RANFS Contact

[lindsayad]

Reason

The Reduced Active Set (RAS) VI method in PETSc is a very robust algorithm that in my experience has shown robust monotonic convergence, e.g. no ping-ponging of the constraint set. However, PETSc's RAS algorithm is limited in that it only supports constraints that involve one degree of freedom. For MOOSE, I propose a more general algorithm called the Reduced Active Nonlinear Function Set (RANFS), name credit to @fdkong. This algorithm supports constraint equations that involve an arbitrary number of DOFs. The idea is that when a constraint is determined to be active, the standard non-linear residual is replaced by a constraint equation residual, thus ensuring that that constraint is enforced. A Lagrange Multiplier (LM) is then applied to the other dofs involved in the constraint. The LM can also be thought of as a slack variable that is equal to the replaced non-linear residual. Because of this equality, we can actually just apply the slack non-linear residual directly to the other dofs involved in the constraint; we do not actually have to create another non-linear variable to represent the LM.

Design

The easiest way to implement this is in constraint objects. These are executed after all other computing objects so we have access to the complete unconstrained residual and Jacobian.

Impact

This algorithm exactly satisfies constraints without introducing an LM variable into the system, which avoids a saddle-point formulation. Hence algorithms like AMG can be used. Moreover, no penalty factors are employed so the conditioning of the matrix is not impacted.

Items

• Frictionless contact (RANFS for contact #14415)
• Frictionless contact Jacobian
• Frictional contact
• Frictional contact Jacobian