NON-STANDARD MULTIGRID TECHNIQUES USING CHECKERED RELAXATION AND INTERMEDIATE GRIDS

Publisher Summary This chapter examines the nonstandard multigrid (MG) techniques using checkered relaxation and intermediate grids. The MG techniques offer sensational perspectives in the numerical treatment of partial differential equations. There are close connections between the MG and the total reduction ideas suggesting certain combinations leading to the so called MGR methods. The quantitative results refer to model problems in the unit square with Dirichlet or Neumann boundary conditions, respectively. With respect to both theoretical rate of convergence, and the computational effort, MG methods turn out to be considerably superior to standard MG methods. MGR-CH-1 and MGR-CH-2 turn out to be the most efficient methods. It is observed that as only five-point operators are used in these methods, they can in principle be applied to very general problems. It is found that checkered relaxation techniques yield considerable improvements also if no intermediate grids are used explicitly.