Add full support for parallelization backends

[efaulhaber]

Based on trixi-framework/PointNeighbors.jl#109.

[codecov]

Codecov Report

Attention: Patch coverage is 89.47368% with 2 lines in your changes missing coverage. Please review.

Project coverage is 70.62%. Comparing base (fb6906f) to head (1d1daa9).

Files with missing lines	Patch %	Lines
src/general/initial_condition.jl	50.00%	1 Missing ⚠️
test/schemes/solid/total_lagrangian_sph/rhs.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #790      +/-   ##
==========================================
+ Coverage   70.61%   70.62%   +0.01%     
==========================================
  Files         103      103              
  Lines        6618     6611       -7     
==========================================
- Hits         4673     4669       -4     
+ Misses       1945     1942       -3     

Flag	Coverage Δ
unit	70.62% <89.47%> (+0.01%)	⬆️

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[efaulhaber]

/run-gpu-tests

[efaulhaber]

/run-gpu-tests

[Copilot]

Pull Request Overview

This PR adds full support for parallelization backends by updating threaded loops, modifying constructors, and adjusting example and documentation files to use explicit backend types rather than booleans.

• Replace “@threaded positions…” with “@threaded default_backend(positions)” in various modules.
• Update function signatures and type checks in semidiscretization to use explicit backend types.
• Amend examples and documentation to use backend constructors (e.g., PolyesterBackend, SerialBackend) instead of primitive booleans.

Reviewed Changes

Copilot reviewed 31 out of 31 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
src/preprocessing/particle_packing/signed_distance.jl	Updated threaded loop to use default_backend for FaceNeighborhoodSearch.
src/preprocessing/geometries/triangle_mesh.jl	Updated threaded loops to use default_backend for face_vertices and vertices_sorted arrays.
src/general/semidiscretization.jl	Modified the Semidiscretization constructor and semidiscretize function; now uses explicit parallelization_backend type checks.
src/general/neighborhood_search.jl	Changed foreach_point_neighbor call to use the new parallelization_backend parameter.
src/general/initial_condition.jl	Updated foreach_point_neighbor calls to use SerialBackend instead of a boolean flag.
src/TrixiParticles.jl	Updated re-exports to include new backend types and default_backend.
Examples (various)	Replaced boolean flag with explicit backend constructors for simulation setups.
docs/*	Adjusted documentation and Project.toml to reflect the new backend usage.

[efaulhaber]

/run-gpu-tests