Abstract

APPENDIX B. TRILINOS 135
B.3.2 LOCA
LOCA (Library of Continuation Algorithms) is the main library I used. This library
contains the continuation routines, including natural continuation, pseudo arc-length
continuation, bifurcation tracking, and stability analysis. It is mostly built from
NOX, Trilinos’s nonlinear solver package described in the next section and interacts
with Anasazi, Trilinos’s eigensolver package. Current research with LOCA involves
efficiently handling turning points, which create ill-conditioned linear solves during
the continuation runs, enhancing bifurcation tracking routines, and multi-parameter
continuation.
B.3.3 NOX
NOX is Trilinos’s nonlinear solver package. It uses Newton’s method to solve the non-
linear equations. Globalization strategies such a line-search methods and trust region
methods are implemented, as well as the ability to handle inexact-Newton method,
where the linear systems are solved with an iterative method instead of a direct
method. For our application, we used Newton-GMRES, where the implementation
of GMRES came from AztecOO, a linear solver package within Trilinos.
B.3.4 AztecOO
AztecOO is a package of preconditioned Krylov iterative methods for systems of
linear equations. Available algorithms include Conjugate Gradient (CG) and General