Short course on multigrid methods:

This is an introductory course to algebraic multigrid (AMG) methods. The focus will be on classical as well as modern adaptive techniques for the solution of large sparse linear systems arising from discretizations of second order elliptic partial differential equations (PDEs).

The following topics will be considered (if time permits):

* Basic ideas of multigrid via one dimensional example (finite elements for boundary value problem in 1D).

* Algebraic multigrid versus geometric multigrid. Similarities and differences (still one dimensional example).

* On the convergence theory. Subspace corrections and hierarchical representation of the error. Exact convergence rate of multilevel method. Exact convergence rate of two level methods.

* Applications of the theory: Compatible relaxation, Energy minimizing coarse grid basis. Adaptive choice of supports of basis vectors.

* More on adaptive AMG: Adaptive smoothed aggregation, adaptive element based AMG (AMGe). Applications.