Computational Methods for Operator-Based Analysis

What it is about

You learn numerical methods for solving large linear systems and for analyzing operators in physical problems (e.g., fluid mechanics). In the end you will be able to apply iterative algorithms and modern Python libraries (e.g., PETSc/SLEPc) and assess the physical significance of stability, transient growth, sensitivity, and resolvent analyses.

What you will be able to do

• Knowledge of linear stability tools
• Recognize relevant application cases for physical interpretation
• Application of dedicated iterative methods for large linear systems
• Critical analysis of the use of iterative methods in research papers
• Use of modern libraries for the implementation of iterative methods
• Application of the methods to a model problem

What the module consists of

• LectureTransmission of theoretical foundations; active learning elements such as short quiz and programming tasks
• Laboratory / ExercisePractical implementation of the methods in Python and work on a model problem
• Project work in pairsApplication of the learned methods to a concrete model problem (in the last third of the semester)
• Presentation of a research articleEngagement with the application of the methods in current research

Teaching method

• Lecture with interactive questions and small coding tasksPromotes understanding of theoretical concepts and prepares for the laboratory tasks
• Laboratory / programming sessions in PythonApplication and implementation of the methods on model problems
• Group projectIn-depth application of the methods to a larger problem; transfer to research context
• Presentation of a research articleConfronts you with practical application and scientific discussion