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Hi,

I have two question about solving an elliptic equation using multigrids.

First, in case of Neumann boundary conditions : Does the error equation, which is solved on the coarse grid, have the same boundary condition than the solution on the fine grid ? In the case of Dirichlet BC, since the value of the solution is known at the boundary exactly, the error is zero there, so I suppose the error equation for dirichlet BC always have homogeneous dirichlet BC (right ?) but what about neumann BCs ?

Second, what happens at the restriction/interpolation steps when I have a non constant coefficient in my differential operator ? Exemple : F(x) - n(xh)*d2F(x)/dx2 = S(x). Is the function n(x) restricted/interpolated the same way the solution F is?

Thanks

Nico

flag	asked Oct 9 2011 at 20:37 Nico 31●1

psd · Answer 1 · 2011-10-10 01:47:43Z UTC

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This is available on google books, and it has an example on page 113 using Neumann boundary conditions.

A multigrid tutorial

By William L. Briggs, Van Emden Henson, Stephen Fahrney McCormick

answered Oct 10 2011 at 1:47

psd
221●1●5

multigrid boundary conditions and variable operator

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A multigrid tutorial

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