Use PrecomputedNeighborhoodSearch for the oscillating beam

[efaulhaber]

Based on trixi-framework/PointNeighbors.jl#9 and trixi-framework/PointNeighbors.jl#35.

1.8x speedup in an isolated interaction benchmark of the default oscillating beam:

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  16.708 μs (1 allocation: 496 bytes)

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  9.250 μs (1 allocation: 496 bytes)

Large simulation with n_particles_y = 65:

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  4.971 ms (1 allocation: 496 bytes)

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  2.024 ms (1 allocation: 496 bytes)

3D:

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  375.000 μs (1 allocation: 496 bytes)

julia> @btime TrixiParticles.interact!($dv_ode, $v_ode, $u_ode, $solid_system, $solid_system, $semi);
  228.000 μs (1 allocation: 496 bytes)

Here is the timer output of the default oscillating beam:

julia> trixi_include("examples/solid/oscillating_beam_2d.jl", saving_callback=nothing, neighborhood_search=GridNeighborhoodSearch{2}());

[...]
────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi simulation finished.  Final time: 5.0  Time steps: 15826 (accepted), 16871 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

 ─────────────────────────────────────────────────────────────────────────────────────────
            TrixiParticles.jl                    Time                    Allocations      
                                        ───────────────────────   ────────────────────────
            Tot / % measured:                12.4s /  86.7%            326MiB /  77.4%    

 Section                        ncalls     time    %tot     avg     alloc    %tot      avg
 ─────────────────────────────────────────────────────────────────────────────────────────
 kick!                            152k    10.5s   97.9%  69.1μs    222MiB   88.1%  1.50KiB
   update systems and nhs         152k    6.58s   61.4%  43.3μs   69.5MiB   27.5%     480B
     stress tensor                152k    6.39s   59.7%  42.1μs   69.5MiB   27.5%     480B
     ~update systems and nhs~     152k    177ms    1.7%  1.16μs   1.47KiB    0.0%    0.01B
     update nhs                   152k   8.61ms    0.1%  56.7ns     0.00B    0.0%    0.00B
   system interaction             152k    3.48s   32.5%  22.9μs    120MiB   47.7%     832B
     solid1-solid1                152k    3.39s   31.6%  22.3μs   71.8MiB   28.4%     496B
     ~system interaction~         152k   93.7ms    0.9%   617ns   48.7MiB   19.3%     336B
   reset ∂v/∂t                    152k    213ms    2.0%  1.40μs     0.00B    0.0%    0.00B
   source terms                   152k    170ms    1.6%  1.12μs   32.4MiB   12.8%     224B
   ~kick!~                        152k   40.0ms    0.4%   264ns   2.94KiB    0.0%    0.02B
 drift!                           152k    230ms    2.1%  1.51μs   30.1MiB   11.9%     208B
   velocity                       152k    152ms    1.4%  1.00μs   30.1MiB   11.9%     208B
   reset ∂u/∂t                    152k   55.8ms    0.5%   367ns     0.00B    0.0%    0.00B
   ~drift!~                       152k   21.8ms    0.2%   144ns   1.47KiB    0.0%    0.01B
 ─────────────────────────────────────────────────────────────────────────────────────────

trixi_include("examples/solid/oscillating_beam_2d.jl", saving_callback=nothing);

[...]
────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi simulation finished.  Final time: 5.0  Time steps: 15726 (accepted), 16676 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

 ─────────────────────────────────────────────────────────────────────────────────────────
            TrixiParticles.jl                    Time                    Allocations      
                                        ───────────────────────   ────────────────────────
            Tot / % measured:                8.47s /  83.1%            311MiB /  80.2%    

 Section                        ncalls     time    %tot     avg     alloc    %tot      avg
 ─────────────────────────────────────────────────────────────────────────────────────────
 kick!                            150k    6.76s   96.1%  45.0μs    220MiB   88.1%  1.50KiB
   update systems and nhs         150k    3.98s   56.5%  26.5μs   68.7MiB   27.5%     480B
     stress tensor                150k    3.81s   54.1%  25.4μs   68.7MiB   27.5%     480B
     ~update systems and nhs~     150k    161ms    2.3%  1.07μs   1.47KiB    0.0%    0.01B
     update nhs                   150k   8.69ms    0.1%  57.9ns     0.00B    0.0%    0.00B
   system interaction             150k    2.33s   33.2%  15.5μs    119MiB   47.7%     832B
     solid1-solid1                150k    2.24s   31.8%  14.9μs   71.0MiB   28.4%     496B
     ~system interaction~         150k   94.8ms    1.3%   631ns   48.1MiB   19.3%     336B
   source terms                   150k    205ms    2.9%  1.37μs   32.1MiB   12.8%     224B
   reset ∂v/∂t                    150k    201ms    2.9%  1.34μs     0.00B    0.0%    0.00B
   ~kick!~                        150k   45.1ms    0.6%   301ns   2.94KiB    0.0%    0.02B
 drift!                           150k    276ms    3.9%  1.84μs   29.8MiB   11.9%     208B
   velocity                       150k    174ms    2.5%  1.16μs   29.8MiB   11.9%     208B
   reset ∂u/∂t                    150k   58.1ms    0.8%   387ns     0.00B    0.0%    0.00B
   ~drift!~                       150k   43.9ms    0.6%   292ns   1.47KiB    0.0%    0.01B
 ─────────────────────────────────────────────────────────────────────────────────────────

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 3 lines in your changes missing coverage. Please review.

Project coverage is 69.50%. Comparing base (c38804c) to head (e8bc21f).

Files	Patch %	Lines
test/count_allocations.jl	0.00%	3 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #544   +/-   ##
=======================================
  Coverage   69.50%   69.50%           
=======================================
  Files          76       76           
  Lines        4611     4611           
=======================================
  Hits         3205     3205           
  Misses       1406     1406           

Flag	Coverage Δ
unit	69.50% <0.00%> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.