Improve differential operators

[GiovanniCanali]

Fixes #525.

To do:

• Remove unneccessary checks;
• Remove multidimensional requirement for div;
• Fix advection;
• Implement divgrad method for laplacian;
• Update documentation;
• Add tests;
• Add fast implementations of differential operators.

[GiovanniCanali]

Hi @ndem0, @dario-coscia, @FilippoOlivo,

Tests for python 3.8 are failing in several different modules, not related to this PR. Since this version is no longer supported, I suggest to remove them.

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Preliminary results in terms of speedup:

• grad: 15% - 20% faster.
• div: 20% - 25% faster.
• laplacian (std method): up to 40% faster.
• laplacian (divgrad method): much slower than std. Not available before.

Reported results are a qualitative average derived from the combination of these values:

• device: [cpu, cuda]
• number of points: [1, 10, 100, 1000, 10000, 100000]
• number of input components: [1, 2, 3, 4, 5]
• number of output components: [1, 2, 3, 4, 5]

[dario-coscia]

Thank you for the PR, really impressive the speedup. Since we are working on this I also suggested further improvements which could speed up even more! We need however to restructure a bit..

Idea:

1. Have fast versions of operators where no checks are performed (nothing). These are exact copies of the ones we already have but with no checks. Why? Sometimes when calling recursively grad we do the same check (but we actually need to do the check only once at the beginning!). We can also think of doing a separate module called fast_operator.py where we put these operators. Of course, we need to raise a warning when imported saying checks are not going to be performed and also write it in the doc.

2. Rewrite our operators by calling the fast versions, avoiding multiple repeated checks

[GiovanniCanali]

Thanks to @dario-coscia for spotting a bug in laplacian and helping writing the new tests, which should now be more complete.

[dario-coscia]

Just a minor change! The tests look good, and I think we are done besides that comment on advection