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

TL;DR

This paper introduces an automated adaptive solver for electromagnetic scattering problems that eliminates manual parameter tuning by dynamically adjusting quadrature and integral computations, ensuring high accuracy and efficiency.

Contribution

The paper presents a novel adaptive Chebyshev-based Boundary Integral Equation solver that automatically selects parameters for high-order accuracy without manual tuning.

Findings

Achieves accuracy comparable to fixed-grid methods

Demonstrates robustness across various geometries

Ensures scalability for large, complex problems

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.