  This paper presents meta-homogenization, a spatially varying homogenization
scheme for knitwear simulation. We are motivated by the observation that
macro-scale fabric dynamics is strongly correlated with its underlying knitting
patterns. Therefore, homogenization towards a single material is less effective
when the knitting is complex and non-repetitive. Our method tackles this
challenge by homogenizing the yarn-level material locally at volumetric
elements. Assigning a virtual volume of a knitting structure enables us to
model bending and twisting effects via a simple volume-preserving penalty and
thus effectively alleviates the material nonlinearity. We employ an adjoint
Gauss-Newton formulation to battle the dimensionality challenge of such
per-element material optimization. This intuitive material model makes the
forward simulation GPU-friendly. To this end, our pipeline also equips a novel
domain-decomposed subspace solver crafted for GPU projective dynamics, which
makes our simulator hundreds of times faster than the yarn-level simulator.
Experiments validate the capability and effectiveness of meta-homogenization.
Our method produces realistic animations of knitwear matching the quality of
full-scale yarn-level simulations. It is also orders of magnitude faster than
existing homogenization techniques in both the training and simulation stages.
