The idea behind this short talk is to present two approaches that help in managing high-dimensional PDEs.
We will first look at the Particle-In-Cell (PIC) method, which combines interesting aspects of random sampling and mesh-based computation.
Then, I will introduce the principles of sparse grids, focusing on the combination technique and hierarchical bases, and discuss how these ideas can interact with the PIC method.
Finally, I will conclude with some examples of applications in plasma physics.