
07/19 Oberwolfach workshop "Computational multiscale methods" (by B. Engquist, D. Peterseim). (Invited talk)
06/19 MAFELAP, Brunel University London. (Invited talk in a minisymposium)
05/19 Computational and Applied Mathematics Seminar, Chalmers University of Technology Gothenburg, Sweden. (Invited seminar talk)
02/19 GAMM Jahrestagung, Wien. (Invited talk in a section)

2018

10/18 GAMM workshop on numerical analysis, Augsburg.
06/18 Workshop on Interplay of multiscale data assimilation and data science with advanced PDE discretizations, ESI Wien. (Invited talk)
06/18 European Finite Element Fair, Heidelberg. (Contributed talk)
03/18 4th Applied Math Symposium Münster.
03/18 (Co-)Organization of the 4th Applied Math Symposium Münster.
03/18 Joint annual meeting of GDMV and DMV, Paderborn.
01/18 Universität Augsburg. (Invited seminar talk)

2017

09/17 ENUMATH 2017, Voss, Norway. (Invited talk in a minisymposium)
07/17 (Co-)Organization of a minisymposium, Equadiff 2017, Bratislava.
07/17 Equadiff 2017, Bratislava. (Minisymposium talk)
07/17 Karlsruhe Institut für Technologie (KIT). (Invited seminar talk)
03/17 Hausdorff-Institut Bonn. (Seminar talk)

2016

11/16 METAMATH workshop, Cargèse, Corse, France. (Invited talk)
05/16 European Finite Element Fair, Bonn. (Contributed talk)
03/16 Joint annual meeting of GAMM and DMV, Braunschweig. (Contributed talk)