One of the main outputs of the research conducted within DyCon ERC Project is the development of new computational methods and tools (algorithms, tutorials, sample codes, software, simulations, and so on), all of which are constantly being integrated in our computational platform.

DyCon Blog offers a higher layer of the computational platform, gathering the work that is currently taking place inside the DyCon team. The goal of this computational blog is to share the valuable knowledge that was collected and gained throughout the DyCon ERC Project's life cycle.

In this tutorial, we will present and elaborate an optimal control strategy for the obstacle problem in two space dimensions using Python's FEniCS toolbox. Different meshes and obstacles are considered.

Formulation of Optimal control problem for rotor imbalance. Explanation of the code to numerically solve the problem.

We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes, and we illustrate that numerical solutions may have unexpected behaviours with respect to the analytic ones.

The aim of this work is to recover the initial sparse sources that lead to a given final measurements using the diffusion equation. It is assumed that the initial condition can be written down as a linear combination of unitary deltas and their weights. In that context, an algorithm that combines the adjoint methodology with least squares is presented. In particular, the adjoint methodology is used to find the localization of the sparse sources and least squares to find the corresponding intensities.

In this tutorial, we investigate the linear infinite dimensional system obtained by implementing an age structure to a given linear dynamical system. We show that if the initial system is null controllable in a time small enough, then the age structured system is also null controllable in a time depending on the various involved parameters.