1. Principle of the test:

A fairly simple mechanical problem involving boundary conditions of type LIAISON_MAIL is solved.

Dualizing these boundary conditions prohibits the use of PETSc’s multigrid solvers

(because of Lagrange’s degrees of freedom).

You must therefore use the ELIM_LAGR =” OUI “feature.

But the code, in order to eliminate each degree of Lagrange’s freedom, is obliged to eliminate one degree of physical freedom.

In the end, some nodes therefore have fewer degrees of freedom than others, which theoretically makes it impossible to use multigrid solvers effectively.

In this case, the code adds fictional degrees of freedom so that all the nodes in the model have the same number of degrees of freedom and so that we can use the “GAMG”, “BOOMER”, and “ML” solvers more effectively.

This test shows that this strategy is interesting: the number of iterations to converge is greatly reduced by adding fictional degrees of freedom:

Solver	BOOMER	ML	GAMG
Without fictional degrees of freedom	375	375	38	478
With fictional degrees of freedom	50	50	24	41

This documentation is deliberately brief.