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

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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

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 crimes, Preprint, submitted for publication, arXiv 
2. 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.: Identifying cracks in membranes via their eigenfrequencies - An analytical and data-based approach, GAMM CSE Workshop, November 10/17, 2023 (virtual)
2. 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
3. Zilk, P.: Approximating Laplace eigenvalues of circular sectors using isogeometric mesh grading, 29th Biennial Numerical Analysis Conference, Glasgow, Scotland, June 27-30, 2023
4. 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
5. Zilk, P.: Introduction to Isogeometric Analysis and its efficiency for solving Laplace eigenvalue problems, invited, CERAMATHS - DMATHS seminar, Valenciennes, France, March 16, 2023
6. 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
7. 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)
• Exercises Mathematics II (HT 2022, HT 2023)
• Exercises Mathematics III (WT 2024)

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)