Efficient Quadrature for Boundary Element Spline Discretizations: A Classification-Free Approach
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We propose a novel quadrature strategy for boundary element methods that eliminates the traditional classification of integrals as nearly singular or regular. Our rule smoothly adapts to the physical distance from singularities in the boundary integral kernels, achieving automatic calibration for improved accuracy. Additionally, we integrate directly over the supports of B-spline basis functions rather than element by element, reducing computational cost, particularly for higher-degree splines. We demonstrate the effectiveness of this method in boundary element simulations of Stokes flow, a key problem in fluid dynamics, porous media, and biomechanics, as well as a stepping stone to more complex models like the Navier-Stokes equations.