A single-level implementation for a fast direct method of moments solver on electrically large scattering problems using a GPU based Reduced Singular Value Decomposition block LU factorization

In recent years there has been considerable advancement in solving large-scale electromagnetic scattering problems using fast direct solve techniques with the traditional Rao-Wilton-Glisson (RWG) Method of Moments (MoM) computational framework, and extensions to Higher Order Basis Functions (HOBF) over curvilinear elements. The direct solve techniques are typically formulated with compression algorithms such as Adaptive-Cross-Approximation (ACA/ACA+). Early attempts for PEC bodies on the CPU (J. Shaeffer, IEEE Trans. Ant. and Prop., vol. 56, no. 8, pp. 2306–2313, Aug. 2008) and dielectric composite bodies on both the CPU and GPU (M. A. Horn, T. N. Killian, and D. L. Faircloth, 2014 IEEE Ant. and Prop. Society International Symposium (APSURSI), Memphis, TN, 2014, pp. 1630–1631) implemented a Single-level (SL) block clustering scheme in which ACA/ACA+ is used for compression in both the fill and block LU factorization. More recent attempts implement Multi-level (ML) block clustering schemes utilizing hierarchical matrix (H -Matrix) theory (W. Chai and D. Jiao, 2010 IEEE Ant. and Prop. Society International Symposium (APSURSI), Toronto, ON, 2010, pp. 1–4). ML schemes rely on the compression preserving properties of the Reduced Singular Value Decomposition (rSVD) and thus do not employ ACA/ACA+ during block LU factorization.