A comprehensive set of tools for performing bifurcation and stability analysis of large-scale applications on parallel computers have been developed. This includes continuation alagoirthms, bifurcation tracking algorithms, and eigenvalue approximation algorithms. When applied benchmark problems in incompressible buoyancy-driven flow applications, the algorithms have successfully been used to detect and track bifurcations of 2D and 3D systems with discretizations of several million unknowns.

We have recently been working on space-time solution methods where the time axis is discretized as well as the spatial dimensions. One application of this capability is to directly track periodic orbits of dynamical systems. By the time of this conference, we hope to be able to present a continuation analysis of a full 4D space-time solution such as a classical CFD application such as buoyancy-driven flow in a differentially-heated cavity or a vortex shedding application.