Feature: search partition

[hannesbrandt]

Partition search for the replicated coarse mesh and tutorial
This PR adds the partition search for forests with replicated coarse mesh using the interface defined in #1286.

Additionally, the search is exercised in a new tutorial t8_tutorial_search_partition.cxx. In the tutorial, a forest is defined on the unit cube and refined adaptively. The coarse mesh can be either a 2x2x2 brick or the hybrid hypercube example cmesh. A set of random query points is created on rank 0 and broadcasted to all processes. The replicated queries are first searched in the local part of the forest using the already existing local search routines. Subsequently, they are searched in the partition of the forest and thereby assigned to processes. The results of the partition search are checked for consistency with the results of the local search across all processes.

This PR is currently just a draft for the following reasons

• The geometric routines required to check for element-query intersections like t8_forest_element_points_inside all expect a local tree id as input. For the partition search it would be convenient to call the same routines for global tree ids as well. As a temporary solution we adapted the required geometric functions to accept a global tree id and use the replicated cmesh instead of the forest to obtain the tree class. A future partition search for distributed cmeshes may even benefit from similar geometric functionalities using the tree class directly as input.
• The refinement method in the tutorial uses some geometric routines like t8_forest_element_centroid, which are not allowed to be called during adaptation, as the forest is temporarily not committed. We temporarily disabled the respective assertions.

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[Davknapp]

Hey @hannesbrandt ,

thank you for this Draft-PR. What do you need to progress further, to convert it into a PR and to merge it into main eventually?

Thank you & have a nice week,
David

[hannesbrandt]

Hey @Davknapp, the implementation of the partition search itself is ready to be merged. However, the example/test program currently relies on some workarounds I implemented in t8_forest.cxx. For example, I changed some functions to use the coarse mesh instead of the forest to retrieve geometry information for all trees during the partition search. I would appreciate your input on if/how to implement these changes in a consistent manner, as I think it would increase the usability of the partition search, if the geometry functions in t8code are able to deal with arbitrary trees in a replicated coarse mesh.

[Davknapp]

I just had a look at it:
I think your work around in the adaptation-criterium is not necessary. As far as I understand you want to evaluate the elements in the "old" non-adapted forest. This can be done by calling the routine with forest_from, which is the already committed forest.

For the global-id part: You can use the function "t8_forest_get_local_id " to get the local-id. That way all the other functions don't need to be changed.

[Davknapp]

Is this change necessary?

[Davknapp]

If you ensure the execution of these functions on commited forests, all of the changes here can be reverted, I think

[Davknapp]

please document all parameters

[Davknapp]

Suggested change

	search_recursion (const t8_locidx_t ltreeid, t8_element_t *element, const t8_scheme *ts, int pfirst, int plast);
	search_recursion (const t8_locidx_t ltreeid, const t8_element_t *element, const t8_scheme *ts, int pfirst, int plast);

[Davknapp]

I think you want to pass a reference here. As far as I understand it you want to change the values of pfirst & plast in this functions, or pass it further down to let it be changed. So int &pfirst should do the trick .

[Davknapp]

Suggested change

	for (il = 0; il < g->global_nlq->elem_count; il++) {
	for (size_t il = 0; il < g->global_nlq->elem_count; il++) {

[Davknapp]

please use a better name than g.

[Davknapp]

please use a better name than g.

[Davknapp]

please use a better name than g.

[Davknapp]

please declare the variables when they are needed, not always at the beginning, especially for variables used as indices in loops.