Gentian Zavalani
Table of contents
Contact
Scientific Assistant
NameMr Gentian Zavalani M.Sc.
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Visiting address:
Zellescher Weg 21-25a, Bürogebäude Z21, Room 246
01069 Dresden
Teaching:
This semester I am teaching a course on Scientific research and writing (S+V) - Approximation Theory. The course discusses both the theoretical foundations and practical aspects of approximating and interpolating functions, with a focus on high-order polynomials, trigonometric series, and rational functions.
Research Priorities
My research focuses on the development of high-order spectral methods for computing scalar and vector fields on smooth and embedded surfaces. I am particularly interested in accurate numerical integration techniques and fast algorithms for solving partial differential equations on complex and evolving domains.
Preprints
- High-Order Integration on Regular Triangulated Manifolds Reaches Super-Algebraic Approximation Rates through Cubical Re-parameterizations (2023). Joint with Oliver Sander and Michael Hecht. arXiv:2311.13909.
Publications
- Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces (2022). Joint with Sachin K. Thekke Veettil, Uwe Hernandez Acosta, Ivo F. Sbalzarini, and Michael Hecht. SIAM Journal on Computing (SICOMP).
- A Note on the Rate of Convergence of Integration Schemes for Closed Surfaces (2023). Joint with Elima Shehu and Michael Hecht. Computational and Applied Mathematics, Springer.
- High-Order Numerical Integration on Regular Embedded Surfaces (2024). Joint with Michael Hecht. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2.