Motivation
The classic reference is (P. J. Lanzkron, D. J. Rose and J. T. Wilkes, An Analysis of Approximate Nonlinear Elimination, SISC, 1996). You want to solve subsystems of your nonlinear systems as a nonlinear preconditioner. This is done in charge transport for silicon (Sharfetter-Gummel iteration) and could be thought of as nonlinear FieldSplit or nonlinear PCPatch.
For this you need two things. First, you need out of band data (the frozen fields) to get to the subproblems. Alex tells me MOOSE does this already. Second, you need to organize the input to subsystems, and output from them, and the global update. PETSc does this already. It just seems like a matter of piecing things together.
Design
Given above
Impact
I believe this will allow us to solve multiphysics systems where some fields are dominating the Newton direction, preventing the update of other fields which are key to convergence. This is known to happen for thermofluid problems where the mechanical dofs (u and p) dominate the Newton step, so T remains wrong, but a global correct T is necessary for overall convergence.
Motivation
The classic reference is (P. J. Lanzkron, D. J. Rose and J. T. Wilkes, An Analysis of Approximate Nonlinear Elimination, SISC, 1996). You want to solve subsystems of your nonlinear systems as a nonlinear preconditioner. This is done in charge transport for silicon (Sharfetter-Gummel iteration) and could be thought of as nonlinear FieldSplit or nonlinear PCPatch.
For this you need two things. First, you need out of band data (the frozen fields) to get to the subproblems. Alex tells me MOOSE does this already. Second, you need to organize the input to subsystems, and output from them, and the global update. PETSc does this already. It just seems like a matter of piecing things together.
Design
Given above
Impact
I believe this will allow us to solve multiphysics systems where some fields are dominating the Newton direction, preventing the update of other fields which are key to convergence. This is known to happen for thermofluid problems where the mechanical dofs (u and p) dominate the Newton step, so T remains wrong, but a global correct T is necessary for overall convergence.