Continuation Methods for Performing Stability Analysis
of Large-Scale Applications

Andy Salinger

Sandia National Laboratories
P.O. Box 5800, MS-1111
Albuquerque, NM 87185


The LOCA Library of Continuation Methods has been developed to perform parameter continuation and bifurcation analysis around large-scale application codes. The algorithms in LOCA are designed to work around codes that use Newton's method for steady-state calculations, and have been chosen to be minimally invasive. Furthermore, the algorithms are scalable to large system sizes, to distributed memory parallel computers, and to work with iterative linear solvers. We will discuss the ramifications of using the minimally invasive formulations, which require linear solves of matrices that are being driven singular, together with iterative linear solvers.

We will present results of using LOCA together with the MPSalsa massively parallel reacting flows code and the Aztec library of preconditioned Krylov iterative solvers to solve bifurcation problems of order 1 million unknowns. By coupling LOCA and a robust eigensolver, based on the Cayley transform and using the P_ARPACK library (Lehoucq and Salinger, IJNMF, 2001), we have created a sophisticated set of stability analysis tools for large-scale applications. (Joint work with Roger Pawlowski, Louis Romero, and Ed Wilkes.)