**G****eneral-****P****urpose Solver (GPS)
for Matrix Equations
**

** ==> ***used in GENOA to win NASA + R&D100 Awards*

**Matrix Solver: [A]{x}={b}**

The General-Purpose equation Solver, GPS, developed by Dr. Olaf O. Storaasli and colleagues at NASA, solves large matrix systems whose equations may be sparse or dense, positive definite or indefinite using minimal computer time and memory. A key to GPS speed is it's novel matrix reorder scheme which reorders a matrix subset by two methods to compute fill and then reorders the full matrix based on minimum fill.

**Development**

Early research at NASA, dating back to the Finite Element Machine on dense, banded and sparse matrix equation solvers on single and multiprocessor computers led to an extremely fast Vector Sparse Solver, VSS, for structural analysis. VSS was renamed GPS when it was extended to solve complex interface structures (involving indefinite matrices) and Electromagnetic and Acoustic applications (involving complex matrices). GPS can solve matrix systems with millions of equation on current PCs. One customizable makefile (courtesy of Mike Puso LLNL) allows users to maximize GPS performance on their computer with no source code changes.

**Significance**

The GPS capability to solve indefinite matrices enables integrated analysis (e.g. wing-fuselage). GPS speed and minimal memory use has enabled the analysis of complex structural, electromagnetic and acoustic applications exceeding 8 million complex equations and the solution of large applications on PCs that formerly required supercomputers. GPS enabled GENOA to speed solutions by 10x and solve 10x larger problems resulting in the 1999 **NASA** Software of the Year Award.

**Status/Plans**

Although "open source", feedback from hundreds of GPS "beta" users is helping bring the code to production quality. In addition to its development and use on supercomputers, GPS has been adapted for high-performance workstations and PCs whether Unix, Windows or OSX.

**Availability**

Dr. Storaasli recently joined Oak Ridge National Laboratory, and is happy to provide a copy of GPS subject to NASA approval via this form. Example data sets are provided in the Sparse Matrix Format.

**Support/User Feedback**

GPS Users are encouraged to provide feedback (via email), post questions, answers, comments, suggest enhancements and even include (as attachments) any software additions others may benefit from.