Successive Constraint Method in the Collocation Reduced Basis Method

Parametric Partial Differential Equations arise in many areas of applied mathematics and the natural sciences. Efficient numerical simulations to these types of problems across a wide range of parameter values presents a stiff computational challenge. The Reduced Basis Method presents an efficient scheme for solving these types of problem. Utilization of this method however, depends on the knowledge of a ’inf-sup’ constant across the parameter domain. Computation of this constant is a nontrivial task, as it is defined in terms of eigenvalue problems. The Successive Constraint Method, by framing the eigenvalue problem as a linear program, offers a computationally efficient way of approximating the inf-sup constant. In this paper we will review the progress made in implementing of this method for the new collocation framework of the RBM.