Some Recent Progress on Numerical Homogenization

In this talk, we will introduce some recent progress on the numerical homogenization of multiscale PDEs with possibly nonseparable scales. We will present the Bayesian/Game theoretical framework for the design of efficient multiscale method and fast solvers, and also the analysis of the exponential decay of the basis and the convergence results. If time allowed, we will also discuss the connection with nonlinear and stochastic numerical homogenization.