# multigrid boundary conditions and variable operator

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

-

## 1 Answer

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

-