Multigrid Methods for Differential Equations
Official Course Description
Many important phenomena in science and engineering are described by partial differential equations. When these equations are solved numerically one uses discretization methods, which give rise to (often enormously) large systems of equations. These may often have several million unknowns. Due to the size of the systems it is necessary to use iterative methods, with multigrid methods belonging to the most efficient techniques.
The course builds directly on FMNN10 Numerical Solution of Differential Equations, and is focused on multigrid methods for elliptic equations. The aim is to give an elementary introduction to multigrid, starting from the self-adjoint two-point boundary value problems studied in FMNxxx. Then the technique is applied to more general elliptic equations, and different variants such as V- and W-iterations are used.