In this paper we describe a methodology for the identification of symmetric quadrature rules
inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The …

In this paper, we construct new high‐order numerical integration schemes for tetrahedra,
with positive weights and integration points that are in the interior of the domain. The …

In this article, we present an algorithm to construct high‐order fully symmetric cubature rules
for tetrahedral and pyramidal elements, with positive weights and integration points that are …

Although symmetric Gauss quadrature rules have been studied extensively, the
investigations of asymmetric Gauss quadrature rules and symmetric Gauss–Lobatto (GL) …

Abstract HiFlow3 Version 2.0 continues the path as a multi-purpose finite element software,
which provides powerful tools for efficient and accurate solution of a wide range of problems …

High-order numerical methods for unstructured grids combine the superior accuracy of high-
order spectral or finite difference methods with the geometric flexibility of low-order finite …

A general and effective numerical integration formula to evaluate all triple integrals with finite
limits is proposed in this paper. The formula is derived by transforming the domain of …

Triangular prism elements are widely used in finite element/volume computational fluid
dynamics (CFD) codes, where one of the major computational expenses is the evaluation of …

This paper gives a numerical integration rule for integrating functions ovor any n-
dimensional cube. The rule is derived using a simple linear transformation of the given n …

A second-order isoparametric 19-node pyramid finite element (PYR19) was developed that
is suitable for use in nonlinear solid mechanics, especially with lumped mass explicit …