Fully Automated Adaptive Parameter Selection for 3-D High-order Nystr\"om Boundary Integral Equation Methods

Abstract

We present an adaptive Chebyshev-based Boundary Integral Equation (CBIE) solver for electromagnetic scattering from smooth perfect electric conductor (PEC) objects. The proposed approach eliminates manual parameter tuning by introducing (i) a unified adaptive quadrature strategy for automatic selection of the near-singular interaction distance and (ii) an adaptive computation of all self- and near-singular precomputation integrals to a prescribed accuracy using Gauss-Kronrod (h-adaptive) or Clenshaw-Curtis (p-adaptive) rules and singularity-resolving changes of variables. Both h-adaptive and p-adaptive schemes are explored within this framework, ensuring high-order accuracy and robustness across a broad range of geometries without loss of efficiency. Numerical results for canonical and complex CAD geometries demonstrate that the adaptive solver achieves accuracy and convergence rates comparable to optimally tuned fixed-grid CBIE implementations, while offering automation and scalability to electrically large, geometrically complex problems.