Trilinos is Sandia's all-purpose, object-oriented, parallel solver for the solution of large-scale, complex multi-physics engineering and scientific applications. Since my arrival at SNL, I have become a Trilinos developer . My particular focus is...

ML is the multilevel preconditioning package in Trilinos. It implements smoothed aggregation algebraic multigrid (AMG) and is an honest-to-goodness industrial strength AMG code. It even runs in parallel using MPI. I've recently put together a MATLAB interface for ML called MLMEX. It's in the release version of Trilinos from 7.0 on.

I've primarily focused on multigrid solvers for Maxwell's equations. This new solver (known as RefMaxwell) was released in Trilinos 8.0. For more information on these techniques, consult An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations [SAND2007-1633J], by P. Bochev, J. Hu, C. Siefert and R. Tuminaro (March 2007).

The Generalized Saddle-Point Preconditioning Toolkit is a C/C++ code for preconditioning generalized saddle-point problem. It works with SuperLU 3.0 for direct solves and the Structured Probing Toolkit. It also has builtin ILU/ILUT builtin (from SPARSKIT).

The Structured Probing Toolkit provides the tools necessary for performing probing on matrices with non-banded structure. The essence of this technique is to choose an a priori sparsity pattern based on knowledge of the target matrix, and then use graph coloring techniques to choose the probing vectors such that a matrix of that sparsity pattern would be reconstructed exactly. If the “big” entries in the matrix correspond to a certain graph, we can choose the a priori sparsity pattern based on the edge locality of the graph.

A parallel structured probing method built on Zoltan's coloring routines will be released as part of Isorropia in Trilinos 10.0 in Fall 2009.

For more information on this technique, consult Probing Methods for Saddle-Point Problems [Technical Report UIUCDCS-R-2005-2540], by C. Siefert and E. de Sturler (ETNA, Volume 22, pp. 163--183, April 2006).

In the context of derivative-free optimization, there are circumstances under which the function evaluations are so expensive, that building a really good model of the problem and then optimizing that is a pretty good idea. For those situations, MAPS may be the package for you. MAPS was developed by Chris Siefert and Amy Yates under the direction of Virginia Torczon.

For more information on this technique, consult Model-Assisted Pattern Search Methods for Optimizing Expensive Computer Simulations by C. Siefert, V. Torczon and M.W. Trosset (Proceedings of the Section on Physical and Engineering Sciences, American Statistical Association, 2002).