  Predictive high-fidelity finite element simulations of human cardiac
mechanics co\-mmon\-ly require a large number of structural degrees of freedom.
Additionally, these models are often coupled with lumped-parameter models of
hemodynamics. High computational demands, however, slow down model calibration
and therefore limit the use of cardiac simulations in clinical practice. As
cardiac models rely on several patient-specific parameters, just one solution
corresponding to one specific parameter set does not at all meet clinical
demands. Moreover, while solving the nonlinear problem, 90\% of the computation
time is spent solving linear systems of equations. We propose a novel approach
to reduce only the structural dimension of the monolithically coupled
structure-windkessel system by projection onto a lower-dimensional subspace. We
obtain a good approximation of the displacement field as well as of key scalar
cardiac outputs even with very few reduced degrees of freedom while achieving
considerable speedups. For subspace generation, we use proper orthogonal
decomposition of displacement snapshots. To incorporate changes in the
parameter set into our reduced order model, we provide a comparison of subspace
interpolation methods. We further show how projection-based model order
reduction can be easily integrated into a gradient-based optimization and
demonstrate its performance in a real-world multivariate inverse analysis
scenario. Using the presented projection-based model order reduction approach
can significantly speed up model personalization and could be used for
many-query tasks in a clinical setting.
