The main issues of focus in the development of the multigrid one-shot methods are h-elliptic discretization, relaxation with the smoothing property and a coarse grid acceleration. Discretization for the partial equation equations, such as the state and the adjoint equations is a well understood subject, and we assume that an h-elliptic discretization has been done for those equations. As far as discretization introduced for the design space there are some points to be discussed here.

- Discretization Issues
- Coarse Grid Optimization Problems
- Relaxation
- Design Space of a Small Dimension
- Design Space of Moderate Size
- Infinite Dimensional Design Space
- Full Multigrid

Shlomo Ta'asan 2001-08-22