Randomized model order reduction

Description

During the last decades (numerical) simulations based on partial differential equations have considerably gained importance in engineering applications, life sciences, environmental issues, and finance. However, especially when multiple simulation requests or a real-time simulation response are desired, standard methods such as finite elements are prohibitive. Model order reduction approaches have been developed to tackle such situations. Here, the key concept is to prepare a problem-adapted low-dimensional subspace of the high-dimensional discretization space in a possibly expensive offline stage to realize a fast simulation response by Galerkin projection on that low-dimensional space in the subsequent online stage.
In this talk we show how randomization as used say in randomized linear algebra or compressed sensing can be exploited both for constructing reduced order models and deriving bounds for the approximation error. We also demonstrate those techniques for the generation of local reduced approximation spaces that can be used within domain decomposition or multiscale methods.

Period	6 Dec 2017
Held at	Centre for Analysis, Scientific computing and Applications (CASA), Netherlands
Degree of Recognition	National