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Advanced Topics in Scientific Computing

Course Type: 
PhD Course
Master Course
Anno (LM): 
Second Year
Academic Year: 
2024-2025
Period: 
October-November
Duration: 
48 h
Description: 

This course provides a high level introduction to the numerical analysis of PDES and related high-performance computing techniques, focusing on problems in mechanics such as fluid dynamics. Students will acquire advanced understanding on Computational modelling techniques, both theoretical and practical. The course will utilise a combination of frontal lectures and live programming demonstrations using the C++ deal.ii (dealii.org) Finite Element Library.

 
 
Course content:
 

Fluid mechanics modelling. Functional analytic setting. Analysis of saddle-point problems.  Analysis of classical Finite Element Methods for the Stokes equations. The discontinuous Galerkin Finite Element Method

A posteriori error estimates. Theory and approximation of the Navier-Stokes problem.

Tools of Finite Element programming. Data structuring and mesh generation. Quadrature, Assembling, and Storage. Numerical linear algebra packages. Solution of nonlinear systems.

High Performance Computing. Parallel computing. Using the Docker.

Introduction to the deal.II Finite Element library. 

Case studies. deal.II Hands-on sessions

 

Suggested readings

1. Programming - Principles and Practice Using C++, Bjarne Stroustrup, Addison-Wesley, May 2014 

2. Learning scientific programming with Python, Christian Hill, Cambridge University Press, October 2020

3. Finite Element Methods for Navier-Stokes Equations, Vivette Giraut & Pierre-Arnaud Raviart, Springer, 1986

4. Mathematical Aspects of Discontinuous Galerkin Methods, Daniele Antonio Di Pietro & Alexandre Ern, Springer, 2012

 

Next Lectures: 
Thursday, October 10, 2024 - 09:00 to 12:00
Friday, October 11, 2024 - 09:00 to 12:00
Thursday, October 17, 2024 - 09:00 to 12:00
Friday, October 18, 2024 - 09:00 to 12:00
Thursday, October 24, 2024 - 09:00 to 12:00
Friday, October 25, 2024 - 09:00 to 12:00
Thursday, October 31, 2024 - 09:00 to 12:00
Thursday, November 7, 2024 - 09:00 to 12:00
Friday, November 8, 2024 - 09:00 to 12:00
Thursday, November 14, 2024 - 09:00 to 12:00
Friday, November 15, 2024 - 09:00 to 12:00
Thursday, November 21, 2024 - 09:00 to 12:00
Friday, November 22, 2024 - 09:00 to 12:00
Thursday, November 28, 2024 - 09:00 to 12:00
Friday, November 29, 2024 - 09:00 to 12:00
Thursday, December 5, 2024 - 09:00 to 12:00
Friday, December 6, 2024 - 09:00 to 12:00

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