The programme will gather numerical analysis experts who are active in the mathematics of novel, “non standard” discretizations for complex partial differential equations (PDEs) featuring multiple fields, multiple scales, and stochastic effects. The aim is a synthesis of advanced and innovative discretizations, such as discontinuous Galerkin methods, isogeometric analysis, virtual element methods, and reduced basis methods, on the one side, with compressive discretizations inspired by computational harmonic analysis (wavelets, directional representation systems), completely new discretization methods based on recent developments in signal processing (compressive sensing and other randomization methods), and novel compression techniques from numerical linear algebra (H-matrix and tensor structured methods), on the other side.
The programme will also include selected application areas where novel computational PDE techniques are expected to make a critical difference for modelling and simulation. We will focus, in particular, on operator equations with stochastic input data, such as Gaussian random fields on manifolds, and multiscale models where solutions exhibit a continuum of scales, or high frequency wave propagation problems. The interplay of PDE simulations and discretizations with methodologies from data science, such as pixel inputs, kernel and neural network PDE input representations, geometry processing will be a focus as well.
The programme contains the following activities.
Interplay of tensor structured formats with advanced PDE discretizations; session on Signal processing techniques and directionally adapted discretizations
June 11-15, 2018 (organizers: Philipp Grohs and Christoph Schwab)
Interplay of multiscale data assimilation and data science with advanced PDE discretizations
June 25-29, 2018 (organizers: Thomas Hou and Markus Melenk)
Interplay of geometric processing, modelling, and adaptivity in Galerkin methods
July 16-20, 2018 (organizers: Annalisa Buffa and Ilaria Perugia)
Francis Filbet (Université Toulouse III), Introduction to Kinetic Theory: The Boltzmann Equation
Monday - Friday, July 30 - August 3, 2018