Move Proper Orthogonal Decomposition (POD) to Core #1260
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@amgebauer The POD files in the linear solver do not seem to fit there. They read a POD basis from file and do stuff with the basis vectors, but they never solve a linear system.
I think we should find a more suitable place for them. I am fine with moving them to core/. What about a new directory core/pod/ or core/mor/?
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That depends on how we want to enable POD for all problem types. I thought of implementing it as a solver for a linear system. So you get a large sparse matrix, then pod will be applied and then your sub-solver solves a much smaller linear system. In this case, it should directly be available for all problem types. |
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Sounds like algebraic multigrid with the POD basis as |
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Regarding the second point of generalizing this feature. We have a |
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In addition, this is more like a |
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I know you just moved the files, but since I had a look at what is happening inside, I left some comments.
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Overall, this looks good to me. Definitely an improved to the old MOR implementation!
I left some comments about naming and documentation for consideration.
| /** | ||
| * @brief Constructs a sparse matrix from a given MultiVector. | ||
| * | ||
| * This function creates a @p Core::LinAlg::SparseMatrix using the provided multivector, | ||
| * range map, and an optional domain map. The multivector contains the data to be | ||
| * represented in sparse matrix form. The rangemap defines the mapping of rows, | ||
| * while the domainmap (if provided) defines the mapping of columns. | ||
| * | ||
| * @param multivect The multivector containing the data to be converted into a sparse matrix. | ||
| * @param rangemap The map specifying the row mapping for the sparse matrix. | ||
| * @param domainmap Optional map specifying the column mapping for the sparse matrix. | ||
| * @return Core::LinAlg::SparseMatrix The constructed sparse matrix. | ||
| */ | ||
| Core::LinAlg::SparseMatrix make_sparse_matrix(const Core::LinAlg::MultiVector<double>& multivect, | ||
| const Core::LinAlg::Map& rangemap, const std::optional<Core::LinAlg::Map>& domainmap); |
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From the code, I understand that a MultiVector with 3 vectors and 100 entries per vector will result in a rectangular 100x3 matrix. The matrix is dense, but stored in a sparse format. If that is true, then I find the comments about the domain map a bit misleading.
If the domain map just decribes, how a vector x in a mat-vec Ax needs to be layed out, such that the mat-vac can be computed, then the domain map just follows standard Petra terminology.
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If the multivector contains zeros, one could potentially filter them out.
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True. I was thinking about the column map, which is "dense". In the end, it's a sparse matrix format that is likely to have a large fill-in. Not a big deal, though.
| void multiply_multi_vectors(const Core::LinAlg::MultiVector<double>& v1, bool trans_v1, | ||
| const Core::LinAlg::MultiVector<double>& v2, bool trans_v2, const Core::LinAlg::Map& red_map, | ||
| const Core::LinAlg::Import& importer, Core::LinAlg::MultiVector<double>& result); |
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red_map -> redundant_map to reflect its meaning in the naming?
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I want to enable MOR for the new structural time integration. Therefore, I now moved the general utilities to core. In a second step, one could generalize it for any problem type.