Author: Randall Bramley, Indiana University

Abstract:

Choosing a solution strategy for solving large sparse linear systems in realistic applications is still an art form. For every currently existing solution method, an application area can be found which gives linear systems that make the solver fail by requiring too much memory or from nonconvergence.

Finding a solution strategy for an application still relies heavily on experimentation and exploration. Unfortunately, not all computational science and engineering research projects can have a numerical linear algebraist on the team. The LSA is a problem-solving environment for application scientists who wish to quickly experiment with a variety of solution strategies and methods for large sparse linear systems of equations, without having to integrate large amounts of disparate code into their application. Once an effective solution strategy is developed, the LSA provides source code that can be integrated into the user's application.

The LSA allows a user to

o Create a solution strategy without knowing the implementation
details of the computational routines.

o Navigate a potentially large parameter space quickly, with
expert advice supplied by the LSA when needed.

o Analyze and compare results from multiple solution strategies.

o Encapsulate a solution strategy as exportable Fortran/C code which
can then be incorporated into an application code.