Boundary integration of polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space
type: Item
instance of: scholarly article
title: Boundary integration of polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space
zbMATH Open document ID: 0938.65055
DOI: 10.1016/S0045-7825(97)00290-9
author: H. T. Rathod
author: S. V. Hiremath
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1999-11-30T00:00:00Z
review text: The authors derive complicated formulas for the exact evaluation of integrals of polynomials over a hexahedron. They consider several methods based on different subdivisions of the hexahedron combined with the reduction of the volume integrals to surface integrals, and for one of the methods, a final reduction to line integrals. The resulting formulas should be suitable for implementation with symbolic algebra systems. A detailed example is used to illustrate the methods. There is a brief discussion of relative efficiencies of the methods, but no comparison is made with simpler methods which could use a standard subdivision of the hexahedron into tetrahedra combined with simple integration formulas that are exact for low-order polynomials.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 26B20
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1372459
zbMATH Keywords: symbolic computation
zbMATH Keywords: boundary integration
zbMATH Keywords: integrals of polynomials
zbMATH Keywords: hexahedron
zbMATH Keywords: subdivisions
zbMATH Keywords: volume integrals
zbMATH Keywords: surface integrals
zbMATH Keywords: line integrals
reviewed by: A. Genz
MaRDI profile type: Publication
cites work: Q3847247
cites work: Boundary integration over linear polyhedra
cites work: Integration of polynomials over \(n\)-dimensional polyhedra
cites work: Integration of polynomials over linear polyhedra in Euclidean three-dimensional space
cites work: Integration of polynomials over an arbitrary tetrahedron in Euclidean three-dimensional space
cites work: Q5647993
cites work: Some analytical integration formulae for a four node isoparametric element
cites work: Q4003663
cites work: Boundary integration of polynomials over an arbitrary linear tetrahedron in Euclidean three-dimensional space
Wikidata QID: Q126643947
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description: scientific article; zbMATH DE number 1372459