TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
Numerical Analysis
2022-12-01 v1 Numerical Analysis
Abstract
In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on a polyhedral element with arbitrary shape. The key tools are the notion of Tchakaloff discretization set and the solution of moment-matching equations by Lawson-Hanson iterations for NonNegative Least-Squares. Several numerical tests are presented. The method is implemented in Matlab as open-source software.
Keywords
Cite
@article{arxiv.2211.16620,
title = {TetraFreeQ: tetrahedra-free quadrature on polyhedral elements},
author = {Alvise Sommariva and Marco Vianello},
journal= {arXiv preprint arXiv:2211.16620},
year = {2022}
}