[WIP] Self gravity (Barnes-Hut version)

First iteration of the gravity solver. This is a copy of the BH code in the Quickhed examples. Compute forces up to quadrupole order.

Comes with the following limitations:

• Not MPI
• Not periodic
• Only fixdt
• Gravity is not softened

The last 2 points are trivial to implement and won't affect the logic.

At the moment there is little logic in scheduler_splittask(), everything is in the tasks themselves. Obvious improvements to the logic would be to not lock a cell when only its multipole is required.

This should not be merged in as it is but it is here for you to look at.

There are three types of task (besides the multipole construction):

• pair: interacts two cells that are neighbours of each others (potentially by recursing).
• self: interacts one cell with itself (potentially by recursing).
• mm: interacts two cells that are NOT neighbours (using particle-multipole interactions, no recursion).

When we are happy, the mm tasks can be replaced by a multipole-multipole interaction to make the algorithm FMM and not Barnes-Hut any more.

Here is a histogram of the relative errors when compared to a stupid N^2 algorithm. We are more accurate than the ~1% achieved by Gadget. This will improve further when softened interactions are used.

@rgb Is that plot sexy enough ?

Title changed from Self gravity (Barnes-Hut version) to [WIP] Self gravity (Barnes-Hut version)

Added 4 commits:

• 0e904f5a - Multiply the accelerations by G, add a softening length to the particles and compute time-step
• f4d59002 - External potential does now compute accelerations / G.
• a9b488bf - Cleaned-up the const.h file
• 417728d0 - Initial work on the gravity kernel functions

Added 1 commit:

• f647b6fa - Compiling but wrong softening

Added 57 commits:

• f647b6fa...b90156c9 - 55 commits from branch master
• fa8062c7 - Merge branch 'master' into Self_gravity_BH
• 09f3bcc2 - Post-merge fixes

Added 2 commits:

• 716001d8 - New formatting style
• 1310ca75 - New formatting style

Added 14 commits:

• 1310ca75...778c4cca - 12 commits from branch master
• bd058d2f - Merge branch 'master' into Self_gravity_BH
• 4f4227c4 - Post-merge fixes

Added 1 commit:

• 9e28ec1e - Upated the kernel functions for gravity. Added a unit test to test it against the Gadget-2 kernel

Added 4 commits:

• 4b3f8b02 - Moved the gravity interaction routines to the correct files.
• 0c8575ca - Multiple time-stepping in the gravity tasks
• b11b3ea6 - Softened gravity in the interactions
• 40d813ed - Softened gravity in the interactions

Gravity softening and multiple time-stepping now in place.

Added 2 commits:

• a59561b9 - Merged master changes
• 5497fe79 - Post-merge fixes

Added 6 commits:

• 5497fe79...78f0419b - 5 commits from branch master
• 8ef31673 - Merge branch 'master' into Self_gravity_BH

Added 12 commits:

• 8ef31673...a4f97e08 - 7 commits from branch master
• b4721778 - Merge branch 'master' into Self_gravity_BH
• 6b6c7c84 - Use definition of atomics everywhere in cell.c
• 487a1f08 - Use atomic definitions
• 111fdbf9 - Set the locking and unlocking of cells for gravity tasks
• c5197e08 - Added function to compute long-range FFT correction term

Added 2 commits:

• d44155a8 - Use the long-range smoothing kernel
• 170d2b7f - Better documentation of the gravity stuff in engine

Added 1 commit:

• e1b31a15 - Better documentation of the gravity stuff in engine

Long-range correction term now in place. Only the FFT task is missing.

Todo-list:

• Give a minimal size to the top-level grid.
• import FFTW.
• Create a long-range task using FFTW.
• Create timers for the gravity tasks.
• Make the scheduler smarter.

Added 2 commits:

• 35bf96ad - Moved the cell neighbour test function to the cell object
• aa075f20 - Added linking of the FFTW 3.x library

Added 2 commits:

• ea0c9ca3 - Make sure we have at least 8 cells on a side when using gravity
• f0728bfb - Modified the mm task to use all the multipoles interacting with one given cell

Added 15 commits:

• f0728bfb...ca0eafb8 - 13 commits from branch master
• 24e3b63a - Merge branch 'master' into Self_gravity_BH
• 01f51f70 - Post-merge fixes