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J Roued June 28, 1999 02:22

Multigrid: AMG GMG FMG

I have a simpel question about different multigrid approaches:

What is the difference between Algebraic Multigrid, Geometric Multigrid Fuld Multigrid




Kaare A Sorensen June 28, 1999 08:12

Re: Multigrid: AMG GMG FMG
Hi Jens,

AMG is an abstraction of traditional multigrid methods (GMG). In AMG you base your approach on the algebraic (hence the name) system Ax=b rather than the physical (PDE-) equations on a geometry (hence ...) where you have the notion of grids. In AMG instead of solving on coarser meshes, you are adding lines in your system of equations. The reason AMG is called a multigrid method even though 'grid' is undefined in its context is that it in some cases is equivalent to the traditional MG approach, and was probably motivated by it. The applicability of AMG seems to be somewhat restricted at the moment, in particular I've only seen it used on linear applications.

FMG is not directly related to the definitions above. Rather FMG is a way to generate a good initial guess for the selected MG procedure by obtaining less expensive solutions on coarser meshes (by f.ex. MG) and mapping the solution itself (not the correction) up to the finest grid.

Ha en god dag!


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