  In this work, a new class of vector-valued phase field models is presented,
where the values of the phase parameters are constrained by a convex set. The
generated phase fields feature the partition of the domain into patches of
distinct phases, separated by thin interfaces. The configuration and dynamics
of the phases are directly dependent on the geometry and topology of the convex
constraint set, which makes it possible to engineer models of this type that
exhibit desired interactions and patterns. An efficient proximal gradient
solver is introduced to study numerically their L2-gradient flow, i.e.~the
associated Allen-Cahn-type equation. Applying the solver together with various
choices for the convex constraint set, yields numerical results that feature a
number of patterns observed in nature and engineering, such as multiphase
grains in metal alloys, traveling waves in reaction-diffusion systems, and
vortices in magnetic materials.
