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editBDDC can be used for nonsymmetric problems and for saddle point problems. See for instance
@article{li2007bai, title={ {BDDC Algorithms for Incompressible Stokes Equations} }, author={Li, J. and Widlund, O.}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, volume={44}, number={6}, pages={2432}, year={2007}, publisher={SIAM SOCIETY FOR INDUSTRIAL AND APPLIED} }
This is to appear in Commun. Appl. Math. Comput. Sci.