Stability analysis algorithms have been developed to work with massively parallel application codes. These algorithms

include an eigenvalue approximation algorithm (for linear stability analysis) and a set of continuation algorithms for

tracking turning point (fold), pitchfork, and Hopf bifurcations. Since our aim is to improve the computational design capability of established engineering codes, we have at first chosen algorithms that are non-invasive over those which are more robust. We will discuss the ramifications of that decision.

With these algorithms we have analyzed several incompressible flow problems, ranging from classical Rayleigh-Benard problems to CVD reactor models to free surface flow manufacturing applications. The algorithms are shown to scale to 3D flow systems with finite element discretizations of millions of unknowns, run on hundreds of processors.

(Joint work with Rich Lehoucq, Roger Pawlowski, Louis Romero, John Shadid, Ed Wilkes, and Nawaf Bou-Rabee.)