Adaptively Weighted Numerical Integration in the Finite Cell Method

In contrast, in AW scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties. In this paper, we demonstrate the computational efficiency of AW over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions. In addition, AW offers a number of advantages including flexibility in the choice of quadrature points and basis functions.