RB Methods in Action: Setting up the problem

Abstract

We show how a parametrized PDE can be transformed into an equivalent problem on a reference (parameter-independent) domain. General mathematical tools for this operation are given, and examples of parametrized PDEs are discussed that are inspired by the four problems of Chap. 2. The primary purpose is to highlight the different role played by physical and geometric parameters. A further critical issue addressed concerns the possible affine parametric dependence of the linear and bilinear forms defined over the reference domain. With the aid of a host of meaningful examples we discuss the way the affine parametric dependence is affected by the problem parametrization.