Alberto,

Now I understand your concern. The boolean flag that is passed as the final 
> parameter to MatrixTools::apply_boundary_values 
> <https://www.dealii.org/8.5.0/doxygen/deal.II/namespaceMatrixTools.html#a9ad0eb7a8662628534586716748d62fb>
>  
> determines whether column elimination is performed. You've set it to false, 
> so this is not done and the RHS is unaltered. So switching it to true (the 
> default) should preserve the symmetry of the system and make the necessary 
> adjustments to the RHS vector.
>
While this is true in general, for PETSc and Trilinos matrices only the 
case "eliminate_columns = false" is implemented [1]. 
This means that your system matrix will not be symmetric if you are using 
MatrixTools::apply_boundary_values, but a CG will likely still work [2, 
Global elimination].

Best,
Daniel

[1] 
https://www.dealii.org/developer/doxygen/deal.II/namespaceMatrixTools.html#a96d8a143c787e0dca41ce6168152dc04
[2] 
https://www.dealii.org/developer/doxygen/deal.II/namespaceMatrixTools.html

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