Abstract
The solution of vector-valued Cahn--Hilliard systems is of interest in many applications. We discuss strategies for the handling of smooth and nonsmooth potentials as well as for different types of constant mobilities. Concerning the nonsmooth systems, the necessary bound constraints are incorporated via the Moreau--Yosida regularization technique. We develop effective preconditioners for the efficient solution of the linear systems in saddle point form. Numerical results illustrate the efficiency of our approach. In particular, we numerically show mesh and phase independence of the developed preconditioner in the smooth case. The results in the nonsmooth case are also satisfying, and the preconditioned version always outperforms the unpreconditioned one.
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