A High-Order Fast Boundary Element Method as a Benchmarking Computational Framework for RCS Analysis of PEC Targets

A fast and accurate boundary element method framework for benchmarking the Radar Cross Section (RCS) of various Perfect Electric Conductor (PEC) targets, including sharp-edge models with electrically large sizes, is proposed. The approach employs a high-order Chebyshev-based Boundary Integral Equation (CBIE) formulation of the Magnetic Field Integral Equation (MFIE). Acceleration is achieved using both the H-matrix framework and distributed parallelism, substantially improving computational efficiency in both time and memory usage. We refer to the resulting solver as H-CBIE and demonstrate its O(h p) error convergence, scalability, and accuracy through extensive numerical results, h being the mesh element size and p the order of discretization. Localized hp-refinement is incorporated for sharp-edge problems to maintain accuracy near edges and junctions. We include a comprehensive complexity analysis of the high-order accelerated framework, detailing the error-dependent cost scaling for each stage of the solution process. The resulting scaling dependencies show that the total solution cost grows quadratically in N with the target accuracy when high-order discretizations are used, whereas it rises exponentially for traditional low-order methods, underscoring the substantial efficiency gains of the proposed approach and its suitability for benchmarking.