401-4671-00L  Advanced Numerical Methods for CSE

SemesterAutumn Semester 2019
LecturersS. Mishra
Periodicityyearly recurring course
Language of instructionEnglish

AbstractThis 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)
ContentA 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 notesLecture 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.