  We present a method for the efficient processing of contact and collision in
volumetric elastic models simulated using the Projective Dynamics paradigm. Our
approach enables interactive simulation of tetrahedral meshes with more than
half a million elements, provided that the model satisfies two fundamental
properties: the region of the model's surface that is susceptible to collision
events needs to be known in advance, and the simulation degrees of freedom
associated with that surface region should be limited to a small fraction (e.g.
5\%) of the total simulation nodes. Despite this conscious delineation of
scope, our hypotheses hold true for common animation subjects, such as
simulated models of the human face and parts of the body. In such scenarios, a
partial Cholesky factorization can abstract away the behavior of the
collision-safe subset of the face into the Schur Complement matrix with respect
to the collision-prone region. We demonstrate how fast and accurate updates of
penalty-based collision terms can be incorporated into this representation, and
solved with high efficiency on the GPU. We also demonstrate the opportunity to
iterate a partial update of the element rotations, akin to a selective
application of the local step, specifically on the smaller collision-prone
region without explicitly paying the cost associated with the rest of the
simulation mesh. We demonstrate efficient and robust interactive simulation in
detailed models from animation and medical applications.
