[WIP][solver] Implement block preconditioner for arrowhead like matrices#1872
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| /** | ||
| * Generic block preconditioner for arrowhead matrices of the form | ||
| * | K^S -M^T | | ||
| * | K^B D^T | | ||
| * | -M D | | ||
| * based on a Gauss-Seidel procedure using a Schur complement. | ||
| */ | ||
| class ArrowHeadPreconditionerFactory : public Teko::GaussSeidelPreconditionerFactory |
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@maxfirmbach Are you focusing on systems with zero block on the main diagonal? If not, the BGS(AMG) FSI preconditioner by Gee et al. (2011) also relies on such an arrowhead layout and, thus, could serve as another test case here.
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@mayrmt Currently yes, but not necessarily in the near future.
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Sure! FSI can also due Schur complements with the fluid block on the main diagonal. It is not part of Gee et al. (2011), but I have written it in my PhD thesis. There is also a paper by Ulrich Langer from 2016, that shows Schur complement preconditioners for FSI.
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@maxfirmbach I assume that such code would normally go into Teko directly, if we were able to update Trilinos, right?
| if (A->matrix(A->rows() - 1, A->cols() - 1).norm_inf() < 1e-12) | ||
| { | ||
| maps.push_back( | ||
| Core::Utils::shared_ptr_from_ref(A->matrix(A->rows() - 1, A->cols() - 1).domain_map())); | ||
| } |
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I'd hope that we can still extract the map from the operator domain map of the blocked operator, since the last blocked column of the blocked operator should be set properly ... at least I hope...
| std::string precStr = "None"; | ||
| if (pl.isParameter(inverse_type)) invStr = pl.get<std::string>(inverse_type); | ||
| if (pl.isParameter(preconditioner_type)) precStr = pl.get<std::string>(preconditioner_type); | ||
| solveType_ = Teko::GS_UseLowerTriangle; |
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This hard-codes BGS. Is that intended?
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| // inserting inverse factory into vector | ||
| std::string invStr2 = pl.get<std::string>(fieldName); | ||
| if (position > (int)inverses.size()) |
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| if (position > (int)inverses.size()) | |
| if (position > static_cast<int>(inverses.size())) |
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| // inserting preconditioner factory into vector | ||
| std::string precStr2 = pl.get<std::string>(fieldName); | ||
| if (position > (int)preconditioners.size()) |
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| if (position > (int)preconditioners.size()) | |
| if (position > static_cast<int>(preconditioners.size())) |
@mayrmt Not necessarily, I think the current implementation is really trimmed to work for a specific block matrix type / layout. Edit: The implementation would look a bit different though I guess. |
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Description and Context
This PR aims to implement a block preconditioner for "arrowhead" like block matrices involving the calculation of a proper Schur complement. This is still WIP as there are a few open questions on the implementation part. This PR presents a first implementation with a respective working test case.