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Rotation matrix wrapper

Ponsuganth Ilangovan Ponkumar Ilango requested to merge ponsuganth/rotation-wrapper into main

This adds a rotation matrix wrapper to the assembled FE matrix, could be applied for any vectorial space operators.

RKR^\top \mathbf{u}_{R} = Rf

  • where,
    • R - Rotation Matrix
    • K - Assembled FE Matrix
    • \mathbf{u}_{R} - Vector field rotated at the boundary, with its radial component pointing in the normal direction
  • The normal vectors (\hat{n}) has to be passed to the operator, with which is the rotation matrix (R) calculated
  • The rotation matrix is calculated for every DoF and applied locally for the whole FE element
  • If the passed normal vector is zero then the rotation matrix is identity matrix
  • The vector is transformed in such a way that (u_x, u_y, u_z) \rightarrow (u_r, u_{\theta}, u_{\phi}), the radial component u_r is pointing in the normal direction (\hat{n})

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