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.
The lecture notes can be accessed here: Approximation Theory.
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.
Publications
- Fast high-order spectral solvers for PDEs on triangulated surfaces with applications to deforming surfaces. (Submitted)
- High-Order Integration on Regular Triangulated Manifolds Reaches Super-Algebraic Approximation Rates through Cubical Re-parameterizations . Joint with Oliver Sander and Michael Hecht. SIAM Journal on Numerical Analysis
- Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces . 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. Joint with Elima Shehu and Michael Hecht. Computational and Applied Mathematics, Springer.
- High-Order Numerical Integration on Regular Embedded Surfaces . Joint with Michael Hecht. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2.