SoSe 23: Numerics IV: Modeling, Simulation, and Optimization
Christof Schütte
Comments
Content:
Geometric partial differential equations are describing the evolution ofand processes on surfaces. Geometric flows such as the now classical mean curvature flow, Willmore flow, and pdes on moving surfaces are typical examples. In this lecture, we will consider various formulations including phase field models of Allen-Cahn and Cahn-Hilliard type and concentrate on basic numerical techniques such as surface finite element methods, adaptivity,unfitted finite element methods, and efficient numerical solvers. Zielgruppe Advanced students in the Master Program Mathematics.Various possible topics for a Master thesis will come up during this course. Voraussetzungen Basic knowledge on partial differential equations and their numericalsolution (e.g. Numerik III).
Target audience:
This lecture is a continuation of the preceding course on "Numerical methods for partial differential equations (Numerik III)". It is intended to broaden the way towards a master thesis in the field of computational PDEs.
Prerequisites:
Participants should have some knowledge about PDEs and their numerical approximation by finite elements as provided, e.g., by the preceing course on "Numerical methods for partial differential equations (Numerik III)".
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closeSuggested reading
- Winkelmann and Schütte (2020): Stochastic Dynamics in Computational Biology, in: Frontiers in Applied Dynamical Systems: Reviews and Tutorials, Volume 8 (Springer)
- Gardiner (2004): Stochastic methods: a handbook for the natural and social sciences (Springer)
- Riley, Hobson and Bence (2002): Mathematical Methods for Physics and Engineering (Cambridge)
- Deuflhard and Roeblitz (2015): A guide to numerical modelling in systems biology Texts in computational science and engineering, Volume 12 (Springer)
14 Class schedule
Regular appointments