In the Intro to FEniCS - Part 2 episode we completed the first step in developing a FEniCS model. We characterised the domain. Then, we selected a governing PDE. We then provided suitable boundary conditions. Finally, we expressed the PDE in weak form. We chosen a generalised Helmholtz equation as our PDE. In this episode we will start using the resulting weak form to develop a model.

In the Intro to FEniCS - Part 1 episode we introduced FEniCS. We compared it to Elmer and covered how to install it on an Ubuntu workstation. This episode will cover the process of deriving the weak form for the Helmholtz equation. We will focus on the mathematics, which are advanced. Still, we will attempt to present the formalism in an approachable manner.

In the previous episodes we used Elmer to develop a few different acoustics models. We were able to verify the accuracy of Elmer with few benchmark problems. Additionally, we studied the effect of mesh order and size on the accuracy. Finally, we started probing vibro-acoustic problems. We only scratched the surface of Elmer capabilities in this field. Still, it is worth to take a step back and reconsider these problems under a different light. The FEniCS project is perfect for this. We will be introducing FEniCS in this episode.