In this presentation we will describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable of identifying a set of rules with a prescribed strength and node count. This is accomplished by the intelligent construction of a non-linear least squares problem which is then solved to arbitrary precision using the Levenberg-Marquardt algorithm. An emphasis is placed on deriving rules which are suitable for use in finite element methods and related numerical schemes. Further, we shall show how by employing this methodology we are able to generate rules of superior quality to those tabulated in the literature.

Freddie Witherden studied Physics with Theoretical Physics at Imperial College London between 2008–2012 earning an MSci degree with first class honours. In September of 2012 Freddie started a PhD in computational fluid dynamics in the department of Aeronautics at Imperial College London under the supervision of Dr Peter Vincent and graduated in December 2015. He is currently an Assistant Professor of Ocean Engineering at Texas A&M University. In 2024 he was named as a Fellow of the Royal Aeronautical Society.