Numerical Multiscale Methods for Nonlinear and Randomly Perturbed Problems

Explore numerical multiscale methods for nonlinear and randomly perturbed problems in this 50-minute lecture by Barbara Verfürth from the Hausdorff Center for Mathematics. Delve into the construction of problem-adapted multiscale basis functions using Localized Orthogonal Decomposition (LOD) methods. Discover how these efficient techniques can be applied to scenarios beyond linear problems with consistent multiscale coefficients. Examine two specific cases: nonlinear problems and multiscale coefficients with defects modeled by random perturbations. Learn about the analysis and construction of linearized multiscale basis functions for nonlinear problems. Investigate an offline-online strategy that enables quick computation of solutions for various realizations of multiscale coefficients with random defects.