We describe the implementation and performance of an efficient parallel Gauss-Seidel algorithm that has been developed for irregular, sparse matrices from electrical power systems applications. Although, Gauss-Seidel algorithms are inherently sequential, by performing specialized orderings on sparse matrices, it is possible to eliminate much of the data dependencies caused by precedence in the calculations. A two-part matrix ordering technique has been developed-first to partition the matrix into block-diagonal-bordered form using diakoptic techniques and then to multi-color the data in the last diagonal block using graph coloring techniques. The ordered matrices often have extensive parallelism, while maintaining the strict precedence relationships in the Gauss-Seidel algorithm. We present timing results for a parallel Gauss-Seidel solver implemented on the Thinking Machines CM-5 distributed memory multi-processor. The algorithm presented here requires active message remote procedure calls in order to minimize communications overhead and obtain good relative speedup.>

A computer model is described to evaluate airborne radio performance in a mixed environment of friendly and hostile emitters. A new performance criterion, the communications operability volume, is introduced. This criterion permits operational, scenario-based comparisons of various radio designs over a range of interference environments. Communications operability volumes can be calculated for different waveforms, receiver antenna patterns (including adaptive arrays), and detection thresholds. An empirical propagation algorithm is used to calculate path losses and/or maximum communications range. The computer model provides several types of graphic outputs that are used to compare antijam or electromagnetic compatibility performance for different radio designs at various locations relative to the sources of interference in a scenario.