Philipp Zilk M.Sc.

Professur für Mathematik
Gebäude 41/100, Zimmer 5123
+49 89 6004 3408

Philipp Zilk M.Sc.


Academic Career

from 03/2021 Doctoral Researcher, Institute for Mathematics and Computer-Based Simulation, University of the Bundeswehr Munich
10/2018-02/2021 Graduate Research & Teaching Assistant, Faculty for Mathematics & Chair for Business Informatics, University of Regensburg
10/2018-02/2021 Master of Science, Mathematics, University of Regensburg
09/2019-01/2020 ERASMUS exchange semester, Master in modeling and numerical analysis, University of Montpellier, France 
10/2015-10/2018 Bachelor of Science in Mathematics, University of Regensburg

Research Interests

  • Eigenvalues and eigenfunctions of differential operators
  • Isogeometric Analysis on domains with singularities, local mesh refinement
  • Spectral theory and application to the isospectral problem
  • Machine Learning for solving inverse problems

Honors and Awards

2023 UKIE SIAM Student Prize, best student presentations at the 29th Biennial Numerical Analysis Conference  web-logo.png


Preprints and Articles Submitted for Publication

  1. Apel, T., Zilk, P.: Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties, graded meshes & variational crimesPreprint, submitted for publication, arXiv web-logo.png
  2. Salcedo Lagunero, R., Fellner, K., Apel, T., Kempf, V., Zilk, P.: Lipolysis on Lipid Droplets: Mathematical Modelling and Numerical DiscretisationPreprint, submitted for publication, arXiv web-logo.png

International Conference and Seminar Contributions with Abstract

  1. Zilk, P.: Approximation of Laplace eigenvalues and eigenfunctions of domains with corners, 10th International Conference on Computational Methods in Applied Mathematics (CMAM-10), Bonn, Germany, June 10-14, 2024
  2. Zilk, P.: Graded isogeometric mesh refinement towards corners of singularly parametrized domains, 9th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2024), Lisbon, Portugal, June 3 - 7, 2024
  3. Zilk, P.: Identifying cracks in membranes via their eigenfrequencies - An analytical and data-based approach, GAMM CSE Workshop, November 10/17, 2023 (virtual)
  4. Zilk, P.: Identifying cracks in membranes via their eigenfrequencies - A theoretical and practical approach, 36th Chemnitz Finite Element Symposium, Leibnitz, Austria, September 11 - 13, 2023
  5. Zilk, P.: Approximating Laplace eigenvalues of circular sectors using isogeometric mesh grading, 29th Biennial Numerical Analysis Conference, Glasgow, Scotland, June 27-30, 2023
  6. Zilk, P.: Isogeometric mesh grading for Laplace eigenvalue problems on circular sectors, 11th International Conference on Isogeometric Analysis (IGA 2023), Lyon, France, June 18-21, 2023
  7. Zilk, P.: Introduction to Isogeometric Analysis and its efficiency for solving Laplace eigenvalue problems, invited, CERAMATHS - DMATHS seminar, Valenciennes, France, March 16, 2023
  8. Zilk, P.: Isogeometric approximation of eigenfrequencies of membranes with cracks and application to shape identification, 35th Chemnitz Finite Element Symposium, Herrsching am Ammersee, Germany, September 15 - 17, 2022
  9. Zilk, P.,  Eckardt, L., Haubner, C., Apel,T. (2021): Numerical study of PDE eigenvalue problems, ECCOMAS Virtual International Conference on Isogeometric Analysis (VIGA), Lyon/Online Conference, September 26-29, 2021


  1. Zilk, P.,  Eckardt, L., Haubner, C., Apel, T. (2021): Numerical study of PDE eigenvalue problems, ECCOMAS Virtual International Conference on Isogeometric Analysis (VIGA), Lyon/Online Conference, September 26-29, 2021, PDF pdf.png


  1. Zilk, P. (2021): Flächen-Cluster und offene Flächen mit minimaler Willmore-Energie (Surface-cluster and open surfaces with minimal Willmore-Energy), Master's thesis, University of Regensburg
  2. Zilk, P. (2018): Schwache Lösungstheorie für das Kirchhoff-Love-Modell für dünne Platten (Weak solution theory for the Kirchhoff-Love-Model for thin plates), Bachelor's thesis, University of Regensburg


Courses & Exercises

Supervised Student Projects / Theses

  • Isogeometric simulation of eigenfrequencies of domains with cracks using locally refined meshes and application for crack identification, Master's thesis (2023)
  • Comparison of models for approximating eigenfrequencies of thin plates, Student project (2023)
  • Adaptive interpolation using neural networks, Bachelor's thesis (2021)