Mathematics

The course "Numerical Solution of PDEs with deal.II" 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.

Aim of the course is to introduce the basic tools of linear and nonlinear functional analysis, and to apply these techniques to problems in PDEs. The course is divided into two parts: the first one concerns spectral theory of linear operators, whose goal is to extend the classical notion of spectrum of a matrix to an infinite dimensional setting. The second part of the course introduces the methods of nonlinear analysis to find the zeros of a nonlinear functional on a Banach space. In particular it gravitates around the implicit function theorem and its variants.

Smooth manifolds and differential topology.

Lectures

Students will acquire a comprehensive understanding of advanced programming concepts, specifically in C++ and Python. They will become familiar with object-oriented and generic programming paradigms, as well as proficient in utilizing common data structures, algorithms, and relevant libraries and frameworks for scientific computing.