Seminar

Many engineering applications require the solutions of a partial differential equation (PDE) for a vast set of parameter configurations. Despite the use of efficient numerical methods and algorithms to solve the PDE, the computational costs associated with repeated solves for different parameter configurations can be prohibitive. The goal of this talk is to provide an introduction to the reduced basis method (RBM) for accelerating parametric simulation campaigns with PDEs. We will first introduce the notion of reductibility, which is an essential ingredient for the success of the RBM. Next, we will present the notion of affine operator, which is a key property for ensuring the efficiency of the RBM. We will then show useful results in a posteriori error estimation which are of paramout importance for ensuring the reliability of the RBM. Various numerical examples will be used to illustrate this presentation (i.e. Laplace, Helmholtz and Maxwell equations).