## 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.

## Advanced topics on the analysis of Finite Element Methods

This course is meant to be complementary to the courses Numerical Solution of PDEs, Numerical Solution of PDEs Using the Finite Element Method, and Advanced FEM Techniques.

## 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:

## An introduction to modern tools for collaborative science (best practices in co-developing and co-authoring)

All lectures are live in Room A-134, and broadcasted on Zoom and YouTube.

https://sissa-it.zoom.us/j/81471012769?pwd=QnNiZnVtbUxvNENybXlPNWVsT1hmQT09

Meeting ID: 814 7101 2769

Passcode: GitRules

Course material: https://github.com/luca-heltai/collaborative-science-2021-2022

Course description

## Advanced Programming

The course aims to provide advanced knowledge of both theoretical and practical programming in C++11 and Python3, with particular regard to the principles of object-oriented programming and best practices of software development.

Due to covid-19 containement rules, this year, videos with pre-recorded lectures will be uploaded weekly, starting from the week of October 5, 2020.

## Theory and practice of Finite Element Methods

This is a shared course between the SISSA PhD track

on Mathematical Analysis, Modeling, and Applications

(math.sissa.it) and the Master in High Performance Computing

(www.mhpc.it). It is a course that follows two parallel lines:

theory of finite element methods (graduate students level, ~20 hours) and

practice of finite element methods (mhpc students levels, ~20 hours).