Find max value in parallel safely

[jhdark]

Proposed changes

fix for #900

use MPI to find max value

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• New feature (non-breaking change which adds functionality)
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• New tests

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.14%. Comparing base (01ab7f9) to head (582c304).
Report is 48 commits behind head on fenicsx.

Additional details and impacted files

@@             Coverage Diff             @@
##           fenicsx     #953      +/-   ##
===========================================
+ Coverage    96.02%   96.14%   +0.12%     
===========================================
  Files           45       46       +1     
  Lines         2490     2571      +81     
===========================================
+ Hits          2391     2472      +81     
  Misses          99       99              

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[RemDelaporteMathurin]

I guess we'll need this for maxinum surface, minimum surface, and minimum volume too

[RemDelaporteMathurin]

1. I believe we still want to use numpy.max instead of native max here for performance purposes, no?
2. what does barrier() do?

[jhdark]

1. Yes sorry, I had just copied an example I had found. Now just using numpy within the `allreduce' function instead

2. It seems the barrier function forces all processes to reach the barrier before any of them can continue execution, however for this case it may not be necessary as all the processors will be following the same logical flow. Do you have any thoughts on this @jorgensd ?

[RemDelaporteMathurin]

Plus shouldn't it be solution.function_space.mesh.comm.barrier() instead of comm world?

[jhdark]

I guess so

[RemDelaporteMathurin]

LGTM, @jorgensd do you know if the barrier call is required?

[jorgensd]

LGTM, @jorgensd do you know if the barrier call is required?

You do not need the barrier as you are using all reduce.

a barrier would be necessary if say only one process does something (or a subset), and the others have to wait for them to finish. I almost exclusively use this whenever I create meshes with gmsh, but not very often otherwise.
It can at times be useful when profiling code as well, to ensure that timings are started in a synchronized fashion