p-Adaptive Quadrature for the Chebyshev-based Boundary Integral Equation Method

The Chebyshev-based Boundary Integral (CBIE) method is a computationally efficient implementation of the Nyström method, which enables discretization and solution of boundary integral problems with high-order accuracy. The far source/target point interactions leverage the Nyström method, whereas self-singular and near-singular interactions are handled by expanding the unknown densities using Chebyshev polynomials and precomputing the interactions of the integral operators and the Chebyshev basis to high numerical accuracy. In this work, we present a p-adaptive quadrature scheme which enables these precomputation integrals to be evaluated efficiently to a desired level of accuracy without requiring any manual fine-tuning or knowledge of the geometry. This approach matches the same level of accuracy achieved by the previous implementations based on fixed-size refined integration grids, while achieving up to a 16.9X speed-up in computing time. The advantages of the p-adaptive approach are demonstrated by comparing it to the prior fixed-grid method for solving the Magnetic Field Integral Equation (MFIE) applied to an edge-refined metallic cube geometry.