Shape Aware Quadratures

With SAQ, more general shape correction factors can be derived based on a variety of sensitivity analysis techniques such as shape sensitivity (SSA) and topological sensitivity (TSA). Using the right kind/order of shape correction factors for moment approximation enables the resulting quadrature (from the moment fitting equations) to efficiently adapt to the shape of the original domain even in the presence of thousands of small features. We derive shape correction factors based on SSA and TSA of moment integrals. We also demonstrate the efficacy of SAQ in integrating bivariate/trivariate polynomials over several 2D/3D domains in the presence of small features.