Papers by Arnold Neumaier:

Title: Failure Modes of Tearing and a Novel Robust Approach
Authors: Ali Baharev, Arnold Neumaier and Hermann Schichl
Abstract:State-of-the-art Modelica implementations may fail in various ways when tearing is turned on: Completely incorrect results are returned without a warning, or the software fails with an obscure error message, or it hangs for several minutes although the problem is solvable in milliseconds without tearing. We give three detailed examples and an in-depth discussion why such failures are inherent in tearing and cannot be fixed within the traditional approach. Without compromising the advantages of tearing, these issues are resolved for the first time with staircase sampling. This is a non-tearing method capable of robustly finding all well-separated solutions of sparse systems of nonlinear equations without any initial guesses. Its robustness is demonstrated on the steady-state simulation of a particularly challenging distillation column. This column has three solutions, one of which is missed by most methods, including problem-specific tearing methods. All three solutions are found with staircase sampling.
Links: Full paper