I will start with two very brief surveys. First is a class of problems, namely variational inequalities (VIs), which generalize PDE problems, and second is a class of solver algorithms, namely full approximation storage (FAS) nonlinear multigrid for PDEs. Motivation for applying FAS to VIs is demonstrated in the standard mathematical model for glacier surface evolution, a very general VI problem relevant to climate modeling. (Residuals for this nonlinear and non-local VI problem are computed by solving a Stokes model.) Some existing nonlinear multilevel VI schemes, based on global (Newton) linearization would seem to be less suited to such general VI problems. From this context I will sketch some work-in-progress toward the scalable solutions of nonlinear and nonlocal VIs by an FAS-type multilevel method.
