Philipp Zilk M.Sc.

 

Academic Career

from 03/2021	PhD Candidate, 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

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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

Publications

Articles in Peer-Reviewed International Journals

1. Apel, T., Zilk, P. (2024): Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties and graded meshes, Computers and Mathematics With Applications, 175:236–254, DOI (Open Access) arXiv 

Preprints and Articles Submitted for Publication

1. Salcedo Lagunero, R., Fellner, K., Apel, T., Kempf, V., Zilk, P.: Lipolysis on Lipid Droplets: Mathematical Modelling and Numerical Discretisation, Preprint, submitted for publication, arXiv 

International Conference and Seminar Contributions with Abstract

1. Zilk, P.: Error estimates for isogeometric analysis on polar domains with corners, GAMM Workshop on Numerical Analysis, Augsburg, Germany, November 13 - 15, 2024
2. Zilk, P.: Local isogeometric mesh refinement in polar-type domains with corners, 37th Chemnitz Finite Element Symposium, Chemnitz, Germany, September 9 - 11, 2024
3. Zilk, P.: Graded isogeometric mesh refinement towards corners of polar-type domains, selected, Lake Como Summer School on Isogeometric Analysis: Theory, Applications, and New Trends, Como, Italy, July 8 - 12, 2024
4. Zilk, P.: Can one hear the shape of a crack? Gaining insights through spectral geometry, simulations and machine learning, invited, Numerics research seminar, Chemnitz, Germany, June 26, 2024
5. 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
6. 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
7. Zilk, P.: Identifying cracks in membranes via their eigenfrequencies - An analytical and data-based approach, GAMM CSE Workshop, November 10/17, 2023 (virtual)
8. 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
9. Zilk, P.: Approximating Laplace eigenvalues of circular sectors using isogeometric mesh grading, 29th Biennial Numerical Analysis Conference, Glasgow, Scotland, June 27-30, 2023
10. 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
11. Zilk, P.: Introduction to Isogeometric Analysis and its efficiency for solving Laplace eigenvalue problems, invited, CERAMATHS - DMATHS seminar, Valenciennes, France, March 16, 2023
12. 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
13. 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

Posters

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

Monographs

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

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Teaching

Courses & Exercises

• Exercises Differential Equations (FT 2021, FT 2022)
• Exercises Partial Differential Equations (WT 2022, WT 2023)
• Exercises Mathematics I (HT 2022, HT 2023, HT 2024)
• Exercises Mathematics II (HT 2022, HT 2023, HT 2024)
• Exercises Mathematics III (WT 2024)

Supervised Student Projects / Theses

• Solving eigenvalue problems with isogeometric collocation methods, Student project (2024)
• 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)