  This paper presents a novel implicit scheme for the constraint resolution in
real-time finite element simulations in the presence of contact and friction.
Instead of using the standard motion correction scheme, we propose an iterative
method where the constraint forces are corrected in Newton iterations. In this
scheme, we are able to update the constraint directions recursively, providing
more accurate contact and friction response. However, updating the constraint
matrices leads to massive computation costs. To address the issue, we propose
separating the constraint direction and geometrical mapping in the contact
Jacobian matrix and reformulating the schur-complement of the system matrix.
When combined with GPU-based parallelization, the reformulation provides a very
efficient updating process for the constraint matrices in the recursive
corrective motion scheme. Our method enables the possibility to handle the
inconsistency of constraint directions at the beginning and the end of time
steps. At the same time, the resolution process is kept as efficient as
possible. We evaluate the performance of our fast-updating scheme in a contact
simulation and compare it with the standard updating scheme.
