On an integration rule for products of barycentric coordinates over simplexes in Rn

Title

On an integration rule for products of barycentric coordinates over simplexes in Rn

 Author

Vermolen, F.J. (TU Delft Numerical Analysis) ORCID 0000-0003-2212-1711
Segal, A. (TU Delft Numerical Analysis)

Date

2018

 Abstract

In finite-element computations, one often needs to calculate integrals of products of powers of monomials over simplexes. In this manuscript, we prove a generalisation of the exact integration formula that was reported and proved for two-dimensional simplexes by Holand & Bell in 1969. We extend the proof to n-dimensional simplexes and to simplexes on d-dimensional manifolds in n-dimensional space. The results are used to develop finite-element and boundary-element simulation tools. The proofs of the theorems are based on mathematical induction and coordinate mappings.


 Subject

Barycentric coordinates
Factorisations
Finite element methods
Integration rule

 To reference this document use:

http://resolver.tudelft.nl/uuid:f2fc2852-f41d-4070-9751-7108643c4b98

 DOI

https://doi.org/10.1016/j.cam.2017.09.013

 Embargo date

2019-09-22

 ISSN

0377-0427

 Source

Journal of Computational and Applied Mathematics, 330, 289-294

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2018 F.J. Vermolen, A. Segal
Files
PDF 42056549.pdf 224.53 KB
Close viewer