Babazadeh, Omid2026-03-272026-03-272026-03-262026-03-262026-03-272026-03-27http://hdl.handle.net/1993/39702This thesis introduces a robust, high-order computational framework for modelling electromagnetic scattering from electrically large perfect electric conductor (PEC) objects. The framework rests on two point-based discretization methods: it is implemented using either an enhanced Locally Corrected Nyström (LCN) scheme or a Chebyshev-based boundary integral equation (CBIE) formulation, accelerated by the hierarchical matrix (H-matrix) framework, which together provide an accurate, fast and memory-efficient kernel-aware discretization of surface-integral equations over complex geometries. An adaptive hp-refinement strategy selects specific element sizes h_i and polynomial orders p_i for different regions in the geometry, capturing edge singularities to the limited digits of accuracy while maintaining high-order accuracy in smooth regions. Storage and runtime are reduced by orders of magnitude via H-matrix compression, whose high-order far-field expansions accelerate matrix–vector products. We implement both direct H-LU and H-matrix preconditioned iterative solvers; blockwise (heterogeneous) tolerances in the H-LU factorization further shorten time to solution without degrading accuracy. Hybrid parallelism, MPI across computing nodes and OpenMP within nodes, maximises data locality and resource utilisation, delivering near-linear scalability on modern HPC platforms. Extensive Radar Cross Section (RCS) benchmarks on canonical and complex PEC targets validate the robustness, precision, and built-in error control in the framework, demonstrating speedups exceeding an order of magnitude and memory reductions of over 90\% compared to conventional dense solvers. By integrating high-order integral equation formulations with \(hp\)-refinement strategy, H-matrix compression, and hybrid parallel computing, this work delivers a practical, scalable toolset for high-fidelity electromagnetic scattering analysis and advances the state of the art in surface integral equation solvers.engSurface Integral Equations; Fast Algorithms; H-Matrix; Hybrid Direct-Iterative Method; LCN; CBIE; MPI;OpenMP;RCS;Benchmarking;