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Numerical Analysis

Advanced Topics in Scientific Computing

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.

Numerical Solution of PDEs Using the Finite Element Method

The course "Numerical Solution of PDEs using the Finite Element Method" offers a focused exploration of solving Partial Differential Equations (PDEs) using the Finite Element Method (FEM), employing the deal.II software library. Key components of the course include an introduction to PDEs, basics of numerical methods and FEM analysis, practical training using deal.II, and hands-on projects. The course will also cover High-Performance Computing (HPC) techniques for parallelizing, optimizing, and load balancing FEM simulations for real-world applications.

Introduction to numerical analysis and scientific computing with python

Syllabus 2023-2024

  • Basics on Scientific Computing
  • Vector spaces, vector norms, matrices, and matrix norms
  • Basic linear algebra: direct solution of linear systems
  • Not so basic linear algebra: iterative solution of linear systems
  • Polynomial interpolation
  • Interpolatory Quadrature rules
  • L2 projection / Least square approximation
  • Introduction to Finite Difference Methods
  • Introduction to Finite Element Methods

Python laboratories

Numerical Solution of PDEs Using the Finite Element Method

Advanced course dedicated to the Numerical Solution of Partial Differential Equations through the deal.II Finite Element Library.

Topics:

Models and applications in Computational Fluid Mechanics

The course refers to the use of computational fluid dynamics techniques to address advanced applications in environmental, cardiovascular and industrial contexts. Each topic will be corroborated by a set of numerical examples to be performed within the open source C++ finite volume library OpenFOAM.

Numerical Solution of PDEs Using the Finite Element Method

Advanced course dedicated to the Numerical Solution of Partial Differential Equations through the deal.II Finite Element Library.

Topics:

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