Implementation of new hand written poisson

[Cmurilochem]

Closes #159.

[Cmurilochem]

@fverdugo and @raar1. The first draft of the new implementation of our hand written poisson is ready. But there are lots of things that we can still optimize.

For example, in assemble_fill and integrate_error_norms (and export_results to a lesser extent) I noticed that the core loops have nearly the same structure and there is a lot of code repetition. Maybe something to look at.

EDIT:

Even though, the timing of our minimal example:

import GalerkinToolkit as GT
using GalerkinToolkitExamples: Poisson

tol = 1.0e-10

n = 10
mesh = GT.cartesian_mesh((0,1,0,1,0,1),(n,n,n))

params = Dict{Symbol,Any}()
params[:implementation] = :hand_written
params[:mesh] = mesh
params[:integration_degree] = 2

@time results = Poisson.main(params)

@assert results[:error_l2_norm] < tol
@assert results[:error_h1_norm] < tol

is nearly optimal:

──────────────────────────────────────────────────────────────────────────────────
                                         Time                    Allocations
                                ───────────────────────   ────────────────────────
       Tot / % measured:             1.82s / 100.0%           1.73GiB / 100.0%

Section                 ncalls     time    %tot     avg     alloc    %tot      avg
──────────────────────────────────────────────────────────────────────────────────
export_results               1    908ms   49.9%   908ms    672MiB   38.0%   672MiB
assemble_system              1    608ms   33.4%   608ms    806MiB   45.6%   806MiB
setup                        1    168ms    9.3%   168ms    144MiB    8.1%   144MiB
solve_system                 1    102ms    5.6%   102ms   91.5MiB    5.2%  91.5MiB
integrate_error_norms        1   31.9ms    1.8%  31.9ms   55.1MiB    3.1%  55.1MiB
──────────────────────────────────────────────────────────────────────────────────
  1.822781 seconds (80.12 M allocations: 1.728 GiB, 5.09% gc time)

[fverdugo]

Perfect! @Cmurilochem can you please remove the old version?

[Cmurilochem]

Perfect! @Cmurilochem can you please remove the old version?

Yes, of course. Done!

[fverdugo]

We are "bending the line" 😀