TY - JOUR
T1 - On an integration rule for products of barycentric coordinates over simplexes in Rn
AU - Vermolen, F.J.
AU - Segal, A.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Barycentric coordinates
KW - Factorisations
KW - Finite element methods
KW - Integration rule
UR - http://www.scopus.com/inward/record.url?scp=85029673743&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:f2fc2852-f41d-4070-9751-7108643c4b98
U2 - 10.1016/j.cam.2017.09.013
DO - 10.1016/j.cam.2017.09.013
M3 - Article
AN - SCOPUS:85029673743
SN - 0377-0427
VL - 330
SP - 289
EP - 294
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -