Interface concentration discontinuities (fenicsx)

[RemDelaporteMathurin]

Proposed changes

A massive thank you to @jorgensd who was instrumental in getting this functionality in FESTIM 🥇

This PR is a first (big) step towards interface discontinuities in the fenicsx branch (#719).

(requires #764)

This new approach to conservation of chemical potential relies on the mixed domain approach implemented in dolfinx 0.8.0 and based off a demo available here

I created a new problem class HTransportProblemDiscontinuous - which is not yet complete - to avoid breaking existing functionality. We will complete this class by integrating transient, post-processing, ICs, etc. Eventually this whole class will be merged with HydrogenTransportProblem.

In the current interface, users need to provide correspondence between surfaces and volumes as well as listing interfaces and which volumes they are connected to:

list_of_interfaces = [F.Interface(6, (left_domain, middle_domain))]
my_model.subdomains = [left_domain, right_domain, left_surface, right_surface]

I believe this can be streamlined by FESTIM under the hood but I'll keep that for a future PR.

Proposed user interface:

import numpy as np

import festim as F

my_model = F.HTransportProblemDiscontinuous()

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)

material_left = F.Material(D_0=2.0, E_D=0.1, K_S_0=2.0, E_K_S=0)
material_mid = F.Material(D_0=2.0, E_D=0.1, K_S_0=4.0, E_K_S=0)
material_right = F.Material(D_0=2.0, E_D=0.1, K_S_0=6.0, E_K_S=0)

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])

# the ids here are arbitrary in 1D, you can put anything as long as it's not the same as the surfaces
my_model.interfaces = [
    F.Interface(6, (left_domain, middle_domain)),
    F.Interface(7, (middle_domain, right_domain)),
]
my_model.surface_to_volume = {right_surface: right_domain, left_surface: left_domain}

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

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

my_model.species = [H, trapped_H]

for species in [H, trapped_H]:
    species.subdomains = [left_domain, middle_domain, right_domain]


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.DirichletBC(left_surface, value=0.05, species=H),
    F.DirichletBC(right_surface, value=0.2, species=H),
]


my_model.temperature = lambda x: 300 + 100 * x[0]

my_model.settings = F.Settings(atol=1e-10, rtol=1e-10, transient=False)

my_model.exports = [
    F.VTXSpeciesExport(
        f"u_{field.name}_{subdomain.id}.bp", field=field, subdomain=subdomain
    )
    for subdomain in my_model.volume_subdomains
    for field in [H, trapped_H]
]

my_model.initialise()
my_model.run()

Types of changes

What types of changes does your code introduce to FESTIM?

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Code refactoring
• Documentation Update (if none of the other choices apply)
• New tests

Checklist

• Black formatted
• Unit tests pass locally with my changes
• I have added tests that prove my fix is effective or that my feature works
• I have added necessary documentation (if appropriate)

[RemDelaporteMathurin]

We probably don't need to keep this

[RemDelaporteMathurin]

Note for future: this is not safe in parallel

[RemDelaporteMathurin]

Should live in Settings

[RemDelaporteMathurin]

Fix bs and ts

[RemDelaporteMathurin]

Needs to go in setter