LOCA: Library of Continuation Algorithms
What is LOCA?LOCA is a new software library for performing bifurcation analysis of large-scale applications. The source code has been available for download since April 19, 2002.
LOCA 1.1 Now Available 10/29/2002
LOCA OverviewThe algorithms in LOCA are being designed as part of an ongoing research project at Sandia National Laboratories in Albuquerque into scalable stability analysis algorithms. When implemented with an application code, LOCA enables the tracking of solution branches as a function of system parameters and the direct tracking of bifurcation points. LOCA (which is written in "C") is designed to drive application codes that use Newton's method to locate steady-state solutions to nonlinear problems. The algorithms are chosen to work for large problems, such as those that arise from discretizations of partial differential equations, and to run on distributed memory parallel machines.
The approach in LOCA for locating and tracking bifurcations begins with augmenting the residual equations defining a steady state with additional equations that describe the bifurcation. A Newton method is then formulated for this augmented system; however, instead of loading up the Jacobian matrix for the entire augmented system (a task that involved second derivatives and dense matrix rows), bordering algorithms are used to decompose the linear solve into several solves with smaller matrices. Almost all of the algorithms just require multiple solves of the Jacobian matrix for the steady state problem to calculate the Newton updates for the augmented system. This greatly simplifies the implementation, since this is the same linear system that an application code using Newton's method will already have invested in. Only the Hopf tracking algorithm requires the solution of a larger matrix, which is the complex matrix involving the Jacobian matrix and an imaginary multiple of the mass matrix.
The following algorithms are available in this version of LOCA:
We are interested in cultivating new collaborations and a few friendly users to this new software. We are looking for feedback on the current algorithms applied to new applications, suggestions for new algorithms, improvements to the LOCA interface, improvements to the implementation manual.
LOCA version 1.1
LOCA PublicationsPublications focused on linear stability (PDF):
Selected LOCA Presentations
What are the plans for LOCA?
FundingThis project has been supported by DOE through the MICS, ASCI, and CSRF programs.
ContactFor more information, please contact Andy Salinger, firstname.lastname@example.org.
LOCA 1.0, Copyright 2001 Sandia Corporation. Under the terms of ContractDE-AC-94AL85000, there is a non-exclusive license for use of this work by or on behalf of the U.S. government. Export of this program may require a license from the United States Government.
Web page last modified 10/02.