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• Subdomains:
• Create a MeshFunction that contains the subdomains
• Materials properties:
• D coeff
• Traps energy
• Traps density
• alpha
• beta
• Other
• Solve in mol/m3 an not at.fr.

For validation purposes, the user should be able to apply BCs and sources terms to every components of vector u.

I noticed that the time and expressions were updating after solving the system which will induce errors.

https://fenicsproject.org/qa/13518/how-to-convert-a-sympy-expression-to-expression-in-fenics/

It would be nice to have a timer and to know how long did the calculation last.

Users should only give sympy expressions in parameters.

Currently BC aren't updating throughout the calculation.
apply_boundary_conditions() should be modified and be called at each time step in order to reassign bcs.

The user should be able to assign initial values for concentrations as parameters.
In case where nothing is set, the default value should be 0 for all the concentrations.

One way to do it would be to keep u_i as concentrations (and not number of traps) and just put N_0 on its own. I think the fact that the boundary conditions are set to zero for the number of traps can complicate things.

Currently the beggining of TDS is hard coded. This has to be changed quick

2 traps + 1 extrinsic one

The user should be able to create sequences for temperature instead of Timp, Trest, TDS, etc...

Should be changed to updating D_0 and E_diff same as alpha and beta

https://github.com/RemiTheWarrior/FESTIM/blob/90530e1f53101c813bf0edc47111514db84df1d9/Main/FESTIM.py#L568-L569

This shouldn't be .sub(0) but rather .sub(component)

The solution yields nan when non flux condition is put on one of the sides

See "Tritium absorption and desorption in ITER relevant materials comparative study of tungsten dust and massive samples" C. Grisolia et al JNM (2015)

• Materials parameters
• Traps parameters
  • intrisic traps
  • extrinsic traps
• Source term
• 1D mesh
• Temperature

As in 3-MOT, users should be able to compute fluxes at surfaces, integrate over subdomains, etc.
The result will then be exported to a csv format for later use.

In parameters:

"exports": {
    "post_processing": {
        "heat_transfers": {
            "surface_flux": [1],
            "total_volume": [1],
            "volume_average": [1],
            "volume_minimum": [1],
            "volume_maximum": [1],
            "custom": [],
            "output_file": "file1.csv",
        },
        "tritium_diffusion": {
            "surface_flux": [1, 2],
            "total_volume": [1],
            "volume_minimum": [1],
            "volume_maximum": [1],
            "custom": ["assemble(res[0]*dx(1))"],
            "output_file": "file2.csv"
        },
    }
}

The error is in FESTIM.initialising_solutions as ini_u is scalar whereas fenics.interpolate expects vector of rank 1.

Fix is to make sure variable expression is a tuple.

Being able to refine the mesh on the left hand side, so that we have roughly 5um/1500 = 0.003 um / cell in the first 5 um.

D must be defined as an Expression or a Function(W) (in this case at each time step iterate through the mesh) in order to be temperature dependent.

Currently it's fixed.

Current: The solver exports every time step in a xdmf file

Wished:

1. The solver exports at several times chosen by the user
2. The solver exports every dt_export
3. The solver also exports as txt file

Users should be able to set time dependent BCs as interpolation of a 2D table.
Something like:

table = [[0, 2],
         [1, 2],
         [4, 5]]

where 0, 1, 4 are times and 2, 2, 5 are values at these times.
This table would then be interpolated and ideally put in an Expression() object that can be updated throughout the calculation.

They should be the same

Being able to plot :

• Solution at specific times (before TDS, before implantation...)

• TDS spectrum

When the initial number of cells is too small, it may happen that all the midpoints found aren't in the refinement zone, leading to an infinite loop.

It would be better to mesh first each material, then join the meshes and only then do the refinement

Users should be able to define non homogeneous trap distribution as FEniCS Expression().

• Simulate a TDS
• Generate .csv file with desorption against time + temperature

The stepsize shouldn't go below a certain value.

Should be able to import xdmf meshes generated with gmsh

In apply_boundary_conditions, it should be V.sub(component) instead of V.sub(0)

Implement a loop that's wait for the file to be close or create a new one, thus avoiding the loss of data.

When solver doesn't converge, a NameError is raised solver is not defined.

The user should be able to :

• define an Expression()
• import from .xml (⚠️ non matching meshes...)
• solve heat equation with a given set of boundary conditions

Instead of just giving the first time step, the user should be able to give an array of times when he/she wants to do the calculation. This has the main advantages of :

1. adding control to the adaptative step size
2. adding the possibility to have the required temporal refinement

Could be cool to export parameters in a json file.
At least :

• BCs
• Volumetric source term
• materials
• traps
• Simulation parameters (time, dt, stepsize change ratio...)

Or allow the user to choose what parameters are to be exported.

This should be done with tot = project(_u_1 + _u_2 + _u_3 + _u_4, W) .

Change from pvd files to xdmf files in order to save space

It would be great to have an adaptative time step in order to optimise computation time. We would need to have a separate script that plots the time step as function of steps.

Find a way to avoid hard coding the number of simulated traps.
Replace:

P1 = FiniteElement('P', interval, 1)
element = MixedElement([P1, P1, P1, P1])
V = FunctionSpace(mesh, element)
W = FunctionSpace(mesh, 'P', 1)
V0 = FunctionSpace(mesh, 'DG', 0)

v_1, v_2, v_3, v_4 = TestFunctions(V)
testfunctions = [v_1, v_2, v_3, v_4]

u_1, u_2, u_3, u_4 = split(u)
solutions = [u_1, u_2, u_3, u_4]

ini_u = Expression(("0", "0", "0", "0"), degree=1)
u_n = interpolate(ini_u, V)
u_n1, u_n2, u_n3, u_n4 = split(u_n)
previous_solutions = [u_n1, u_n2, u_n3, u_n4]

    _u_1, _u_2, _u_3, _u_4 = u.split()

    # Save solution to file (.xdmf)
    _u_1.rename("solute", "label")
    _u_2.rename("trap_1", "label")
    _u_3.rename("trap_2", "label")
    _u_4.rename("trap_3", "label")
    xdmf_u_1.write(_u_1, t)
    xdmf_u_2.write(_u_2, t)
    xdmf_u_3.write(_u_3, t)
    xdmf_u_4.write(_u_4, t)

    total_trap1 = assemble(_u_2*dx)
    total_trap2 = assemble(_u_3*dx)
    total_trap3 = assemble(_u_4*dx)
    total_trap = total_trap1 + total_trap2 + total_trap3
    total_sol = assemble(_u_1*dx)

"traps": [
    {
        "energy": 0.87,
        "density": 1.3e-3*6.3e28,
        "materials": [1]
    },
    {
        "energy": 1.0,
        "density": 4e-4*6.3e28,
        "materials": [1]
    }],

"xdmf": {
    "functions": ['solute', '1', '2', '3', '4', 'retention'],
    "labels":  ['solute', 'trap_1', 'trap_2',
                'trap_3', 'trap_4', 'retention'],
    "folder": 'Solution'

here len(solutions) list will be 3+1 (retention) = 4 whereas len(["xdmf"]["functions"]) is 5. This should raise an error.