We present strategies for combining Newton and ASPEN to accelerate the nonlinear solution process. The main feature is a set of novel monitoring strategies and systematic switching criteria that prevent oversolving and enable us to optimize the choice of solution strategy. At the start of each nonlinear iteration, convergence monitors are computed and can be used to choose the type of nonlinear iteration to perform as well as methods, tolerances, and other parameters used for the optional local domain solves. The convergence monitors and switching criteria are inexpensive to compute.
We observe the advantages and disadvantages of local-global domain decomposition for practical models of interest for oil recovery and CO2 storage and demonstrate how the computational runtime can be (significantly) reduced by adaptively switching to regular Newton's method when nonlinearities are balanced throughout the physical domain and the local solves provide little benefit relative to their computational cost.