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this was originally a criticism of MG, but we're past that stage now |
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'''Multigrid''' ('''MG''') '''methods''' in [[numerical analysis]] are a group of [[algorithm]]s for solving [[differential equations]] using a [[hierarchy]] of [[discretization]]s. The idea is similar to [[extrapolation]] between coarser and finer grids. The typical application for multigrid is in the numerical solution of [[elliptic operator|elliptic]] [[partial differential equation]]s in two or more dimensions.
MG can be applied in combination with any of the common discretization techniques. In these cases, multigrid is among the fastest solution techniques known today. In contrast to other methods, multigrid is general in that it can treat arbitrary regions and [[boundary condition]]s. It does not depend on the separability of the equations or other special properties of the equation. MG is also directly applicable to more-complicated non-symmetric and nonlinear systems of equations, like the [[Lamé system]] of [[elasticity]] or the [[Navier-Stokes equations]].
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* [[Finite element method]]
* [[Finite difference]]
* [[Spectral method]]
== References and external links ==
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