Improved and Extended Equation Solver for Complex Structures


Develop solver which can efficiently handle a very broad class of complex structural systems.


Develop a General-Purpose equation Solver, GPS, for complex structural systems whose equation set may be sparse or dense, positive definite or indefinite and which has minimal memory requirements.


Initial development of dense, banded and sparse equation solvers on single and multiprocessor computers led to an extremely fast sparse equation solver, VSS, for traditional structural analysis. The solution of complex structures (where interfaces may result in indefinite matrices) and large-scale structures (that cannot fit in memory) led to indefinite and "out-of-core" extensions, respectively. These extensions were made along with the performance improvements shown in Figure 1 for an 88,416 equation high-speed aircraft model. Figure 1 shows the calculation of displacements (right of Figure) which took 140 seconds with the best band solver on one Cray C90 processor was reduced to 26 seconds using the GPS. On 4 processors, the reduction was by a factor of 4. The same calculation with GPS on an IBM RS6000 took 49 seconds. The solver is now used for rapid computation of displacements and stresses for complex structures (with indefinite matrices) and large-scale structures that require more memory than is available on the computer (i.e. "out-of-core"). The capability to solve complex matrices was added and found to reduce (often by an order of magnitude) the time to solve electromagnetic and acoustic applications. One installation file allows users to customize GPS to their application and computer with no source code changes. In addition, the GPS was converted to the C++ and JAVA computer languages for use on the World-Wide Web.


The indefinite matrix capability of the GPS is the enabling technology for future integrated analysis. The speed of the GPS solution and "out-of-core" capability enables the solution of complex structures (as well as electromagnetic and acoustic applications) on workstations and PCs that formerly required supercomputers. Moreover, GPS is one of the most-frequently requested NASA software packages.


Feedback from hundreds of GPS "beta" users is helping bring the code to production quality. Non-symmetric matrix capability has recently been developed and is being added to the GPS. In addition to its use in the HPCC program, the GPS will also be used in the Next Generation Analysis and Design Environment (NEXTGRADE) Program to provide near- real-time interactive design.

Point of Contact

Olaf O. Storaasli
NASA Langley Research Center
(757) 864-2927

Figure 1: GPS solution time reduction for high-speed aircraft model.