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.
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