Add equidistribution marking#4187
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| /// @param[in] theta Parameter, 0 < θ < 1 | ||
| /// @param[in] comm Communicator over which the total marker is computed. | ||
| /// @return Indices (local) of marker elements, which satisfy: marker_i ≥ θ | ||
| /// (sum_i marker_i^2)^1/2 / N^1/2. |
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Please correct me if I'm wrong, but there is probably no need to do so many square root operations - assuming markers/indicators and theta are always positive, you can square both sides:
marker_i^2 ≥ θ^2 (sum_i marker_i^2) / N.
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That's true but we would sacrifice the shared code path of mark_threshold. Since it's 2x sqrt's not critical?
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Not really - in the vast majority of cases I'm familiar with, one naturally assembles the square of the entity estimator, so your approach effectively requires the user to do many square roots outside this function.
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See e.g. https://doi.org/10.1016/j.camwa.2022.11.009 eq A.1, A.4, 3.15 (which should really be squared on both sides).
| count = comm.allreduce(marker.size) | ||
| assert np.allclose( | ||
| marked_cells, | ||
| np.argwhere(marker > theta * norm / np.sqrt(count)).flatten(), |
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If my square-rootless version is correct, still keep this alternative version as-is in the test.
| spdlog::info("Marking (max) {} / {} (local) entities.", indices.size(), | ||
| /// @brief Equidistribution marking of a marker. | ||
| /// | ||
| /// @param[in] marker Input marker (local) - usually an error indicator per |
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The terminology is non-standard. Marker is normally denoted eta and called an error indicator per entity.
Furthermore, and see my comment below, it is usually most efficient to take eta_i^2 - this often saves a square root in user code.
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Implements an equidistribution marking criterion for AFEM schemes, i.e. for$\theta \in (0, 1)$ and a marker $\eta \in \mathbb{R}^N$ , computes
Work towards #4141.
Fixes #3133.