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[GeoMechanicsApplication] Extract a static utility function for the calculation of the Damping Matrix (D) #12366

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markelov208 opened this issue May 10, 2024 · 0 comments · Fixed by #12368
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@markelov208
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As a developer, I would like to have a utility function which can calculate the damping matrix, such that this can be re-used.

Acceptance Criteria

  • The calculation of the damping matrix is available as a utility function, which takes the mass and stiffness matrices and the rayleigh coefficients ($\alpha$ and $\beta$)
  • 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 D 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:
$$D = \alpha_R M + \beta_R K$$

Where $M$ and $K$ are the mass and damping matrices respectively and $\alpha_R$ and $\beta_R$ are the coefficients from the Rayleigh Method.

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