Isogeometric Analysis: Theory and Practice

What it is about

You learn B-Splines/NURBS from the CAD side through approximation theory to application in isogeometric finite element methods. In the end you will be able to derive weak formulations for elliptic, Maxwell, and Stokes problems, explain their properties, and implement corresponding finite-element solvers in Python.

What you will be able to do

• Understanding of B-Splines/NURBS in CAD and their properties
• Knowledge of the approximation behavior of B-Splines
• Application of B-Splines in isogeometric finite element methods
• Deriving and analyzing weak formulations (elliptic, Maxwell, Stokes)
• Implementation of finite-element solvers in Python
• Foundations of spectral analysis of the associated matrices
• Use of multigrid-based solvers for IGA

What the module consists of

• VorlesungTransmission of the theoretical foundations on CAD, approximation and algebraic aspects of B-Splines as well as IGA methods
• Übung/PraktikumExercises with proof sketches, model derivations and Python implementations for deepening understanding

Teaching method

• Tafelvorlesung und VorlesungsunterlagenPresentation of the geometric, approximative and algebraic perspectives on B-Splines
• Übungsblätter mit Lösungen und Programmieraufgaben (Python)Deepening through proofs, model derivations and practical implementation