This page contains the material for a practical course on modeling, simulation, and optimization that was thaught in the summer semester 2022 at the Friedrich-Alexander Universität Erlangen-Nürnberg. This course provides a practical introduction to some of the most commonly used discretization methods for PDEs (finite differences and finite elements) and their implementation in matlab. It also covers some of the basics of gradient-based optimization focused on (PDE-constrained) optimal control problems. Some basic programming skills in matlab or a similar programming language is recommended but not required.
The course consists of two parts. In the first part students learn the basics about finite differences, time discretization, finite elements, and optimization in a concentrated version of the course thaught in 2021. This knowledge is applied in a final project in the second half of the course.
Topics for the first six lectures are