Scientific Computing and Numerics (SCAN) Seminar
Applications that require multiple simulation requests or a real-time simulation response and phenomena that exhibit multiscale features are ubiquitous in science and engineering. However, finite element or finite volume methods require an often prohibitively large amount of computational time for such tasks. Approaches developed to tackle these problems comprise multiscale methods that are based on ansatz functions which incorporate the local behavior of the (numerical) solution of the partial differential equation (PDE), model order reduction techniques, in which the problem is (approximately) solved in a carefully chosen subspace of the high-dimensional discretization space, or combinations of multiscale and model order reduction methods. Methods that combine the two approaches are sometimes called localized model order reduction methods.
While there has been a significant progress in recent years for the construction of local reduced spaces for linear PDEs, very few results have been obtained so far for nonlinear PDEs. In this talk, we will show how randomized methods and their probabilistic numerical analysis can be exploited for the construction and numerical analysis of local reduced models for nonlinear PDEs.