Highvoltage transformers contain oil as their insulating dielectric. When a critical electric field is exceeded, conduction paths grow at microsecond speeds through the oil, in the form of branched trees, called streamers. These can lead
to destructive breakdown.
The intense ionization occurring at the branch tips is highspeed and submicroscopic in size, so that it connot be observed directly. Overall shape, growth pattern, and timing of the streamer trees can be recorded. We simulate these features by a detailed probability model, which provides threedimensional graphical
output suitable for comparison against highspeed shadow photographs obtained in experiment.
The Dielectric Breakdown Model has been parallelized.

Why Parallelize Dielectric Breakdown?
The detailed electricfield distribution around the growing tree must be repeatedly calculated at each step of the growth process. This requires a highresolution threedimensional treatment. The streamer tree ia a selfavoiding, selfscreening fractal structure. Laying the model out on a large rectangular grid (128 X
128 X 128) displays these characteristics well.


How is the Parallelization Realized?
A simplified method minimizes programming difficulty. The large cube domain is broken into regular rectangular blocks, which communicate at their interface planes. This creates processes of reasonable size, which operate in parallel like small copies of the original code. The instructions are in Fortran 90; DPARLIB, a
NISTdeveloped extension library, handles the interface communications between processors invisibly.
The program makes extensive use of Fortran 90 arraydirected commands, with physical quantities such as voltage field treated as large arrays. For example, neighbor sites to the tree are selected through a set of cshift instructions. By this method the local model, which closely describes events surrounding one lattice site, is enlarged with great detail across the full domain of over two million sites.
Multiple parallel algorithms were implemented to speed the runs.

Spatial decomposition through block decomposition required each
processor to track only its part of the space. 

Parallel breakdown was implemented using a randomized redblack algorithm. 

Laplace's equation was solved in parallel using SOR. 

Time compression was used to reduce the empty (no breakdown) steps for
periods of low breakdown probability. 


What is the Performance of the parallel Code?
Depending on the stringency of the growthtriggering instructions, the code runs on one to 30 hours on 9 nodes of the IBM SP2, and at similar rates on an analogous SGI multiprocessor.. This makes for convenient turnaround time in the development cycle of results  a task which would greatly exceed the practical capability of a single processor.





Modeling Streamertree Growth
Various forms of streamertree growth have been approximated by different powerlaw responses to the electric field, and by the thresholdvoltage setting. A linear filter produces dense, multibranched trees; such streamers are seen in experiment at voltages just moderately above threshold. A fourthpower filter gives rise to sparse, forwarddirected trees, of a type seen experimentally at high overvoltages. Thus, the method has shown a range and capability to closely simulate some features of experiment.


Papers/Presentations

Howland Fowler, Judith Devaney and John Hagedorn, Growth Model for Filamentary Streamers in an Ambient Field,
IEEE Transactions on Dielectrics and Electrical Insulation, 10
(1)
,
February 2003.
Links:
postscript and pdf.


H.A. Fowler, J.E. Devaney, J.G. Hagedorn and F.E. Sullivan (IDA),
Dielectric Breakdown in a Simplified Parallel Model
in Computers in Physics, 12
(5)
,
American Institute of Physics,
1998,
pp. 478487.


Howland A. Fowler, Judith E. Devaney, John G. Hagedorn and Francis Sullivan,
Dielectric Breakdown in a Simplified Parallel Model,
June 1998.
Available as NISTIR 6174.


Howland Fowler, Judith Devaney and John Hagedorn,
Shaping of Filamentary Streamers by the Ambient Field
delivered at 1999 Conference on Electrical Insulation and Dielectric Phenomena, Austin, TX,
October 1721, 1999.
Links:
postscript and pdf.


Howland A. Fowler, Judith E. Devaney and John G. Hagedorn,
User Guide to CADMUS, a Simplified Parallel Code for Laplacian Fractal
Growth,
June 1998.
Available as NISTIR 6180.
Links:
postscript and pdf.


James S. Sims, John G. Hagedorn, Peter M. Ketcham, Steven G. Satterfield, Terence J. Griffin, William L. George, Howland A. Fowler, Barbara A. am Ende, Howard K. Hung, Robert B. Bohn, John E. Koontz, Nicos S. Martys, Charles E. Bouldin, James A. Warren, David L. Feder, Charles W. Clark, B. James Filla and Judith E. Devaney, Accelerating Scientific Discovery Through Computation
and Visualization,
NIST Journal of Research, 105
(6)
,
NovemberDecember, 2000,
pp. 875894.
Links:
postscript and pdf.


James S. Sims, John G. Hagedorn, Peter M. Ketcham, Steven G. Satterfield, Terence J. Griffin, William L. George, Howland A. Fowler, Barbara A. am Ende, Howard K. Hung, Robert B. Bohn, John E. Koontz, Nicos S. Martys, Charles E. Bouldin, James A. Warren, David L. Feder, Charles W. Clark, B. James Filla and Judith E. Devaney,
Accelerating Scientific Discovery Through Computation
and Visualization ,
2000726.
Available as NISTIR 6709.
Links:
postscript and pdf.



