Add InterfaceExactDerivativeMatrix for conforming meshes

[PaulineVidal]

Add an operator which computes the coupled interface derivatives along a direction with the exact formula.

Description

InterfaceDerivativeMatrix solves the following matrix system,

$$\begin{bmatrix} s'(\mathcal{X}_1) \\\ \vdots \\\ s'(\mathcal{X}_I) \\\ \vdots \\\ s'(\mathcal{X}_{N-1}) \end{bmatrix} = \begin{bmatrix} 1 & -a^1 & \dots & & \\\ -b^2 & 1 & -a^2 & \dots & \\\ \vdots & & & & \\\ & & \ddots & & \\\ & \cdots & -b^{N-1} & 1 & \\\ \end{bmatrix} \begin{bmatrix} c^1 - b^1 s'(\mathcal{X}_0) \\\ \vdots \\\ c^I \\\ \vdots \\\ c^{N-1} - a^{N-1}s'(\mathcal{X}_{N}) \end{bmatrix}$$

We write it as follows, $S = (I -M)^{-1}C.$

It allows us to compute the interface derivatives in 1D.

InterfaceDerivativeMatrix operator deals with 2D patches applying this 1D formula.

It means on the following case, (implemented test case)

we build a InterfaceDerivativeMatrix in the directions,

• 1|2|3 with periodic boundary conditions,
• 4|5|6 with periodic boundary conditions,
• 7|8|9 with periodic boundary conditions,
• 1|4|7 with "Greville" boundary conditions,
• 2|5|8 with "Greville" boundary conditions,
• 3|6|9 with "Greville" boundary conditions.

InterfaceDerivativeMatrix stores SingleInterfaceDerivativeCalcultor defined and instantiated before.
The matrix $(I-M)$ can be defined at the instantiation of InterfaceDerivativeMatrix and only depends on the mesh.

When the InterfaceDerivativeMatrix::solve() operator is called, the vector $C$ is defined from the function values.
The operator solves the matrix system $S = (I -M)^{-1}C$. Then, it fills in the derivative fields given as parameters
with the values in the $S$ solution vector.

---

Please complete the checklist to ensure that all tasks are completed before marking your pull request as ready for review.

All Submissions

• Have you ensured that all lines changed in this PR are justified by a comment found in the description ?
• Have you updated the CHANGELOG.md ?
• Have you linked any issues that should be closed when this PR is merged (using closing keywords) ?
• Have you checked that the AUTHORS file is up to date ?
• Have you checked that the copyright information in the LICENCE file is up to date (including dates) ?
• Do you follow the conventions specified in our coding standards ?

New Feature Submissions

• Have you added tests for the new functionalities ?
• Have you documented the new functionalities:
  • API documentation describing the available methods, when each should be used and how to use them ?
  • User-friendly documentation in README files (which may link to the API documentation).
  • If the new functionality is non-trivial to use, provide a tutorial or example ? (optional)

Changes to Existing Features

• Have you checked that existing tests cover all code after the changes ?
• Have you checked that existing tests are still passing ?
• Have you checked that the existing documentation is still accurate (API and README files) ?

Changes to the CI

• Have you made the same changes to both the GitHub CI and the GitLab CI (for the private fork) ?

[github-actions]

This PR is failing tests so it has been put back into draft. Please remove the draft status when the tests pass.