RFC: Source terms via callback

[benegee]

This is to demonstrate how an external function could be called to evaluate source terms.

Issues:

• Path to shared object is currently hard-coded.
• Global buffer variable in libelixir to prevent subsequent allocations in source_term_callback

Some rough timing results:

Timing libtrixi

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 2.0  Time steps: 229 (accepted), 229 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────


*** Trixi controller ***   Finalize Trixi simulation
 ────────────────────────────────────────────────────────────────────────────────────
              Trixi.jl                      Time                    Allocations
                                   ───────────────────────   ────────────────────────
         Tot / % measured:              2.39s /  19.5%            129MiB /  14.2%

 Section                   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────────────────────
 I/O                            5    200ms   43.0%  40.1ms   10.6MiB   57.4%  2.11MiB
   save solution                4    124ms   26.6%  31.0ms   10.3MiB   56.1%  2.59MiB
   ~I/O~                        5   76.3ms   16.4%  15.3ms    230KiB    1.2%  46.1KiB
   get element variables        4   1.52μs    0.0%   380ns     0.00B    0.0%    0.00B
   save mesh                    4    501ns    0.0%   125ns     0.00B    0.0%    0.00B
   get node variables           4   88.0ns    0.0%  22.0ns     0.00B    0.0%    0.00B
 rhs!                       1.15k    174ms   37.3%   152μs   5.14KiB    0.0%    4.59B
   source terms             1.15k   80.7ms   17.3%  70.4μs     0.00B    0.0%    0.00B
   volume integral          1.15k   45.9ms    9.8%  40.0μs     0.00B    0.0%    0.00B
   interface flux           1.15k   29.7ms    6.4%  25.9μs     0.00B    0.0%    0.00B
   surface integral         1.15k   10.8ms    2.3%  9.44μs     0.00B    0.0%    0.00B
   Jacobian                 1.15k   4.16ms    0.9%  3.63μs     0.00B    0.0%    0.00B
   reset ∂u/∂t              1.15k   2.20ms    0.5%  1.92μs     0.00B    0.0%    0.00B
   ~rhs!~                   1.15k    523μs    0.1%   457ns   5.14KiB    0.0%    4.59B
   boundary flux            1.15k   21.4μs    0.0%  18.7ns     0.00B    0.0%    0.00B
 analyze solution               4   87.2ms   18.7%  21.8ms   7.85MiB   42.6%  1.96MiB
 calculate dt                 230   4.44ms    1.0%  19.3μs     0.00B    0.0%    0.00B
 ────────────────────────────────────────────────────────────────────────────────────

Timing Trixi.jl

────────────────────────────────────────────────────────────────────────────────────
              Trixi.jl                      Time                    Allocations
                                   ───────────────────────   ────────────────────────
         Tot / % measured:              164ms /  94.0%           2.00MiB /  90.6%

 Section                   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────────────────────
 rhs!                       1.15k    144ms   93.2%   126μs   5.14KiB    0.3%    4.59B
   source terms             1.15k   59.7ms   38.7%  52.1μs     0.00B    0.0%    0.00B
   volume integral          1.15k   41.5ms   26.9%  36.2μs     0.00B    0.0%    0.00B
   interface flux           1.15k   26.6ms   17.3%  23.2μs     0.00B    0.0%    0.00B
   surface integral         1.15k   9.68ms    6.3%  8.44μs     0.00B    0.0%    0.00B
   Jacobian                 1.15k   3.82ms    2.5%  3.34μs     0.00B    0.0%    0.00B
   reset ∂u/∂t              1.15k   1.99ms    1.3%  1.73μs     0.00B    0.0%    0.00B
   ~rhs!~                   1.15k    498μs    0.3%   434ns   5.14KiB    0.3%    4.59B
   boundary flux            1.15k   28.8μs    0.0%  25.2ns     0.00B    0.0%    0.00B
 I/O                            5   4.82ms    3.1%   964μs   1.56MiB   85.9%   319KiB
   save solution                4   4.31ms    2.8%  1.08ms   1.55MiB   85.4%   397KiB
   ~I/O~                        5    507μs    0.3%   101μs   8.83KiB    0.5%  1.77KiB
   get element variables        4    765ns    0.0%   191ns     0.00B    0.0%    0.00B
   save mesh                    4    488ns    0.0%   122ns     0.00B    0.0%    0.00B
   get node variables           4    342ns    0.0%  85.5ns     0.00B    0.0%    0.00B
 calculate dt                 230   4.04ms    2.6%  17.6μs     0.00B    0.0%    0.00B
 analyze solution               4   1.59ms    1.0%   396μs    258KiB   13.9%  64.5KiB
 ────────────────────────────────────────────────────────────────────────────────────

Confer #173

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 15 lines in your changes missing coverage. Please review.

Project coverage is 82.51%. Comparing base (07845ab) to head (a8d2058).

Files with missing lines	Patch %	Lines
examples/source_terms.c	0.00%	15 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #172      +/-   ##
==========================================
- Coverage   83.92%   82.51%   -1.42%     
==========================================
  Files          21       22       +1     
  Lines         877      892      +15     
  Branches       52       52              
==========================================
  Hits          736      736              
- Misses        137      152      +15     
  Partials        4        4              

Flag	Coverage Δ
unittests	82.51% <0.00%> (-1.42%)	⬇️

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