Change of variable method for interface discontinuities

[RemDelaporteMathurin]

needs #909

This implements the change of variable method we use in FESTIM 1 to handle interface discontinuities.

Example usage:

import festim as F
import numpy as np

my_model = F.HydrogenTransportProblemDiscontinuousChangeVar()

interface_1 = 0.2
interface_2 = 0.8

vertices = np.concatenate(
    [
        np.linspace(0, interface_1, num=100),
        np.linspace(interface_1, interface_2, num=100),
        np.linspace(interface_2, 1, num=100),
    ]
)

my_model.mesh = F.Mesh1D(vertices)

H = F.SpeciesChangeVar("H", mobile=True)
H2 = F.SpeciesChangeVar("H2", mobile=True)
trapped_H = F.SpeciesChangeVar("H_trapped", mobile=False)
empty_trap = F.ImplicitSpecies(n=0.5, others=[trapped_H])

my_model.species = [H, H2, trapped_H]

material_left = F.Material(D_0=2.0, E_D=0.1, K_S_0=2.0, E_K_S=0.1)
material_mid = F.Material(D_0=2.0, E_D=0.1, K_S_0=2.0, E_K_S=0.1)
material_right = F.Material(
    D_0=2.0, E_D=0.1, K_S_0={H: 2.0, H2: 4.0}, E_K_S={H: 0.1, H2: 0.1}
)

left_domain = F.VolumeSubdomain1D(3, borders=[0, interface_1], material=material_left)
middle_domain = F.VolumeSubdomain1D(
    4, borders=[interface_1, interface_2], material=material_mid
)
right_domain = F.VolumeSubdomain1D(5, borders=[interface_2, 1], material=material_right)

left_surface = F.SurfaceSubdomain1D(id=1, x=vertices[0])
right_surface = F.SurfaceSubdomain1D(id=2, x=vertices[-1])

my_model.subdomains = [
    left_domain,
    middle_domain,
    right_domain,
    left_surface,
    right_surface,
]

my_model.reactions = [
    F.Reaction(
        reactant=[H, empty_trap],
        product=[trapped_H],
        k_0=2,
        E_k=0,
        p_0=0.1,
        E_p=0,
        volume=domain,
    )
    for domain in [left_domain, middle_domain, right_domain]
]

my_model.boundary_conditions = [
    F.FixedConcentrationBC(left_surface, value=2, species=H),
    F.FixedConcentrationBC(right_surface, value=2, species=H),
    F.FixedConcentrationBC(left_surface, value=2, species=H2),
    F.FixedConcentrationBC(right_surface, value=2, species=H2),
]

my_model.temperature = lambda x, t: 400 + 100 * t + 100 * x[0]

my_model.settings = F.Settings(
    atol=1e-10,
    rtol=1e-10,
    final_time=10,
)
my_model.settings.stepsize = F.Stepsize(1)

my_model.exports = [
    F.VTXSpeciesExport(f"u_{field}.bp", field=field)
    for field in [H, trapped_H, H2]
]
my_model.initialise()
my_model.run()

[codecov]

Codecov Report

Attention: Patch coverage is 80.46512% with 42 lines in your changes missing coverage. Please review.

Project coverage is 96.02%. Comparing base (819379a) to head (22d5d79).
Report is 341 commits behind head on fenicsx.

Files with missing lines	Patch %	Lines
src/festim/material.py	25.00%	18 Missing ⚠️
src/festim/problem_change_of_var.py	88.97%	14 Missing ⚠️
src/festim/boundary_conditions/dirichlet_bc.py	70.00%	9 Missing ⚠️
src/festim/hydrogen_transport_problem.py	94.73%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           fenicsx     #904      +/-   ##
===========================================
- Coverage    97.53%   96.02%   -1.52%     
===========================================
  Files           44       45       +1     
  Lines         2233     2439     +206     
===========================================
+ Hits          2178     2342     +164     
- Misses          55       97      +42     

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[RemDelaporteMathurin]

I fixed a bunch of things and it's now time to merge this.

There's quite a lot of tidy up to do but I'll do it in a separate PR