Disputation
Spectral discretizations on surfaces: high-order methods for integration and PDE solvers
Gentian Zavalani, PhD student, Dresden University of Technology and CASUS Young Investigator Group “Mathematical Foundations of Complex System Science”
Abstract of the talk// During his PhD, Gentian focused on numerical methods for solving partial differential equations (PDEs) posed on smooth two-dimensional surfaces embedded in $\mathbb{R}^3$. His work is motivated by applications in biology and physics and involves developing fast algorithms and spectral methods for solving PDEs efficiently on complex geometries.
It centers on three main themes:
– High-order polynomial approximations of curved surfaces
– Accurate computation of surface integrals
– Fast direct solvers for elliptic partial differential equations on static and dynamic surfaces
CV// Gentian received his MSc and BSc degrees in Mathematical Engineering from Polytechnic University of Tirana, Albania, where he also worked as a teaching assistant. In spring of 2021 he moved to Saxony to work on his PhD project, first at CASUS in Görlitz and later at the Institute of Numerical Mathematics of TU Dresden in Dresden. He gives a lecture on approximation theory at TU Dresden in the winter semester 2025/26.
Gentian will be talking live in Dresden. However, as the event is organized in a hybrid format that includes a videoconferencing tool by Zoom Inc., people not present in Dresden and interested in the topic have the chance to also join the talk by using the following link.
room Z21 250, Zellescher Weg 21, 23, 25, 25 a, 01069 Dresden, Germany
11 March 2026, 1 pm