An important Question
Hi everybody, I use a Full Multigrid algorithm and I wonder something.
With Neumann boundary condition, we know that the restriction of point near the boundary is special but what about the Neumann Operator: ( u(1)-u(-1)/dx ) = f where f is the neumann condition imposed).
Is it important to restrict this Neumann operator, or should I use 'f' ( the same neumann condition ) on the coarser grid ???
Hope this is clear... Thanks for your response...
Re: An important Question
I am not sure to understand right. Normally I would apply exactly the same neumann bc to the coarser meshes. I would strongly recommand this.
But you have to take care when one face has more than 1 neighbour face (local refinements). In this case you have to modify the bc's for the refined cells, because multigrid solves on each coarser mesh with the accuracy of the top level fine mesh, which depends strongly to the cell size. As a result you would see clearly the refinement borders in you contour plots.
So, when you have refinements at the boundary area, I would suggest to mesh this area with face to face cells (means no local refinements). But of course it is possible to overcome this problem, but is not easy to discribe.
I don't know if this was your problem.
Best regards Hubert Janocha
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