Analytic integration for Bx and By

[MaxThevenet]

@SaVicente we can use this discussion as a chat, so we can interact more easily. I created a timeline here #356, listing the tasks on a weekly basis, so we can look at the progress and clearly see the next steps. Could you look at it, tick the boxes regularly for tasks already done, and let me know ahead of time if you need help for a task? If you have any question, just post a message in this discussion.

[MaxThevenet]

Hi @SaVicente,
We merged a large PR yesterday, so that your branch new_bxby is now deprecated. In order to fix this, I created a fresh branch solvebxby from the new development and reproduced the changes in new_bxby. Could you port your changes in new_bxby to solvebxby? Then I will delete new_bxby, and everything will happen in solvebxby from now on.
You can see the diff between solvebxby and development here: https://github.com/Hi-PACE/hipace/compare/solvebxby
From now on, could you push commits regularly to solvebxby?

[MaxThevenet]

@SaVicente have you tried to compile your code? I implemented the calculation of jxx etc., but I get compilation errors in SolveBxBy.

[MaxThevenet]

@SaVicente I proposed to reactivate CI on branch new_bxby. This is done in #428. In particular it checks that:

• the code doesn't have tabs and end-of-line whitespaces
• Each new function parameter is documented
• The code still runs and deliver correct results

This will help keep the code clean.

[MaxThevenet]

@SaVicente I just fixed a few compilation warnings, now the code compile and runs well even when calling your function (but of course the function doesn't modify existing arrays, as the Helmholtz solver is not called).

[MaxThevenet]

Hipace++ has style guidelines, in particular no tab and no end-of-line whitespaces. Could you make sure your editor complies?

[MaxThevenet]

@SaVicente When do you think you'll have time to clean up the calculation of the source terms? When you give me a green light I'll take care of calling the solver, so we can run the actual first simulation with this option. Looking forward!

[MaxThevenet]

PR #437 shows that the fields are not correct with the analytic integration approach, so there's probably a bug somewhere. To reproduce the image, after compiling the code on new_bxby do:

rm -r diags ; ../../build/bin/hipace inputs_normalized hipace.wandpic=1

And then execute the following Python lines:

import numpy as np
%matplotlib notebook
import matplotlib.pyplot as plt
from openpmd_viewer import OpenPMDTimeSeries

field = 'Ez'
ts = OpenPMDTimeSeries('./diags/hdf5/')
F,m = ts.get_field(field=field, iteration=1)
plt.figure()
plt.imshow(F[:,F.shape[1]//2,:], aspect='auto')
plt.colorbar()
plt.tight_layout()

The input file is

amr.n_cell = 128 128 200 # 64 64 100
geometry.prob_lo     = -8.   -8.   -6    # physical domain
geometry.prob_hi     =  8.    8.    6
hipace.verbose = 2
hipace.normalized_units = 1
hipace.predcorr_max_iterations = 100
hipace.predcorr_B_mixing_factor = 0.02
hipace.predcorr_B_error_tolerance = .02
amr.blocking_factor = 2
amr.max_level = 0
max_step = 1
hipace.output_period = 1
hipace.numprocs_x = 1
hipace.numprocs_y = 1
hipace.depos_order_xy = 2
geometry.coord_sys   = 0                  # 0: Cartesian
geometry.is_periodic = 1     1     0      # Is periodic?
beams.names = beam
beam.injection_type = fixed_ppc
beam.profile = gaussian
beam.zmin = -5.9
beam.zmax = 5.9
beam.radius = 1.2
beam.density = 3.
beam.u_mean = 0. 0. 2000
beam.u_std = 0. 0. 0.
beam.position_mean = 0. 0. 0
beam.position_std = 0.3 0.3 1.41
beam.ppc = 1 1 1
plasmas.names = plasma
plasma.density = 1.
plasma.ppc = 1 1
plasma.u_mean = 0.0 0.0 0.
plasma.element = electron
diagnostic.diag_type = xyz

[MaxThevenet]

@WeiqunZhang the input file in the previous message is good for correctness testing. If you want to look at performance, I suggest using this one:
inputs.txt

this one has a fixed number of beam particles while the other one has a variable number (fixed number per cell, which spuriously dominates everything when going to higher resolution).