On the Use of Compressed Polyhedral Quadrature Formulas in Embedded Interface Methods

The main idea of this paper is to apply a recent quadrature compression technique to algebraic quadrature formulas on complex polyhedra. The quadrature compression substantially reduces the number of integration points but preserves the accuracy of integration. The compression is easy to achieve since it is entirely based on the fundamental methods of numerical linear algebra. The resulting compressed formulas are applied in an embedded interface method to integrate the weak form of the Navier--Stokes equations. Simulations of flow past stationary and moving interface problems demonstrate that the compressed quadratures improve the efficiency of performing the weak form integration, while preserving accuracy and order of convergence.