  Large-scale 3D martensitic microstructure evolution problems are studied
using a finite-element discretization of a finite-strain phase-field model. The
model admits an arbitrary crystallography of transformation and arbitrary
elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a
penalty-regularized double-obstacle potential, and viscous dissipation. The
finite-element discretization of the model is performed in Firedrake and relies
on the PETSc solver library. The large systems of linear equations arising are
efficiently solved using GMRES and a geometric multigrid preconditioner with a
carefully chosen relaxation. The modeling capabilities are illustrated through
a 3D simulation of the microstructure evolution in a pseudoelastic CuAlNi
single crystal during nano-indentation, with all six orthorhombic martensite
variants taken into account. Robustness and a good parallel scaling performance
have been demonstrated, with the problem size reaching 150 million degrees of
freedom.
