> I think this is a more important point then you and Jed may give it > credit for. It is not clear to me that the worse convergence (of the linear > solve) with the number of subdomains is the chief issue you should be > concerned about. An equally important issue is that the ILU(0) is not a good > preconditioner (and while user a more direct solver, LU or ILU(2)) helps the > convergence it is too expensive). Are you using AIJ matrix (and hence it is > point ILU?) see below
> Is Jed is correct on this? That you have equal order elements hence all > the degrees of freedom live at the same points, then you can switch to BAIJ > matrix format and ILU becomes automatically point block ILU and it may work > much better as Jed indicates. But you can make this change before mucking > with coarse grid solves or multilevel methods. I'm guess that the point-block > ILU will be a good bit better and since this is easily checked (just create a > BAIJ matrix and set the block size appropriately and leave the rest of the > code unchanged (well interlace the variables if they are not currently > interlaced). Unfortunately, it is not that easy to switch to BAIJ. I only have a local XFEM basis. That is, I have variable numbers of degrees of freedom throughout the domain (nodes of elements cut by the fluid interface have on additional "XFEM unknown"). At the moment, I don't know how or if I can handle the XFEM block when using BAIJ. Best, Henning
