Dielectric breakdown in a simplified parallel model

The growth of streamer trees in insulating fluids ~a submicrosecond process that triggers high-voltage breakdown! has been simulated with a combination of parallel-coding tools. Large grids and arrays display well the multifractal, self-avoiding character of the streamer trees. Three physical cases have been approximated by different power-law weightings of the statistical growth filter: dense anode trees, in the uniform field; sparse cathode trees ~a rarer experimental case!; and ultrasparse anode trees ~seen in some fluids of higher viscosity!. The model is contained in a software package that is written in Fortran 90 with data parallel extensions for distributed execution. These extensions encapsulate an underlying, invisible message-passing environment, thus enabling the solution of memory-intensive problems on a group of limited-memory processors. Block partitioning creates processes of reasonable size, which operate in parallel like small copies of the original code. The user needs only to express his model in transparent array-directed commands; parallel interfacing between blocks is handled invisibly. Breakdown is performed in parallel in each of the local blocks. Results are presented for experiments run on eight and nine nodes of the IBM SP2, and four and eight nodes of the SGI Onyx and Origin, three examples of multiple-processor machines. Display is carried out in three dimensions. Timing of the growth can be shown by color banding or by frame animation of the results. The adequacy of the growth rules and size scaling are tested by comparing the simulations against snapshots from high-voltage discharge events. @S0894-1866~98!01805-7#