Block sub-structure issues associated with fast direct solutions of integral equations for composite bodies

Summary form only given. In recent years there has been considerable advancement in solving large-scale electromagnetic scattering problems using fast direct solve techniques within the traditional Rao-Wilton-Glisson (RWG) Method of Moments (MoM) computational framework. The direct solve techniques are typically centered on compression algorithms such as Adaptive-Cross-Approximation (ACA or ACA+) (J. Shaeffer, IEEE Trans. Antennas Propagat., 56, 2306-2313, 2008) or Multilevel Matrix Decomposition Algorithm (MLDMA) (H. Guo, J. Hu, and E. Michielssen, IEEE Antennas Wireless Propagat. Lett., 12, 31-34, 2013) in which compression is realized in both the fill and block-LU solve part of the framework. In this work, we first demonstrate a subtle block decoupling phenomena that can adversely impact the generic ACA / ACA+ algorithm implementation on multi-body objects with various mixed PEC and material components. The block decoupling arises during matrix fill and is due to the group-to-group interactions of heterogeneous mesh element clusters in which the coupling between the various PEC and material components can cause zero-filled sub-blocks within the given matrix block. We show that this often results in partial ACA / ACA+ compression and, at times, catastrophic loss of accuracy. Several common block decoupling sub-structure scenarios are presented in which partial ACA / ACA+ compression results. We present a novel algorithmic scheme to overcome these complications while still retaining the ACA / ACA+ compression performance. Additionally, block-LU decomposition with ACA compression is used and has been extended to multiple Graphics Processing Units (GPUs) with fast Out-of-Core memory augmentation. A commodity workstation featuring two Xeon oct-core processors, 2 K10 GPUs, 256 GB of RAM, and SSD RAID array, affords us solutions for a broad range of complex scattering problems, previously demonstrated with over 1.7 million RWG degrees of freedom, which cannot be obtain- d using iterative algorithms such as the Multi-Level-Fast-Multipole-Algorithm (MLFMA).