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[GeoMechanicsApplication] Extract a static utility function for the calculation of the Mass Matrix (M) #12279

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markelov208 opened this issue Apr 15, 2024 · 0 comments · Fixed by #12299
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markelov208 commented Apr 15, 2024

As a developer, I would like to have a utility function which can calculate the mass matrix, such that this can be re-used.

Acceptance Criteria

  • The calculation of the mass matrix is available as a utility function, which takes the displacement shape function, integration coefficient and soil density for all integration points and returns the element matrix.
  • This calculation is defined once and re-used at all locations where this calculation is done in the geomechanics application.
  • The utility function is documented and unit-tested.

Background
This issue handles the M in the equation describing our UPw system of equations:

$$ \begin{bmatrix} M & 0 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} \ddot{u} \\ \ddot{p} \end{bmatrix} + \begin{bmatrix} D & 0 \\ Q^T & C \end{bmatrix} \begin{bmatrix} \dot{u} \\ \dot{p} \end{bmatrix} + \begin{bmatrix} K & -Q \\ 0 & H \end{bmatrix} \begin{bmatrix} u \\ p \end{bmatrix} = \begin{bmatrix} f_u \\ f_p \end{bmatrix} $$

The mathematical definition is:
$$M = \int_\Omega N_{u}^T \rho N_u d\Omega$$

Where $\Omega$ is the domain, $N_u$ is the displacement shape function and $\rho$ is the density.

@markelov208 markelov208 converted this from a draft issue Apr 15, 2024
@markelov208 markelov208 moved this from 📋 Sprint Backlog to 👷 In Progress in Kratos Product Backlog Apr 15, 2024
@rfaasse rfaasse moved this from 👷 In Progress to 👀 In Review in Kratos Product Backlog Apr 26, 2024
@github-project-automation github-project-automation bot moved this from 👀 In Review to ✅ Done in Kratos Product Backlog May 10, 2024
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