Adaptive Quadrature for the Chebyshev-Based Boundary Integral Equation Method

The recently presented Chebyshev-based Nyström method enables efficient, high-order discretization and solution of boundary integral equation problems. The approach handles far-interactions using the Nyström method by leveraging a high-order quadrature rule and treats the self-singular and near-singular interactions by expanding the unknown densities in terms of Chebyshev polynomials and precomputing the interactions of the integral operators against the Chebyshev-basis to high accuracy. This work presents an adaptive quadrature scheme which enables evaluating these precomputation integrals to a prescribed accuracy threshold. The approach is able to achieve the same accuracy as the prior static refined-integration-grid based method while being up to a factor of 6.6X faster for certain challenging geometries. An example is presented which highlights the advantages of the adaptive approach using the Magnetic Field Integral Equation (MFIE) to model a NURBS-based hummingbird CAD model.