Abstract : This presentation will be kept at a basic level, both continuous and algebraic versions of the methods will be given in their most common variants and the main ingredients of domain decomposition methods will be presented. The content will follow the lines of the chapters 1 and 3 from the domain decomposition book. A short introduction to Freefem software will be given which will allow the students to use quickly the codes illustrating the methods.
Outcomes: At the end of this first lecture, students will have a basic understanding of the methods but also of their implementation.

Keywords : domain decomposition; Schwarz methods; preconditioners