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Introduce inclusion_mapping operation #3581

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@schnellerhase schnellerhase commented Dec 29, 2024

Given two meshes $T_\text{from}$, $T_\text{to}$ that are contained in one another $T_\text{from} \subset T_\text{to}$, in the sense of vertices being a subset, and mesh produced as a (possibly local) refinement procedure, the inclusion_mapping function computes the global indices in $T_\text{to}$ of the 'vertices in $T_\text{from}$.

The computed index mapping thus generally describes how one refined mesh is contained in another and is a first step for a multi grid implementation.

Performs a local identification first to detect the vertices. For this to succeed the spatial parallelization of $T_\text{from}$ and $T_\text{to}$ must match. I.e. every vertex in $T_\text{from}$ that is part of $T_\text{to}$ as well must be available on the same process.
If this local check is not exhaustive a global vertex list is gathered and used for the computation (does not scale, needs to be treated with care and can be improved on with some kind of localization check to rule out which processes may contain the vertices - overlap of bounding boxes?).

@schnellerhase schnellerhase marked this pull request as ready for review January 4, 2025 10:31
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