A data-driven approach to cut-cell quadrature using spline interpolation

This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.