Comparison of Parallel Solution of Electrically Large Structures on a Cluster and Multi-core Workstation

Electromagnetic simulation of electrically large arbitrarily-shaped three-dimensional structures is computationally very demanding. Rigorous Method of Moments (MoM) analysis based on surface integral equations using higher order basis functions and quadrilateral mesh [1] requires only about 30 unknowns per wavelength squared for metallic structures. This efficient technique, applied in WIPL-D 3D EM solver [2], enables simulation of large and complex structures on PC computers equipped with widely-spread single-core processors. Electrical size limits imposed by the amount of RAM can be extended by application of the out-of-core solver which uses the hard drive for storage during computations. However, simulation becomes prohibitively long for extremely large problems. Therefore, a logical solution to further increase electrical size capacity is parallelization. In this paper, we present an overview of parallelization of WIPL-D 3D EM solver on two platforms: 8-node computer cluster and a workstation equipped with a quad-core processor. Efficiency of LU decomposition is investigated on both platforms. A model of a helicopter up to 51 λ long was used as a benchmark example for illustrating parallelization efficiency. Radar cross section of a 51 λ long helicopter is calculated in 72 minutes on a 8-node cluster, while the same model requires 2.5 hours using out-of-core solver on the quad-core workstation. A model of a 180 λ long payload fairing with a dipole in its vicinity was simulated on the quad-core workstation, using the adaptive expansion order reduction presented in [3]. The order reduction allows modeling of an electrically large antenna placement setup with several times less unknowns than in case of rigorous formulation, with only a slight loss of accuracy. The simulation was done in 10.2 hours using the out-of-core solver. On a lower frequency, the payload fairing model measured 144 λ in length, and took 97 minutes on a 8-node cluster.