With ever increasing computing power available today, numerical analysis and scientific computing is becoming more and more important. In the areas of engineering and physics, numerical simulations of PDE’s provide a great substitute to materials/mechanics testing. These can be extremely useful for design optimization and for testing predictions.
Yet, a natural problem that still exists is when solutions need to be computed quickly with high accuracy or when solutions need to be recomputed. This can be the case for PDE’s that depend on parameters. Reducing the computational costs for these problems, is a primary focus of Reduced Basis Methods  (in general reduced Order Modelling).
In this talk, I’ll be giving an introduction to Reduced Basis Methods for parametrized PDE’s. I’ll be describing the general problem, going through some necessary conditions for the methods to work, as well as describing the procedure of constructing the Reduced Basis.