A Software Framework for Reduced Basis Methods using DUNE-RB and RBMATLAB

Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis approach is a suitable means to reduce computational time. The method is based on a projection of an underlying high dimensional numerical scheme onto a low dimensional function space. In this contribution, a new software framework is introduced that allows fast development of reduced schemes for a large class of discretizations of evolution equations implemented in DUNE. The approach provides a strict separation of low-dimensional and high-dimensional computations, each implemented by its own software package RBMATLAB, respectively DUNE-RB. The functionality of the framework is exemplified for a finite volume approximation of an instationary linear convection–diffusion problem.