Short CV

• 2023– now Post-Doc @ University Of Vienna
• 2021–2023 Post-Doc @ Georg-August-Universität Göttingen
• 2017–2021 PhD @ University Of Vienna
• 2016–2018 Mathematics and Models @ riskine GmbH
• 2014–2017 MSc Applied Mathematics @ University Of Vienna
• 2011–2014 BSc Mathematics @ University Of Vienna

Advanced applications & analysis of Trefftz methods

The goal of this project is to turn Trefftz methods into a versatile and widely usable tool in numerical simulation.

Project details

🎓 Funding program	ESPRIT
⏳ Status	ongoing
🚀 Start	July 1, 2024
🏁 End	June 30, 2027
💶 Funding amount	340819 €
🏢 Host institution	University of Vienna
👤 Principal Investigator	Paul Stocker
🌐 Grant website	fwf.ac.at
🔗 Grant DOI	10.55776/ESP4389824

Read more

Publications

1. A unified framework for Trefftz-like discretization methods
   Philip L. Lederer, Christoph Lehrenfeld, PS, Igor Voulis
   arXiv:2412.00806, 2024 [pdf,cite]
2. Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation
   Sergio Gómez, Chiara Perinati, PS
   arXiv:2411.14819, 2024 [pdf,cite]
3. Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
   Lise-Marie Imbert-Gérard, Andrea Moiola, Chiara Perinati, PS
   IMA J. Numer. Anal., 2024 [pdf,cite]
4. Sparsity comparison of polytopal finite element methods
   Christoph Lehrenfeld, PS, Maximilian Zienecker
   Proceedings Appl. Math. Mech., 2024 [pdf,cite]
5. Trefftz Discontinuous Galerkin discretization for the Stokes problem
   Philip L. Lederer, Christoph Lehrenfeld, PS
   Numer. Math., 2023 [pdf,cite]
6. On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
   Sergio Gómez, Andrea Moiola, Ilaria Perugia, PS
   Appl. Math. Lett., 2023 [pdf,cite]
7. Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
   Fabian Heimann, Christoph Lehrenfeld, PS, Henry von Wahl
   ESAIM: M2AN, 2022 [pdf,cite]
8. A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun’s equation
   Martin Halla, Christoph Lehrenfeld, PS
   IMA J. Numer. Anal., 2022 [pdf,cite,slides]
9. Robust finite element discretizations for a simplified Galbrun’s equation
   Tilman Alemán, Martin Halla, Christoph Lehrenfeld, PS
   eccomas2022, 2022 [pdf,cite]
10. NGSTrefftz: Add-on to NGSolve for Trefftz methods
    PS
    J. Open Source Soft., 2022 [pdf,cite,slides]
11. Embedded Trefftz discontinuous Galerkin methods
    Christoph Lehrenfeld, PS
    Int. J. Numer. Methods Eng., 2022 [pdf,cite,slides]
12. A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
    Lise-Marie Imbert-Gérard, Andrea Moiola, PS
    Math. Comp., 2020 [pdf,cite]
13. An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization
    Marcel Braukhoff, Ilaria Perugia, PS
    SIAM J. Numer. Anal., 2020 [pdf,cite,slides]
14. Tent pitching and Trefftz-DG method for the acoustic wave equation
    Ilaria Perugia, Joachim Schöberl, PS, Christoph Wintersteiger
    Comput. Math. Appl., 2020 [pdf,cite]

Read more

Co-Supervised Master’s theses

• Embedded Trefftz Trace DG Methods for PDEs on unfitted Surfaces, Erik Schlesinger, 2023 [http]
• Robust Finite Element Discretizations for a PDE arising in Helioseismology, Tilman Alemán, 2022 [http]

Teaching

• 2024WS PS Numerical Mathematics
• 2022WS VO Partielle Differentialgleichungen
• 2022SS Mathematisch orientiertes Programmieren
• 2021WS Einführung in Python und Computeralgebra
• 2019SS UE Analysis for Physicists II
• 2018WS UE Problem session to Linear Algebra for Physicists

Research visits

• University of Göttingen, Germany, 31/03/25 → 04/04/25,
  working with C. Lehrenfeld and I. Voulis
• University of Arizona, USA, 24/02/25 → 28/02/25,
  working with L.-M. Imbert-Gérard
• University of Göttingen, Germany, 18/08/24 → 24/08/24,
  working with C. Lehrenfeld and I. Voulis
• University of Pavia, Italy, 18/03/24 → 22/03/24,
  working with A. Moiola, S. Gómez, and C. Perinati
• Research in Pairs, Trento, Italy 25/06/23 → 01/07/23,
  working with A. Moiola and L.-M. Imbert-Gérard
• Kyoto University, Japan, 08/03/20 → 12/04/20,
  working with K. Svadlenka and G. Favre
• University of Pavia, Italy, 01/10/19 → 29/02/20,
  working with A. Moiola

Conferences and Workshops

2025

• 8th ECCOMAS Young Investigators Conference
  17/09 → 19/09, Pescara, IT
• ENUMATH 2025
  01/09 → 05/09, Heidelberg, DE
• 6th NGSolve User Meeting
  11/06 → 13/06, Hamburg, DE
• Austrian Numerical Analysis Day 2025
  08/05 → 09/05, Salzburg, AT
• SIAM Conference on Computational Science and Engineering
  03/03 → 07/03, Fort Worth, Texas, USA

Read more

Posts

• Oct 16, 2023 - git dark magic
• Oct 11, 2022 - Some debugging notes
• Sep 13, 2022 - Softwave docu using Sphinx
• Jan 21, 2022 - Pypi - creating a python package
• Nov 01, 2021 - NGSTrefftz on the cluster in Göttingen
• Sep 07, 2021 - Quasi-Trefftz DG for the wave equation
• Jun 08, 2021 - Boulderproblem
• Oct 10, 2020 - Space-time Maxwell-Stefan equation
• Jan 23, 2020 - How to create this website
• Oct 11, 2019 - Space-time Trefftz-DG on tent pitched meshes