401-4671-00L Advanced Numerical Methods for CSE
|Semester||Autumn Semester 2019|
|Periodicity||yearly recurring course|
|Language of instruction||English|
|Abstract||This course will focus on teaching different advanced topics in numerical methods for science and engineering. The main aim would be introduce novel algorithms and discuss their implementation.|
|Objective||--Presentation of state of the art numerical methods in computational fluid dynamics. |
--Advanced implementation in C++
-- Introduction of the role of data in scientific computing, particularly in the context of uncertainty quantification (UQ) and machine learning (deep learning)
|Content||A selection of the following topics will be covered:|
1. Advanced numerical methods in fluid dynamics:
-- Finite volume schemes
-- High-resolution schemes on both structured and unstructured grids
-- ENO/WENO methods for structured grids.
-- DG methods for unstructured grids.
2. Uncertainty quantification in fluid dynamics
-- Modeling of uncertainty in terms of random fields.
-- Monte Carlo methods
-- Multi-level Monte Carlo methods.
-- Quasi-Monte Carlo methods.
3. Deep learning in CFD
-- Introduction to deep learning
--Machine learning and DG methods
--Deep learning observables in CFD.
-- UQ with deep learning
|Lecture notes||Lecture material will be created during the course and will be made available.|
|Prerequisites / Notice||- Familiarity with basic numerical methods |
(as taught in the course "Numerical Methods for CSE").
- Knowledge of numerical methods for differential equations (as covered in the course "Numerical Methods for Partial Differential Equations").
- Some knowledge of HPC.