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.. _Tyings:
******
Tyings
******
| :download:`GooseFEM/TyingsPeriodic.h <../../include/GooseFEM/TyingsPeriodic.h>`
| :download:`GooseFEM/TyingsPeriodic.hpp <../../include/GooseFEM/TyingsPeriodic.hpp>`
Tyings::Periodic
================
Periodic nodal tyings: partition the system (renumber the DOFs) in the following order [iii, iid]: first the independent DOFs and the the dependent DOFs. If, in addition, independent DOFs are prescribed the partitioning is [iiu, iip, iid], where iii = [iiu, iip]: first the unknown and then the prescribed DOFs.
Tyings::Periodic::nnd()
-----------------------
Return the dependent DOF-numbers.
Tyings::Periodic::nni()
-----------------------
Return the independent DOF-numbers.
Tyings::Periodic::nnu()
-----------------------
Return the unknown DOF-numbers.
Tyings::Periodic::nnp()
-----------------------
Return the prescribed DOF-numbers.
Tyings::Periodic::dofs()
------------------------
Renumbered DOFs per node [nnode, ndim].
Tyings::Periodic::control()
---------------------------
Control DOF, that should be fixed [ndim].
Tyings::Periodic::iid()
-----------------------
Return the dependent DOFs.
Tyings::Periodic::iii()
-----------------------
Return the independent DOFs.
Tyings::Periodic::iiu()
-----------------------
Return the unknown DOFs.
Tyings::Periodic::iip()
-----------------------
Return the prescribed DOFs.
Tyings::Periodic::Cdi()
-----------------------
Return the tying matrix, such that
.. math::
u_d = C_{di} u_i
In addition, the tying matrix in terms of the partitioned system can be obtained:
.. math::
u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
Tyings::Periodic::Cdu()
-----------------------
Return the tying matrix, such that:
.. math::
u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
Tyings::Periodic::Cdp()
-----------------------
Return the tying matrix, such that:
.. math::
u_d = [C_{du}, C_{dp}]^T [u_u, u_p] = C_{du} u_u + C_{dp} u_p
Tyings::Control
===============
Add virtual control nodes to the system.
Tyings::Control::coor()
-----------------------
Nodal coordinates, including the virtual control nodes [nnode, ndim].
Tyings::Control::dofs()
-----------------------
DOFs, including the virtual control nodes [nnode, ndim].
Tyings::Control::controlDofs()
------------------------------
Virtual control DOFs [ndim, ndim].
Tyings::Control::controlNodes()
-------------------------------
Virtual control nodes [ndim].
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