  A recent theoretical result on optimized Schwarz algorithms demonstrated at
the algebraic level enables the modification of an existing Schwarz procedure
to its optimized counterpart. In this work, it is shown how to modify a
bilinear FEM based Schwarz preconditioning strategy originally presented in
[Fischer, JCP 133:84 1997] to its optimized version. The latter is employed to
precondition the pseudo--Laplacian operator arising from the spectral element
discretization of the magnetohydrodynamic equations in Elsasser form.
