Recent improvements to Riverside Research’s computational electromagnetics (CEM) prediction capability have focused on the use of the Adaptive Cross Approximation (ACA) technique, hierarchical matrix decomposition, and reduced rank solvers. We created a modular software library with well-defined and documented interfaces that enables this new capability to both accelerate our prediction code and allow it to be employed by virtually any other CEM code. The figure below shows the reduction in solution time for a typical test model using the new capability. The previous code was run on a Cray X1 system, using 48 cores (153.6 gflops), while the new code was run on Riverside’s SGI Altix UV system, using 16 cores (128.0 gflops), which is made possible owing to the large matrix compression (>98%) afforded by ACA. The new ACA-enabled version of our CEM code offers a reduction in run-time of nearly a factor of 88 relative to the previous version. This result is even more striking by the realization that the cost of the Cray system is approximately $5M versus the SGI Altix system cost of approximately $100K. Using the full complement of 32 cores (256 gflops) on our SGI Altix machine, the test model (1,002,963 unknowns) was solved at 1 GHz in 19.6 hours.
Ongoing development efforts are expected to further improve the solution run-times for our CEM predictions. Key among these efforts is the exploitation of the symmetry inherent in the method of moments (MoM) impedance matrix under most circumstances. Implementation of this capability within the hierarchical formalism is expected to yield an additional factor of 2 run-time reduction (e.g., typical models with 1M unknowns would be solved in approximately 10 hours). Additional improvements in progress include single processor optimization of the hierarchical Lower Upper Decomposition (LUD), improved load balancing schemes for Schur complement calculations, and use of the Oak Ridge National Laboratory PLASMA math library.