Hi Lawrence,
Block Jacobi is a broad church, can you describe what you mean in more detail? Do you want to use a block diagonal preconditioner where the blocks are the three variables.
I want to do this:
Or do you want to decouple into columns and invert all the variables in the same column simultaneously.
However, I realise that this might not be entirely well defined. For spaces which are horizontally discontinuous, I want to treat all variables that are associated with the same horizontal grid cell as one block. For a horizontally continuous space I probably want to treat all variables as one block which correspond to the same basis function in the 3d reference element of the base cell in a vertical column. So for example, looking at the grid from the side: For a horizontally discontinuous space: +-A-A-+ ! A A ! +-A-A-+ ! A A ! +-A-A-+ For a horizontally continuous space: +—B—+ A C +—B—+ A C +—B—+ (variables with the same letter are in the same block). I’m not necessarily saying that that makes sense mathematically, and that the preconditioner will be effective. Thanks, Eike
Or something else?
Cheers,
Lawrence _______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake