RFC: source terms via global vector storage

[benegee]

This demonstrates how source terms can be evaluated via a global shared storage.

Issues:

• Data vectors need to be access via an index. Trixi.jl's source_terms function works with the local coordinate x. Therefore a mapping x -> index is required or a change in Trixi.jl to allow for a source_terms function operating on indices.
• In this demonstration also a vector of node coordinates is fetched. This would become obsolete if a (t8code) mesh existed both in the calling program and within libtrixi.

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:              2.45s /  16.8%            137MiB /  13.5%

 Section                   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────────────────────
 I/O                            5    199ms   48.4%  39.7ms   10.6MiB   57.4%  2.11MiB
   save solution                4    123ms   29.9%  30.7ms   10.3MiB   56.1%  2.59MiB
   ~I/O~                        5   76.0ms   18.5%  15.2ms    230KiB    1.2%  46.1KiB
   save mesh                    4    664ns    0.0%   166ns     0.00B    0.0%    0.00B
   get element variables        4    415ns    0.0%   104ns     0.00B    0.0%    0.00B
   get node variables           4   87.0ns    0.0%  21.8ns     0.00B    0.0%    0.00B
 rhs!                       1.15k    119ms   29.0%   104μs   5.14KiB    0.0%    4.59B
   volume integral          1.15k   48.2ms   11.7%  42.1μs     0.00B    0.0%    0.00B
   interface flux           1.15k   30.9ms    7.5%  27.0μs     0.00B    0.0%    0.00B
   source terms             1.15k   21.2ms    5.2%  18.5μs     0.00B    0.0%    0.00B
   surface integral         1.15k   11.5ms    2.8%  10.1μs     0.00B    0.0%    0.00B
   Jacobian                 1.15k   4.40ms    1.1%  3.84μs     0.00B    0.0%    0.00B
   reset ∂u/∂t              1.15k   2.29ms    0.6%  2.00μs     0.00B    0.0%    0.00B
   ~rhs!~                   1.15k    563μs    0.1%   491ns   5.14KiB    0.0%    4.59B
   boundary flux            1.15k   22.1μs    0.0%  19.3ns     0.00B    0.0%    0.00B
 analyze solution               4   88.4ms   21.5%  22.1ms   7.85MiB   42.6%  1.96MiB
 calculate dt                 230   4.59ms    1.1%  19.9μs     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 #172

[benegee]

Fortran interface is still missing.